The pH scale is [[Measurement traceability|traceable]] to a set of standard solutions whose pH is established by international agreement.<ref name="covington2">{{cite journal |last1=Covington |first1=A. K. |last2=Bates |first2=R. G. |last3=Durst |first3=R. A. |year=1985 |title=Definitions of pH scales, standard reference values, measurement of pH, and related terminology |url=http://www.iupac.org/publications/pac/1985/pdf/5703x0531.pdf |url-status=live |journal=Pure Appl. Chem. |volume=57 |issue=3 |pages=531–542 |doi=10.1351/pac198557030531 |s2cid=14182410 |archive-url=https://web.archive.org/web/20070924235637/http://www.iupac.org/publications/pac/1985/pdf/5703x0531.pdf |archive-date=24 September 2007}}</ref> Primary pH standard values are determined using a [[Galvanic cell|concentration cell with transference]] by measuring the potential difference between a [[hydrogen electrode]] and a [[Standard electrode potential (data page)|standard electrode]] such as the [[silver chloride electrode]]. The pH of aqueous solutions can be measured with a [[glass electrode]] and a [[pH meter]] or a color-changing [[PH indicator|indicator]]. Measurements of pH are important in [[chemistry]], [[agronomy]], medicine, water treatment, and many other applications.
The pH scale is [[Measurement traceability|traceable]] to a set of standard solutions whose pH is established by international agreement.<ref name="covington2">{{cite journal |last1=Covington |first1=A. K. |last2=Bates |first2=R. G. |last3=Durst |first3=R. A. |year=1985 |title=Definitions of pH scales, standard reference values, measurement of pH, and related terminology |url=http://www.iupac.org/publications/pac/1985/pdf/5703x0531.pdf |url-status=live |journal=Pure Appl. Chem. |volume=57 |issue=3 |pages=531–542 |doi=10.1351/pac198557030531 |s2cid=14182410 |archive-url=https://web.archive.org/web/20070924235637/http://www.iupac.org/publications/pac/1985/pdf/5703x0531.pdf |archive-date=24 September 2007}}</ref> Primary pH standard values are determined using a [[Galvanic cell|concentration cell with transference]] by measuring the potential difference between a [[hydrogen electrode]] and a [[Standard electrode potential (data page)|standard electrode]] such as the [[silver chloride electrode]]. The pH of aqueous solutions can be measured with a [[glass electrode]] and a [[pH meter]] or a color-changing [[PH indicator|indicator]]. Measurements of pH are important in [[chemistry]], [[agronomy]], medicine, water treatment, and many other applications.
[TOC]
==History==
==History==
In 1909, the [[Danish people|Danish]] chemist [[Søren Peder Lauritz Sørensen|Søren Peter Lauritz Sørensen]] introduced the concept of pH at the [[Carlsberg Laboratory]]<ref name="Sørensen2">{{cite journal |last1=Sørensen |first1=S. P. L. |year=1909 |title=Über die Messung und die Bedeutung der Wasserstoffionenkonzentration bei enzymatischen Prozessen |url=https://core.ac.uk/download/pdf/14517358.pdf |url-status=live |journal=Biochem. Z. |volume=21 |pages=131–304 |archive-url=https://web.archive.org/web/20210415205740/https://core.ac.uk/download/pdf/14517358.pdf |archive-date=15 April 2021 |access-date=22 March 2021 |quote=Original German: Für die Zahl p schlage ich den Namen Wasserstoffionenexponent und die Schreibweise p<sub>H</sub>• vor. Unter dem Wasserstoffionexponenten (p<sub>H</sub>•) einer Lösungwird dann der Briggsche Logarithmus des reziproken Wertes des auf Wasserstoffionenbezagenen Normalitäts faktors de Lösungverstanden.}} Two other publications appeared in 1909, one in French and one in Danish.</ref>, originally using the notation "pH•", with H• as a subscript to the lowercase p. The concept was later revised in 1924 to the modern pH to accommodate definitions and measurements in terms of electrochemical cells.<blockquote>For the sign ''p'', I propose the name 'hydrogen ion exponent' and the symbol p<sub>H</sub>•. Then, for the hydrogen ion exponent (p<sub>H</sub>•) of a solution, the negative value of the [[Common logarithm|Briggsian logarithm]] of the related hydrogen ion [[Equivalent concentration|normality factor]] is to be understood.<ref name="Sørensen2" /></blockquote>Sørensen did not explain why he used the letter p, and the exact meaning of the letter is still disputed.<ref>{{Cite journal |last=Francl |first=Michelle |date=August 2010 |title=Urban legends of chemistry |url=https://www.nature.com/articles/nchem.750.epdf |url-status=live |journal=Nature Chemistry |volume=2 |issue=8 |pages=600–601 |bibcode=2010NatCh...2..600F |doi=10.1038/nchem.750 |issn=1755-4330 |pmid=20651711 |archive-url=https://web.archive.org/web/20200806053215/https://www.nature.com/articles/nchem.750.epdf |archive-date=6 August 2020 |access-date=21 July 2019}}</ref> Sørensen described a way of measuring pH using ''potential'' differences, and it represents the negative ''power'' of 10 in the concentration of hydrogen ions. The letter ''p'' could stand for the French ''puissance,'' German ''Potenz,'' or Danish ''potens'', all meaning "power", or it could mean "potential". All of these words start with the letter ''p'' in [[French language|French]], [[German language|German]], and [[Danish language|Danish]], which where the languages Sørensen published in (Carlsberg Laboratory was French-speaking, German was the dominant language of scientific publishing, and Sørensen was Danish). He also used the letter ''q'' in much the same way elsewhere in the paper, and he might have arbitrarily labelled the test solution "p" and the reference solution "q"; these letters are often paired.<ref>{{cite journal |last1=Myers |first1=Rollie J. |year=2010 |title=One-Hundred Years of pH |journal=Journal of Chemical Education |volume=87 |issue=1 |pages=30–32 |bibcode=2010JChEd..87...30M |doi=10.1021/ed800002c}}</ref> Some literature sources suggest that "pH" stands for the [[Latin language|Latin term]] ''pondus hydrogenii'' (quantity of hydrogen) or ''potentia hydrogenii'' (power of hydrogen), although this is not supported by Sørensen's writings.<ref name="Otterson2">{{cite journal |last1=Otterson |first1=David W. |date=2015 |title=Tech Talk: (11) pH Measurement and Control Basics. |url=https://journals.sagepub.com/doi/pdf/10.1177/0020294015600474 |journal=Measurement and Control |volume=48 |issue=10 |pages=309–312 |doi=10.1177/0020294015600474 |s2cid=110716297 |access-date=16 June 2022}}</ref><ref name="Lian2">{{cite journal |last1=Lian |first1=Ying |last2=Zhang |first2=Wei |last3=Ding |first3=Longjiang |last4=Zhang |first4=Xiaoai |last5=Zhang |first5=Yinglu |last6=Wang |first6=Xu-dong |date=2019 |title=Nanomaterials for Intracellular pH Sensing and Imaging. |url=https://www.sciencedirect.com/science/article/pii/B9780128144978000084 |journal=Novel Nanomaterials for Biomedical, Environmental and Energy Applications. |series=Micro and Nano Technologies |pages=241–273 |doi=10.1016/B978-0-12-814497-8.00008-4 |isbn=9780128144978 |s2cid=104410918 |access-date=16 June 2022}}</ref><ref name="Bradley2">{{cite news |last1=Bradley |first1=David |date=21 February 2018 |title=When it comes to caustic wit and an acid tongue, mind your Ps and Qs. |publisher=Materials Today |url=https://www.materialstoday.com/materials-chemistry/comment/caustic-wit-acid-tongues-mind-your-ps-and-qs/ |access-date=16 June 2022}}</ref>
In 1909, the [[Danish people|Danish]] chemist [[Søren Peder Lauritz Sørensen|Søren Peter Lauritz Sørensen]] introduced the concept of pH at the [[Carlsberg Laboratory]]<ref name="Sørensen2">{{cite journal |last1=Sørensen |first1=S. P. L. |year=1909 |title=Über die Messung und die Bedeutung der Wasserstoffionenkonzentration bei enzymatischen Prozessen |url=https://core.ac.uk/download/pdf/14517358.pdf |url-status=live |journal=Biochem. Z. |volume=21 |pages=131–304 |archive-url=https://web.archive.org/web/20210415205740/https://core.ac.uk/download/pdf/14517358.pdf |archive-date=15 April 2021 |access-date=22 March 2021 |quote=Original German: Für die Zahl p schlage ich den Namen Wasserstoffionenexponent und die Schreibweise p<sub>H</sub>• vor. Unter dem Wasserstoffionexponenten (p<sub>H</sub>•) einer Lösungwird dann der Briggsche Logarithmus des reziproken Wertes des auf Wasserstoffionenbezagenen Normalitäts faktors de Lösungverstanden.}} Two other publications appeared in 1909, one in French and one in Danish.</ref>, originally using the notation "p<sub>H•</sub>", with H• as a subscript to the lowercase p. The concept was later revised in 1924 to the modern pH to accommodate definitions and measurements in terms of electrochemical cells.<blockquote>For the sign ''p'', I propose the name 'hydrogen ion exponent' and the symbol p<sub>H•</sub>. Then, for the hydrogen ion exponent (p<sub>H•</sub>) of a solution, the negative value of the [[Common logarithm|Briggsian logarithm]] of the related hydrogen ion [[Equivalent concentration|normality factor]] is to be understood.<ref name="Sørensen2" /></blockquote>Sørensen did not explain why he used the letter p, and the exact meaning of the letter is still disputed.<ref>{{Cite journal |last=Francl |first=Michelle |date=August 2010 |title=Urban legends of chemistry |url=https://www.nature.com/articles/nchem.750.epdf |url-status=live |journal=Nature Chemistry |volume=2 |issue=8 |pages=600–601 |bibcode=2010NatCh...2..600F |doi=10.1038/nchem.750 |issn=1755-4330 |pmid=20651711 |archive-url=https://web.archive.org/web/20200806053215/https://www.nature.com/articles/nchem.750.epdf |archive-date=6 August 2020 |access-date=21 July 2019}}</ref> Sørensen described a way of measuring pH using ''potential'' differences, and it represents the negative ''power'' of 10 in the concentration of hydrogen ions. The letter ''p'' could stand for the French ''puissance,'' German ''Potenz,'' or Danish ''potens'', all meaning "power", or it could mean "potential". All of these words start with the letter ''p'' in [[French language|French]], [[German language|German]], and [[Danish language|Danish]], which where the languages Sørensen published in (Carlsberg Laboratory was French-speaking, German was the dominant language of scientific publishing, and Sørensen was Danish). He also used the letter ''q'' in much the same way elsewhere in the paper, and he might have arbitrarily labelled the test solution "p" and the reference solution "q"; these letters are often paired.<ref>{{cite journal |last1=Myers |first1=Rollie J. |year=2010 |title=One-Hundred Years of pH |journal=Journal of Chemical Education |volume=87 |issue=1 |pages=30–32 |bibcode=2010JChEd..87...30M |doi=10.1021/ed800002c}}</ref> Some literature sources suggest that "pH" stands for the [[Latin language|Latin term]] ''pondus hydrogenii'' (quantity of hydrogen) or ''potentia hydrogenii'' (power of hydrogen), although this is not supported by Sørensen's writings.<ref name="Otterson2">{{cite journal |last1=Otterson |first1=David W. |date=2015 |title=Tech Talk: (11) pH Measurement and Control Basics. |url=https://journals.sagepub.com/doi/pdf/10.1177/0020294015600474 |journal=Measurement and Control |volume=48 |issue=10 |pages=309–312 |doi=10.1177/0020294015600474 |s2cid=110716297 |access-date=16 June 2022}}</ref><ref name="Lian2">{{cite journal |last1=Lian |first1=Ying |last2=Zhang |first2=Wei |last3=Ding |first3=Longjiang |last4=Zhang |first4=Xiaoai |last5=Zhang |first5=Yinglu |last6=Wang |first6=Xu-dong |date=2019 |title=Nanomaterials for Intracellular pH Sensing and Imaging. |url=https://www.sciencedirect.com/science/article/pii/B9780128144978000084 |journal=Novel Nanomaterials for Biomedical, Environmental and Energy Applications. |series=Micro and Nano Technologies |pages=241–273 |doi=10.1016/B978-0-12-814497-8.00008-4 |isbn=9780128144978 |s2cid=104410918 |access-date=16 June 2022}}</ref><ref name="Bradley2">{{cite news |last1=Bradley |first1=David |date=21 February 2018 |title=When it comes to caustic wit and an acid tongue, mind your Ps and Qs. |publisher=Materials Today |url=https://www.materialstoday.com/materials-chemistry/comment/caustic-wit-acid-tongues-mind-your-ps-and-qs/ |access-date=16 June 2022}}</ref>
In modern [[chemistry]], the p stands for "the negative [[Common logarithm|decimal logarithm of]]", and is used in the term p''K''<sub>a</sub> for [[Acid dissociation constant|acid dissociation constants]]<ref name="Jens2">{{cite journal |author=Nørby, Jens |year=2000 |title=The origin and the meaning of the little p in pH |journal=Trends in Biochemical Sciences |volume=25 |issue=1 |pages=36–37 |doi=10.1016/S0968-0004(99)01517-0 |pmid=10637613}}</ref>andpOHfor theequivalent for [[hydroxide]]ions.
In modern [[chemistry]], the p stands for "the negative [[Common logarithm|decimal logarithm of]]", and is used in the term p''K''<sub>a</sub> for [[Acid dissociation constant|acid dissociation constants]]<ref name="Jens2">{{cite journal |author=Nørby, Jens |year=2000 |title=The origin and the meaning of the little p in pH |journal=Trends in Biochemical Sciences |volume=25 |issue=1 |pages=36–37 |doi=10.1016/S0968-0004(99)01517-0 |pmid=10637613}}</ref>,sopHis"thenegative [[Common logarithm|decimal logarithm of]]H<sup>+</sup> ion concentration", while pOH is "the negative decimal logarithm of OH- ion concentration".
Bacteriologist [[Alice Catherine Evans]], who influenced [[Dairy|dairying]] and [[food safety]], credited William Mansfield Clark and colleagues, including herself, with developing pH measuring methods in the 1910s, which had a wide influence on laboratory and industrial use thereafter. In her memoir, she does not mention how much, or how little, Clark and colleagues knew about Sørensen's work a few years prior.<ref name="Evans-Memoirs2">{{cite web |last1=Evans |first1=Alice C. |author-link=Alice Catherine Evans |year=1963 |title=Memoirs |url=https://history.nih.gov/archives/downloads/aliceevans.pdf |url-status=dead |archive-url=https://web.archive.org/web/20171215000804/https://history.nih.gov/archives/downloads/aliceevans.pdf |archive-date=15 December 2017 |access-date=2018-03-27 |website=NIH Office of History |publisher=National Institutes of Health Office of History}}</ref> She said:<blockquote>In these studies [of bacterial metabolism] Dr. Clark's attention was directed to the effect of acid on the growth of bacteria. He found that it is the intensity of the acid in terms of hydrogen-ion concentration that affects their growth. But existing methods of measuring acidity determined the quantity, not the intensity, of the acid. Next, with his collaborators, Dr. Clark developed accurate methods for measuring hydrogen-ion concentration. These methods replaced the inaccurate titration method of determining the acid content in use in biologic laboratories throughout the world. Also they were found to be applicable in many industrial and other processes in which they came into wide usage.<ref name="Evans-Memoirs2" /></blockquote>The first [[Electronics|electronic]] method for measuring pH was invented by [[Arnold Orville Beckman]], a professor at the [[California Institute of Technology]] in 1934.<ref>{{cite web |title=Origins: Birth of the pH Meter |url=https://eands.caltech.edu/origins-birth-of-the-ph-meter/ |url-status=dead |archive-url=https://web.archive.org/web/20181106180207/https://eands.caltech.edu/origins-birth-of-the-ph-meter/ |archive-date=6 November 2018 |access-date=11 March 2018 |website=Caltech Engineering & Science Magazine}}</ref> It was in response to a request from the local citrus grower [[Sunkist Growers, Incorporated|Sunkist]], which wanted a better method for quickly testing the pH of lemons they were picking from their nearby orchards.<ref>{{cite web |last1=Tetrault |first1=Sharon |date=June 2002 |title=The Beckmans |url=https://books.google.com/books?id=nf0DAAAAMBAJ&q=ph+caltech+beckman+sunkist&pg=PA96 |url-status=live |archive-url=https://web.archive.org/web/20210415222325/https://books.google.com/books?id=nf0DAAAAMBAJ&q=ph+caltech+beckman+sunkist&pg=PA96 |archive-date=15 April 2021 |access-date=11 March 2018 |website=Orange Coast |publisher=Orange Coast Magazine}}</ref>
Bacteriologist [[Alice Catherine Evans]], who influenced [[Dairy|dairying]] and [[food safety]], credited William Mansfield Clark and colleagues, including herself, with developing pH measuring methods in the 1910s, which had a wide influence on laboratory and industrial use thereafter. In her memoir, she does not mention how much, or how little, Clark and colleagues knew about Sørensen's work a few years prior.<ref name="Evans-Memoirs2">{{cite web |last1=Evans |first1=Alice C. |author-link=Alice Catherine Evans |year=1963 |title=Memoirs |url=https://history.nih.gov/archives/downloads/aliceevans.pdf |url-status=dead |archive-url=https://web.archive.org/web/20171215000804/https://history.nih.gov/archives/downloads/aliceevans.pdf |archive-date=15 December 2017 |access-date=2018-03-27 |website=NIH Office of History |publisher=National Institutes of Health Office of History}}</ref> She said:<blockquote>In these studies [of bacterial metabolism] Dr. Clark's attention was directed to the effect of acid on the growth of bacteria. He found that it is the intensity of the acid in terms of hydrogen-ion concentration that affects their growth. But existing methods of measuring acidity determined the quantity, not the intensity, of the acid. Next, with his collaborators, Dr. Clark developed accurate methods for measuring hydrogen-ion concentration. These methods replaced the inaccurate titration method of determining the acid content in use in biologic laboratories throughout the world. Also they were found to be applicable in many industrial and other processes in which they came into wide usage.<ref name="Evans-Memoirs2" /></blockquote>The first [[Electronics|electronic]] method for measuring pH was invented by [[Arnold Orville Beckman]], a professor at the [[California Institute of Technology]] in 1934.<ref>{{cite web |title=Origins: Birth of the pH Meter |url=https://eands.caltech.edu/origins-birth-of-the-ph-meter/ |url-status=dead |archive-url=https://web.archive.org/web/20181106180207/https://eands.caltech.edu/origins-birth-of-the-ph-meter/ |archive-date=6 November 2018 |access-date=11 March 2018 |website=Caltech Engineering & Science Magazine}}</ref> It was in response to a request from the local citrus grower [[Sunkist Growers, Incorporated|Sunkist]], which wanted a better method for quickly testing the pH of lemons they were picking from their nearby orchards.<ref>{{cite web |last1=Tetrault |first1=Sharon |date=June 2002 |title=The Beckmans |url=https://books.google.com/books?id=nf0DAAAAMBAJ&q=ph+caltech+beckman+sunkist&pg=PA96 |url-status=live |archive-url=https://web.archive.org/web/20210415222325/https://books.google.com/books?id=nf0DAAAAMBAJ&q=ph+caltech+beckman+sunkist&pg=PA96 |archive-date=15 April 2021 |access-date=11 March 2018 |website=Orange Coast |publisher=Orange Coast Magazine}}</ref>
==Definitionand measurement==
==Definition ==
===pH===
===pH===
pH is defined as the decimal [[logarithm]] of the reciprocal of the [[hydrogen ion]] [[activity (chemistry)|activity]], ''a''<sub>H</sub>+, in a solution.<ref name=covington>{{cite journal |doi=10.1351/pac198557030531 |last1=Covington |url=http://www.iupac.org/publications/pac/1985/pdf/5703x0531.pdf |first1=A. K. |last2=Bates |first2=R. G. |last3=Durst |first3=R. A. |title=Definitions of pH scales, standard reference values, measurement of pH, and related terminology |journal=Pure Appl. Chem. |year=1985 |volume=57 |pages=531–542 |issue=3 |s2cid=14182410 |url-status=live |archive-url=https://web.archive.org/web/20070924235637/http://www.iupac.org/publications/pac/1985/pdf/5703x0531.pdf |archive-date=24 September 2007}}</ref>
ThepH of a solution is defined as the decimal [[logarithm]] of the reciprocal of the [[hydrogen ion]] [[Activity (chemistry)|activity]], ''a''<sub>H</sub>+.<ref name="covington22">{{cite journal |last1=Covington |first1=A. K. |last2=Bates |first2=R. G. |last3=Durst |first3=R. A. |year=1985 |title=Definitions of pH scales, standard reference values, measurement of pH, and related terminology |url=http://www.iupac.org/publications/pac/1985/pdf/5703x0531.pdf |url-status=live |journal=Pure Appl. Chem. |volume=57 |issue=3 |pages=531–542 |doi=10.1351/pac198557030531 |s2cid=14182410 |archive-url=https://web.archive.org/web/20070924235637/http://www.iupac.org/publications/pac/1985/pdf/5703x0531.pdf |archive-date=24 September 2007}}</ref> Mathematically, pH is expressed as:
For example, for a solution with a hydrogen ion activity of 5×10<sup>−6</sup> (i.e., the concentration of hydrogen ions in [[Mole (unit)|moles]] per litre), the pH of the solution can be calculated as follows:
The concept of pH was developed because [[Ion-selective electrode|ion-selective electrodes]], which are used to measure pH, respond to activity. The electrode potential, ''E'', follows the [[Nernst equation]] for the hydrogen ion, which can be expressed as:
For example, for a solution with a hydrogen ion activity of 5×10<sup>−6</sup> (at that level, this is essentially the number of [[Mole (unit)|moles]] of hydrogen ions per litre of solution) the argument of the logarithm is 1/(5×10<sup>−6</sup>) = 2×10<sup>5</sup>; thus such a solution has a pH of log<sub>10</sub>(2×10<sup>5</sup>) = 5.3. Consider the following example: a quantity of 10<sup>7</sup> moles of pure water at 25 °C (pH = 7), or 180 metric tonnes (18×10<sup>7</sup> g), contains close to 18 grams of [[Dissociation (chemistry)|dissociated]] hydrogen ions.
where ''E'' is a measured potential, ''E''<sup>0</sup> is the standard electrode potential, ''R'' is the [[gas constant]], ''T'' is the temperature in [[Kelvin|kelvins]], ''F'' is the [[Faraday constant]]. For {{chem2|H+}}, the number of electrons transferred is one. The electrode potential is proportional to pH when pH is defined in terms of activity.
Note that pH depends on temperature. For instance at 0 °C the pH of pure water is about 7.47. At 25 °C it is 7.00, and at 100 °C it is 6.14.
This definition was adopted because [[ion-selective electrode]]s, which are used to measure pH, respond to activity. Ideally, the electrode potential, ''E'', follows the [[Nernst equation]], which for the hydrogen ion can be written as
The precise measurement of pH is presented in International Standard [[ISO 31-8]] as follows:<ref>Quantities and units – Part 8: Physical chemistry and molecular physics, Annex C (normative): pH. [[International Organization for Standardization]], 1992.</ref> A [[galvanic cell]] is set up to measure the [[electromotive force]] (e.m.f.) between a reference electrode and an electrode sensitive to the hydrogen ion activity when they are both immersed in the same aqueous solution. The reference electrode may be a [[silver chloride electrode]] or a [[Saturated calomel electrode|calomel electrode]], and the hydrogen-ion selective electrode is a [[standard hydrogen electrode]].
: <span>Reference electrode | concentrated solution of KCl || test solution | H<sub>2</sub> | Pt</span>
where ''E'' is a measured potential, ''E''<sup>0</sup> is the standard electrode potential, ''R'' is the [[gas constant]], ''T'' is the temperature in [[kelvin]]s, ''F'' is the [[Faraday constant]]. For {{chem2|H+}} the number of electrons transferred is one. It follows that the electrode potential is proportional to pH when pH is defined in terms of activity. Precise measurement of pH is presented in International Standard [[ISO 31-8]] as follows:<ref>Quantities and units – Part 8: Physical chemistry and molecular physics, Annex C (normative): pH. [[International Organization for Standardization]], 1992.</ref> A [[galvanic cell]] is set up to measure the [[electromotive force]] (e.m.f.) between a reference electrode and an electrode sensitive to the hydrogen ion activity when they are both immersed in the same aqueous solution. The reference electrode may be a [[silver chloride electrode]] or a [[Saturated calomel electrode|calomel electrode]]. The hydrogen-ion selective electrode is a [[standard hydrogen electrode]].
:<span>Reference electrode | concentrated solution of KCl || test solution | H<sub>2</sub> | Pt</span>{{clarify|date=October 2014}}
Firstly, the cell is filled with a solution of known hydrogen ion activity and the electromotive force, ''E''<sub>S</sub>, is measured. Then the electromotive force, ''E''<sub>X</sub>, of the same cell containing the solution of unknown pH is measured.
Firstly, the cell is filled with a solution of known hydrogen ion activity and the electromotive force, ''E''<sub>S</sub>, is measured. Then the electromotive force, ''E''<sub>X</sub>, of the same cell containing the solution of unknown pH is measured.
The difference between the two measured electromotive force values is proportional to pH. This method of calibration avoids the need to know the [[standard electrode potential]]. The proportionality constant, 1/''z'', is ideally equal to <math>\frac{1}{2.303RT/F}\ </math>, the "Nernstian slope".
The difference between the two measured electromotive force values is proportional to pH. This method of calibration avoids the need to know the [[standard electrode potential]]. The proportionality constant, 1/''z'', is ideally equal to <math>\frac{1}{2.303RT/F}\ </math>, the "Nernstian slope".
To apply this process in practice, a [[glass electrode]] is used rather than the cumbersome hydrogen electrode. A combined glass electrode has an in-built reference electrode. It is calibrated against [[buffer solution]]s of known hydrogen ion activity. [[IUPAC]] (International Union of Pure and Applied Chemistry) has proposed the use of a set of buffer solutions of known {{chem2|H+}} activity.<ref name=covington/> Two or more buffer solutions are used in order to accommodate the fact that the "slope" may differ slightly from ideal. To implement this approach to calibration, the electrode is first immersed in a standard solution and the reading on a [[pH meter]] is adjusted to be equal to the standard buffer's value. The reading from a second standard buffer solution is then adjusted, using the "slope" control, to be equal to the pH for that solution. Further details, are given in the [[IUPAC]] recommendations.<ref name=covington/> When more than two buffer solutions are used the electrode is calibrated by fitting observed pH values to a straight line with respect to standard buffer values. Commercial standard buffer solutions usually come with information on the value at 25 °C and a correction factor to be applied for other temperatures.
In practice, a [[glass electrode]] is used instead of the cumbersome hydrogen electrode. A combined glass electrode has an in-built reference electrode. It is calibrated against [[Buffer solution|buffer solutions]] of known hydrogen ion activity. [[IUPAC]] (International Union of Pure and Applied Chemistry) has proposed the use of a set of buffer solutions of known {{chem2|H+}} activity.<ref name="covington3">{{cite journal |last1=Covington |first1=A. K. |last2=Bates |first2=R. G. |last3=Durst |first3=R. A. |year=1985 |title=Definitions of pH scales, standard reference values, measurement of pH, and related terminology |url=http://www.iupac.org/publications/pac/1985/pdf/5703x0531.pdf |url-status=live |journal=Pure Appl. Chem. |volume=57 |issue=3 |pages=531–542 |doi=10.1351/pac198557030531 |s2cid=14182410 |archive-url=https://web.archive.org/web/20070924235637/http://www.iupac.org/publications/pac/1985/pdf/5703x0531.pdf |archive-date=24 September 2007}}</ref> Two or more buffer solutions are used in order to accommodate the fact that the "slope" may differ slightly from ideal. To calibrate the electrode, it is first immersed in a standard solution, and the reading on a [[pH meter]] is adjusted to be equal to the standard buffer's value. The reading from a second standard buffer solution is then adjusted using the "slope" control to be equal to the pH for that solution. Further details, are given in the [[IUPAC]] recommendations.<ref name="covington22" /> When more than two buffer solutions are used the electrode is calibrated by fitting observed pH values to a straight line with respect to standard buffer values. Commercial standard buffer solutions usually come with information on the value at 25 °C and a correction factor to be applied for other temperatures.
The pH scale is logarithmic and therefore pH is a [[dimensionless quantity]].
===p[H]===
This was the original definition of Sørensen in 1909,<ref name="Sor">{{cite web|url=http://www.carlsberggroup.com/Company/heritage/Research/Pages/pHValue.aspx |title=Carlsberg Group Company History Page |publisher=Carlsberggroup.com |archive-url=https://web.archive.org/web/20140118043012/http://www.carlsberggroup.com/Company/heritage/Research/Pages/pHValue.aspx |archive-date=18 January 2014 |url-status=live |access-date=7 May 2013}}</ref> which was superseded in favor of pH in 1924. [H] is the concentration of hydrogen ions, denoted [{{chem2|H(+)}}] in modern chemistry, which appears to have units of concentration. More correctly, the [[thermodynamic activity]] of {{chem2|H(+)}} in dilute solution should be replaced by [{{chem2|H(+)}}]/c<sub>0</sub>, where the standard state concentration c<sub>0</sub> = 1 mol/L. This ratio is a pure number whose logarithm can be defined.
The pH scale is logarithmic and therefore pH is a [[dimensionless quantity]].<ref>{{Cite book |url=https://goldbook.iupac.org/ |title=The IUPAC Compendium of Chemical Terminology: The Gold Book |date=2019 |publisher=International Union of Pure and Applied Chemistry (IUPAC) |editor-last=Gold |editor-first=Victor |edition=4 |location=Research Triangle Park, NC |language=en |doi=10.1351/goldbook.p04525}}</ref> The pH scale ranges from 0 to 14, with a pH of 7 indicating neutrality, values less than 7 indicating acidity, and values greater than 7 indicating basicity. The pH scale is based on the hydrogen ion concentration, with each pH unit representing a tenfold difference in hydrogen ion concentration.
However, it is possible to measure the concentration of hydrogen ions directly, if the electrode is calibrated in terms of hydrogen ion concentrations. One way to do this, which has been used extensively, is to [[titration|titrate]] a solution of known concentration of a strong acid with a solution of known concentration of strong alkaline in the presence of a relatively high concentration of background electrolyte. Since the concentrations of acid and alkaline are known, it is easy to calculate the concentration of hydrogen ions so that the measured potential can be correlated with concentrations. The calibration is usually carried out using a [[Gran plot#Electrode calibration|Gran plot]].<ref>{{cite journal| volume=42 |doi=10.1021/ed042p375| last=Rossotti| first=F.J.C.|author2=Rossotti, H.|year=1965|title=Potentiometric titrations solution containing the background electrolyte. |journal=J. Chem. Educ.}}</ref> Thus, the effect of using this procedure is to make activity equal to the numerical value of concentration.
=== p[H] ===
The glass electrode (and other [[ion selective electrode]]s) should be calibrated in a medium similar to the one being investigated. For instance, if one wishes to measure the pH of a seawater sample, the electrode should be calibrated in a solution resembling seawater in its chemical composition, as detailed below.
This was the original definition of Sørensen in 1909,<ref name="Sor2">{{cite web |title=Carlsberg Group Company History Page |url=http://www.carlsberggroup.com/Company/heritage/Research/Pages/pHValue.aspx |url-status=live |archive-url=https://web.archive.org/web/20140118043012/http://www.carlsberggroup.com/Company/heritage/Research/Pages/pHValue.aspx |archive-date=18 January 2014 |access-date=7 May 2013 |publisher=Carlsberggroup.com}}</ref> which was superseded in favor of pH in 1924. [H] is the concentration of hydrogen ions, denoted [{{chem2|H(+)}}] in modern chemistry, which appears to have units of concentration. More correctly, the [[thermodynamic activity]] of {{chem2|H(+)}} in dilute solution should be replaced by [{{chem2|H(+)}}]/c<sub>0</sub>, where the standard state concentration c<sub>0</sub> = 1 mol/L. This ratio is a pure number whose logarithm can be defined.
The difference between p[H] and pH is quite small. It has been stated<ref>{{VogelQuantitative}}, Section 13.23, "Determination of pH"</ref> that pH = p[H] + 0.04. It is common practice to use the term "pH" for both types of measurement.
It is possible to measure the concentration of hydrogen ions directly using an electrode calibrated in terms of hydrogen ion concentrations. One common method is to [[Titration|titrate]] a solution of known concentration of a strong acid with a solution of known concentration of strong base in the presence of a relatively high concentration of background electrolyte. By knowing the concentrations of the acid and base, the concentration of hydrogen ions can be calculated and the measured potential can be correlated with concentrations. The calibration is usually carried out using a [[Gran plot#Electrode calibration|Gran plot]].<ref>{{cite journal |last=Rossotti |first=F.J.C. |author2=Rossotti, H. |year=1965 |title=Potentiometric titrations solution containing the background electrolyte. |journal=J. Chem. Educ. |volume=42 |doi=10.1021/ed042p375}}</ref> This procedure makes the activity of hydrogen ions equal to the numerical value of concentration.
===pH indicators===
{{Main|pH indicator}}
The glass electrode (and other [[Ion selective electrode|ion selective electrodes]]) should be calibrated in a medium similar to the one being investigated. For instance, if one wishes to measure the pH of a seawater sample, the electrode should be calibrated in a solution resembling seawater in its chemical composition.
The difference between p[H] and pH is quite small, and it has been stated that pH = p[H] + 0.04.<ref>{{VogelQuantitative}}, Section 13.23, "Determination of pH"</ref> However, it is common practice to use the term "pH" for both types of measurement.
=== pOH ===
[[File:PHscalenolang.svg|thumb|Relation between pH and pOH. Red represents the acidic region. Blue represents the basic region.]]
pOH is sometimes used as a measure of the concentration of hydroxide ions, {{chem2|OH−}}. pOH values are derived from pH measurements. The concentration of hydroxide ions in water is related to the concentration of hydrogen ions by
So, at room temperature, pOH ≈ 14 − pH. However this relationship is not strictly valid in other circumstances, such as in measurements of [[Alkaline soils|soil alkalinity]].
pH can be measured using indicators, which change color depending on the pH of the solution they are in. By comparing the color of a test solution to a standard color chart, the pH can be estimated to the nearest whole number. For more precise measurements, the color can be measured using a [[Colorimeter (chemistry)|colorimeter]] or [[spectrophotometer]]. [[Universal indicator]] is a mixture of several indicators that can provide a continuous color change over a range of pH values, typically from about pH 2 to pH 10. Universal indicator paper is made from absorbent paper that has been impregnated with universal indicator. An alternative method of measuring pH is using an electronic [[pH meter]], which directly measures the voltage difference between a pH-sensitive electrode and a reference electrode.
===Non-aqueous solutions===
Indicators may be used to measure pH, by making use of the fact that their color changes with pH. Visual comparison of the color of a test solution with a standard color chart provides a means to measure pH accurate to the nearest whole number. More precise measurements are possible if the color is measured spectrophotometrically, using a [[Colorimeter (chemistry)|colorimeter]] or [[spectrophotometer]].
pH values can be measured in non-aqueous solutions, but they are based on a different scale from aqueous pH values, because the [[Standard state|standard states]] used for calculating hydrogen ion concentrations ([[Activity (chemistry)|activities]]) are different. The hydrogen ion activity, ''a<sub>H<sup>+</sup></sub>'', is defined<ref name="GoldBook2">{{GoldBookRef|title=activity (relative activity), ''a''|file=A00115}}</ref><ref name="GreenBook2">{{GreenBookRef2nd|pages=49–50}}</ref> as:
[[Universal indicator]] consists of a mixture of indicators such that there is a continuous color change from about pH 2 to pH 10. Universal indicator paper is made from absorbent paper that has been impregnated with universal indicator. Another method of measuring pH is using an electronic [[pH meter]].
[[Image:PHscalenolang.svg|thumb|upright=1.2|Relation between pH and pOH. Red represents the acidic region. Blue represents the basic region.]]
where ''μ''<sub>H<sup>+</sup></sub> is the [[chemical potential]] of the hydrogen ion, <math chem="">\mu^{\ominus}_\ce{H+}</math> is its chemical potential in the chosen standard state, ''R'' is the [[gas constant]] and ''T'' is the [[thermodynamic temperature]]. Therefore, pH values on the different scales cannot be compared directly because of differences in the solvated proton ions, such as lyonium ions, which require an intersolvent scale which involves the transfer activity coefficient of [[Lyonium ion|hydronium/lyonium ion]].
pOH is sometimes used as a measure of the concentration of hydroxide ions, {{chem2|OH−}}. pOH values are derived from pH measurements. The concentration of hydroxide ions in water is related to the concentration of hydrogen ions by
pH is an example of an [[acidity function]], but there are others that can be defined. For example, the [[Hammett acidity function]], ''H''<sub>0</sub>, has been developed in connection with [[Superacid|superacids]].
where ''K''<sub>W</sub> is the [[self-ionization of water|self-ionization]] constant of water. Taking [[logarithm]]s
In 2010, a new approach to measuring pH was proposed, called the "unified absolute pH scale". This approach allows for a common reference standard to be used across different solutions, regardless of their pH range. The unified absolute pH scale is based on the absolute chemical potential of the proton, as defined by the [[Lewis acids and bases|Lewis acid–base]] theory. This scale is applicable to liquids, gases, and even solids.<ref name="Krossing2">{{Cite journal |last1=Himmel |first1=Daniel |last2=Goll |first2=Sascha K. |last3=Leito |first3=Ivo |last4=Krossing |first4=Ingo |date=2010-08-16 |title=A Unified pH Scale for All Phases |journal=Angewandte Chemie International Edition |volume=49 |issue=38 |pages=6885–6888 |doi=10.1002/anie.201000252 |issn=1433-7851 |pmid=20715223}}</ref>
The measurement of pH can become difficult at extremely acidic or alkaline conditions, such as below pH 2.5 (ca. 0.003 [[Mole (unit)|mol]]/dm<sup>3</sup> acid) or above pH 10.5 (ca. 0.0003 mol/dm<sup>3</sup> alkaline). This is due to the breakdown of the [[Nernst equation]] in this conditions when using a glass electrode. There are several factors contribute to this problem. Firstly, [[Liquid junction potential|liquid junction potentials]] may not be independent of pH.<ref name="Feldman2">{{cite journal |author=Feldman, Isaac |year=1956 |title=Use and Abuse of pH measurements |journal=Analytical Chemistry |volume=28 |issue=12 |pages=1859–1866 |doi=10.1021/ac60120a014}}</ref> Secondly, the high [[ionic strength]] of concentrated solutions can affect the electrode potentials. At high pH the glass electrode may be affected by "alkaline error", because the electrode becomes sensitive to the concentration of cations such as {{chem2|Na+}} and {{chem2|K+}} in the solution.<ref>{{VogelQuantitative}}, Section 13.19 The glass electrode</ref> To overcome these problems, specially constructed electrodes are available.
Runoff from mines or mine tailings can produce some extremely low pH values.<ref>{{cite journal |last1=Nordstrom |first1=D. Kirk |last2=Alpers |first2=Charles N. |date=March 1999 |title=Negative pH, efflorescent mineralogy, and consequences for environmental restoration at the Iron Mountain Superfund site, California |url=http://digitalcommons.unl.edu/cgi/viewcontent.cgi?article=1495&context=usgsstaffpub |url-status=live |journal=Proceedings of the National Academy of Sciences of the United States of America |volume=96 |issue=7 |pages=3455–62 |bibcode=1999PNAS...96.3455N |doi=10.1073/pnas.96.7.3455 |pmc=34288 |pmid=10097057 |archive-url=https://web.archive.org/web/20170923012227/http://digitalcommons.unl.edu/cgi/viewcontent.cgi?article=1495&context=usgsstaffpub |archive-date=23 September 2017 |access-date=4 November 2018 |doi-access=free}}</ref>
So, at room temperature, pOH ≈ 14 − pH. However this relationship is not strictly valid in other circumstances, such as in measurements of [[Alkaline soils|soil alkalinity]].
===Extremes of pH===
Measurement of pH below about 2.5 (ca. 0.003 [[mole (unit)|mol]]/dm<sup>3</sup> acid) and above about 10.5 (ca. 0.0003 mol/dm<sup>3</sup> alkaline) requires special procedures because, when using the glass electrode, the [[Nernst equation|Nernst law]] breaks down under those conditions. Various factors contribute to this. It cannot be assumed that [[liquid junction potential]]s are independent of pH.<ref name=Feldman>{{cite journal|doi=10.1021/ac60120a014|title=Use and Abuse of pH measurements|journal=Analytical Chemistry|author=Feldman, Isaac |volume=28|pages=1859–1866|year=1956|issue=12}}</ref> Also, extreme pH implies that the solution is concentrated, so electrode potentials are affected by [[ionic strength]] variation. At high pH the glass electrode may be affected by "alkaline error", because the electrode becomes sensitive to the concentration of cations such as {{chem2|Na+}} and {{chem2|K+}} in the solution.<ref>{{VogelQuantitative}}, Section 13.19 The glass electrode</ref> Specially constructed electrodes are available which partly overcome these problems.
Runoff from mines or mine tailings can produce some very low pH values.<ref>{{cite journal |last1=Nordstrom |first1=D. Kirk |last2=Alpers |first2=Charles N. |title=Negative pH, efflorescent mineralogy, and consequences for environmental restoration at the Iron Mountain Superfund site, California |date=March 1999 |pmid=10097057 |doi=10.1073/pnas.96.7.3455 |volume=96 |issue=7 |pages=3455–62 |pmc=34288 |journal=Proceedings of the National Academy of Sciences of the United States of America |bibcode=1999PNAS...96.3455N |url=http://digitalcommons.unl.edu/cgi/viewcontent.cgi?article=1495&context=usgsstaffpub |doi-access=free |access-date=4 November 2018 |archive-date=23 September 2017 |archive-url=https://web.archive.org/web/20170923012227/http://digitalcommons.unl.edu/cgi/viewcontent.cgi?article=1495&context=usgsstaffpub |url-status=live }}</ref>
===Non-aqueous solutions===
Hydrogen ion concentrations (activities) can be measured in non-aqueous solvents. pH values based on these measurements belong to a different scale from aqueous pH values, because [[activity (chemistry)|activities]] relate to different [[standard state]]s. Hydrogen ion activity, ''a<sub>H<sup>+</sup></sub>'', can be defined<ref name="GoldBook">{{GoldBookRef|title=activity (relative activity), ''a''|file=A00115}}</ref><ref name="GreenBook">{{GreenBookRef2nd|pages=49–50}}</ref> as:
where ''μ''<sub>H<sup>+</sup></sub> is the [[chemical potential]] of the hydrogen ion, <math chem>\mu^{\ominus}_\ce{H+}</math> is its chemical potential in the chosen standard state, ''R'' is the [[gas constant]] and ''T'' is the [[thermodynamic temperature]]. Therefore, pH values on the different scales cannot be compared directly due to different solvated proton ions such as lyonium ions, requiring an intersolvent scale which involves the transfer activity coefficient of [[lyonium ion|hydronium/lyonium ion]].
pH is an example of an [[acidity function]]. Other acidity functions can be defined. For example, the [[Hammett acidity function]], ''H''<sub>0</sub>, has been developed in connection with [[superacid]]s.
===Unified absolute pH scale===
In 2010, a new "unified absolute pH scale" has been proposed that would allow various pH ranges across different solutions to use a common proton reference standard. It has been developed on the basis of the absolute chemical potential of the proton. This model uses the [[Lewis acids and bases|Lewis acid–base]] definition. This scale applies to liquids, gases and even solids.<ref name=Krossing>{{Cite journal|last1=Himmel|first1=Daniel|last2=Goll|first2=Sascha K.|last3=Leito|first3=Ivo|last4=Krossing|first4=Ingo|date=2010-08-16|title=A Unified pH Scale for All Phases|journal=Angewandte Chemie International Edition|volume=49|issue=38|pages=6885–6888|doi=10.1002/anie.201000252|pmid=20715223|issn=1433-7851}}</ref>
==Applications==
==Applications==
The pH scale ranges from 0 to 14, with 7 being neutral. Pure water has a pH of 7 at 25°C, meaning it is neutral. When an [[acid]] is dissolved in water, the pH will be less than 7, while a [[Base (chemistry)|base]], or [[alkali]], will have a pH greater than 7. A strong acid, such as [[hydrochloric acid]], at concentration 1 mol dm<sup>−3</sup> has a pH of 0, while a strong alkali like [[sodium hydroxide]], at the same concentration, has a pH of 14. Since pH is a logarithmic scale, a difference of one in pH is equivalent to a tenfold difference in hydrogen ion concentration.
<!-- [[File:PH scale 2.png|thumb|right|Another visual representation of the pH scale.]]
[[File:Hydrangea macrophylla - Hortensia hydrangea.jpg|right|thumb|''[[Hydrangea macrophylla]]'' blossoms vary from [[pink]] to [[blue]], according to a pH-dependent mobilization and uptake of soil aluminium into the plants.]] -->
Pure water is neutral. When an [[acid]] is dissolved in water, the pH will be less than 7 (25 °C). When a [[base (chemistry)|base]], or specifically an [[alkali]], is dissolved in water, the pH will be greater than 7. A solution of a strong acid, such as [[hydrochloric acid]], at concentration 1 mol dm<sup>−3</sup> has a pH of 0. A solution of a strong alkali, such as [[sodium hydroxide]], at concentration 1 mol dm<sup>−3</sup>, has a pH of 14. Thus, measured pH values will lie mostly in the range 0 to 14, though negative pH values and values above 14 are entirely possible. Since pH is a logarithmic scale, a difference of one pH unit is equivalent to a tenfold difference in hydrogen ion concentration.
The pH of neutrality is not exactly 7 (25 °C), although this is a good approximation in most cases. Neutrality is defined as the condition where [{{chem2|H+}}] = [{{chem2|OH−}}] (or the activities are equal). Since [[self-ionization of water]] holds the product of these concentration [{{chem2|H+}}]/M×[{{chem2|OH−}}]/M = K<sub>w</sub>, it can be seen that at neutrality [{{chem2|H+}}]/M = [{{chem2|OH−}}]/M = {{radic|K<sub>w</sub>}}, or pH = pK<sub>w</sub>/2. pK<sub>w</sub> is approximately 14 but depends on ionic strength and temperature, and so the pH of neutrality does also. Pure water and a solution of [[sodium chloride|NaCl]] in pure water are both neutral, since [[Self-ionization of water|dissociation of water]] produces equal numbers of both ions. However the pH of the neutral NaCl solution will be slightly different from that of neutral pure water because the hydrogen and hydroxide ions' activity is dependent on [[ionic strength]], so K<sub>w</sub> varies with ionic strength.
It's important to note that neutrality isn't exactly 7 at 25°C, although it's a good approximation in most cases. Neutrality occurs when the concentration of hydrogen ions ([{{chem2|H+}}]) equals the concentration of hydroxide ions ([{{chem2|OH−}}]), or when their activities are equal. Since [[self-ionization of water]] holds the product of these concentration [{{chem2|H+}}]/M×[{{chem2|OH−}}]/M = K<sub>w</sub>, it can be seen that at neutrality [{{chem2|H+}}]/M = [{{chem2|OH−}}]/M = {{radic|K<sub>w</sub>}}, or pH = pK<sub>w</sub>/2. pK<sub>w</sub> is approximately 14 but depends on ionic strength and temperature, and so the pH of neutrality does also. Pure water and a solution of [[Sodium chloride|NaCl]] in pure water are both neutral, since [[Self-ionization of water|dissociation of water]] produces equal numbers of both ions. However the pH of the neutral NaCl solution will be slightly different from that of neutral pure water because the hydrogen and hydroxide ions' activity is dependent on [[ionic strength]], so K<sub>w</sub> varies with ionic strength.
If pure water is exposed to air it becomes mildly acidic. This is because water absorbs [[carbon dioxide]] from the air, which is then slowly converted into [[bicarbonate]] and hydrogen ions (essentially creating [[carbonic acid]]).
:{{chem|CO|2| + H|2|O {{eqm}} HCO|3|-| + H|+}}
When pure water is exposed to air, it becomes mildly acidic. This is because water absorbs [[carbon dioxide]] from the air, which is then slowly converted into [[bicarbonate]] and hydrogen ions (essentially creating [[carbonic acid]]).
===pH in soil===
: {{chem|CO|2|+ H|2|O {{eqm}} HCO|3|-|+ H|+}}
====Classification of soil pH ranges====
[[Image:Soil pH effect on nutrient availability.svg|thumb|upright=2.1|Nutritional elements availability within soil varies with pH. Light blue color represents the ideal range for most plants.]]
=== pH in Soil ===
The United States Department of Agriculture [[Natural Resources Conservation Service]], formerly Soil Conservation Service classifies [[soil pH]] ranges as follows:<ref>{{cite web|author=Soil Survey Division Staff|url= http://soils.usda.gov/technical/manual/contents/chapter3.html |title=Soil survey manual.1993. Chapter 3, selected chemical properties. |publisher=Soil Conservation Service. U.S. Department of Agriculture Handbook 18 |access-date=2011-03-12 |url-status=dead |archive-url=https://web.archive.org/web/20110514151830/http://soils.usda.gov/technical/manual/contents/chapter3.html |archive-date=14 May 2011}}</ref>
==== {{See also|Soil pH}}Classification of soil pH ranges ====
{|class="wikitable"
[[File:Soil_pH_effect_on_nutrient_availability.svg|thumb|Nutritional elements availability within soil varies with pH. Light blue color represents the ideal range for most plants.]]
The United States Department of Agriculture [[Natural Resources Conservation Service]], formerly Soil Conservation Service classifies [[soil pH]] ranges as follows:<ref>{{cite web |author=Soil Survey Division Staff |title=Soil survey manual.1993. Chapter 3, selected chemical properties. |url=http://soils.usda.gov/technical/manual/contents/chapter3.html |url-status=dead |archive-url=https://web.archive.org/web/20110514151830/http://soils.usda.gov/technical/manual/contents/chapter3.html |archive-date=14 May 2011 |access-date=2011-03-12 |publisher=Soil Conservation Service. U.S. Department of Agriculture Handbook 18}}</ref>
{|
! scope="col" |Denomination
! scope="col" |pH range
|-
|-
|Ultra acidic
!scope="col"|Denomination
|< 3.5
!scope="col"|pH range
|-
|-
|Ultra acidic|| < 3.5
|Extremely acidic
|3.5–4.4
|-
|-
|Very strongly acidic
|Extremely acidic|| 3.5–4.4
|4.5–5.0
|-
|-
|Strongly acidic
|Very strongly acidic|| 4.5–5.0 <!-- BTW to which range belong the value 4.45? was the article written by scientists or by record clerks? -->
|5.1–5.5
|-
|-
|Strongly acidic|| 5.1–5.5
|Moderately acidic
|5.6–6.0
|-
|-
|Moderately acidic|| 5.6–6.0
|Slightly acidic
|6.1–6.5
|-
|-
|Neutral
|Slightly acidic|| 6.1–6.5
|6.6–7.3
|-
|-
|Slightly alkaline
|Neutral|| 6.6–7.3
|7.4–7.8
|-
|-
|Slightly alkaline|| 7.4–7.8
|Moderately alkaline
|7.9–8.4
|-
|-
|Moderately alkaline|| 7.9–8.4
|Strongly alkaline
|8.5–9.0
|-
|-
|Very strongly alkaline
|Strongly alkaline|| 8.5–9.0
|9.0–10.5
|-
|-
|Very strongly alkaline|| 9.0–10.5
|Hyper alkaline
|> 10.5
|-
|Hyper alkaline || > 10.5
|}
|}
In Europe, topsoil pH is influenced by soil parent material, erosional effects, climate and vegetation. A recent map<ref>{{Cite journal|last1=Ballabio|first1=Cristiano|last2=Lugato|first2=Emanuele|last3=Fernández-Ugalde|first3=Oihane|last4=Orgiazzi|first4=Alberto|last5=Jones|first5=Arwyn|last6=Borrelli|first6=Pasquale|last7=Montanarella|first7=Luca|last8=Panagos|first8=Panos|date=2019|title=Mapping LUCAS topsoil chemical properties at European scale using Gaussian process regression|journal=Geoderma|language=en|volume=355|pages=113912|doi=10.1016/j.geoderma.2019.113912|pmid=31798185|pmc=6743211|bibcode=2019Geode.355k3912B|doi-access=free}}</ref> of topsoil pH in Europe shows the alkaline soils in Mediterranean, Hungary, East Romania, North France. Scandinavian countries, Portugal, Poland and North Germany have more acid soils.
In Europe, topsoil pH is influenced by soil parent material, erosional effects, climate and vegetation. A recent map<ref>{{Cite journal|last1=Ballabio|first1=Cristiano|last2=Lugato|first2=Emanuele|last3=Fernández-Ugalde|first3=Oihane|last4=Orgiazzi|first4=Alberto|last5=Jones|first5=Arwyn|last6=Borrelli|first6=Pasquale|last7=Montanarella|first7=Luca|last8=Panagos|first8=Panos|date=2019|title=Mapping LUCAS topsoil chemical properties at European scale using Gaussian process regression|journal=Geoderma|language=en|volume=355|pages=113912 |bibcode=2019Geode.355k3912B|doi=10.1016/j.geoderma.2019.113912|pmc=6743211|pmid=31798185|doi-access=free}}</ref> of topsoil pH in Europe shows the alkaline soils in Mediterranean, Hungary, East Romania, North France. Scandinavian countries, Portugal, Poland and North Germany have more acid soils.
==== Measuring soil pH ====
==== Measuring soil pH ====
Soil in the field is a heterogeneous colloidal system that comprises sand, silt, clays, microorganisms, plant roots, and myriad other living cells and decaying organic material.Soil pH is amastervariable that affectsmyriad processes and propertiesofinterest to soil and environmental scientists, farmers, and engineers.<ref name=":0">{{Cite book |last=McBride |first=Murray |title=Environmental chemistry of soils|publisher=Oxford University Press|year=1994|isbn=0-19-507011-9|location=New York |pages=169–174}}</ref> Toquantify the concentration of the H<sup>+</sup> insuchacomplexsystem, soil samples from agivensoilhorizonarebrought to the laboratorywherethey are homogenized, sieved, and sometimes driedprior to analysis. A mass of soil (for example, 5 g field-moist to best represent field conditions) is mixed into a slurry with distilled water or 0.01 M CaCl<sub>2</sub> (for example, 10 mL). After mixing well, the suspension is stirred vigorously and allowed to stand for 15–20 minutes, during which time, the sand and silt particles settle out and the clays and other colloids remain suspended in the overlying water, known as the aqueous phase. A pH electrode connected to a pH meter is calibrated with buffered solutions of known pH (for example, pH 4 and 7) before being inserting into the upper portion of the aqueous phase, and the pH is measured. A combination pH electrode incorporates both the H<sup>+</sup> sensing electrode (glass electrode) and a reference electrode that provides a pH-insensitive reference voltage and a salt bridge to the hydrogen electrode. In other configurations, the glass and reference electrodes are separate and attach to the pH meter in two ports. The pH meter measures the potential (voltage) difference between the two electrodes and converts it to pH. The separate reference electrode is usually the [[calomel electrode]], the silver-[[silver chloride electrode]] is used in the combination electrode.<ref name=":0" />
Soil in the field is a[[heterogeneous]][[Colloid|colloidal]] system that comprises sand, silt, clays, microorganisms, plant roots, and other living cells and decaying organic material.The pH of soil is acriticalfactor that affectsmany processes and properties,including thoserelevant to soil and environmental scientists, farmers, and engineers.<ref name=":02">{{Cite book |last=McBride |first=Murray |title=Environmental chemistry of soils|publisher=Oxford University Press|year=1994|isbn=0-19-507011-9|location=New York |pages=169–174}}</ref> Tomeasure the concentration of the H<sup>+</sup> insoil,researcherstypicallytake soil samples from aspecificdepthandbringthem to the laboratory.Thesamples are then homogenized, sieved, and sometimes driedbefore analysis.
There are numerous uncertainties in operationally defining soil pH in the above way. Since an electrical potential difference between the glass and reference electrodes is what is measured, the activity of H<sup>+</sup> is really being quantified, rather than concentration. The H<sup>+</sup> activity is sometimes called the "effective H<sup>+</sup> concentration" and is directly related to the chemical potential of the proton and its ability to do chemical and electrical work in the soil solution in equilibrium with the solid phases.<ref>{{Cite book|last=Essington|first=Michael E.|title=Soil and Water Chemistry|publisher=CRC Press|year=2004|isbn=0-8493-1258-2|location=Boca Raton, Florida|pages=474–482}}</ref> Clay and organic matter particles carry negative charge on their surfaces, and H<sup>+</sup> ions attracted to them are in equilibrium with H<sup>+</sup> ions in the soil solution. The measured pH is quantified in the aqueous phase only, by definition, but the value obtained is affected by the presence and nature of the soil colloids and the ionic strength of the aqueous phase. Changing the water-to-soil ratio in the slurry can change the pH by disturbing the water-colloid equilibrium, particularly the ionic strength. The use of 0.01 M CaCl<sub>2</sub> instead of water obviates this effect of water-to-soil ratio and gives a more consistent approximation of "soil pH" that relates to plant root growth, rhizosphere and microbial activity, drainage water acidity, and chemical processes in the soil. Using 0.01 M CaCl<sub>2</sub> brings all of the soluble ions in the aqueous phase closer to the colloidal surfaces, and allows the H<sup>+</sup> activity to be measured closer to them. Using the 0.01 M CaCl<sub>2</sub> solution thereby allows a more consistent, quantitative estimation of H<sup>+</sup> activity, especially if diverse soil samples are being compared in space and time.
To determine the pH of the soil sample, a small amount of soil (typically 5 grams of field-moist soil) is mixed with distilled water or 0.01 M CaCl<sub>2</sub> solution. The mixture is stirred vigorously and allowed to settle for 15–20 minutes, during which time the sand and silt particles settle out while the clays and other colloids remain suspended in the overlying water (aqueous phase). A pH electrode connected to a pH meter is calibrated with buffered solutions of known pH before being inserting into the upper portion of the aqueous phase, and the pH is measured. A combination pH electrode incorporates both the H<sup>+</sup> sensing electrode (glass electrode) and a reference electrode that provides a pH-insensitive reference voltage and a salt bridge to the hydrogen electrode. In other configurations, the glass and reference electrodes are separate and attach to the pH meter in two ports. The pH meter measures the potential (voltage) difference between the two electrodes and converts it to pH. The separate reference electrode is usually the [[calomel electrode]], the silver-[[silver chloride electrode]] is used in the combination electrode.<ref name=":02" />
There are several uncertainties in measuring soil pH this way. Since an electrical potential difference between the glass and reference electrodes is measured, the activity of H<sup>+</sup> is quantified, rather than concentration. The H<sup>+</sup> activity is sometimes called the "effective H<sup>+</sup> concentration" and is related to the chemical potential of the proton and its ability to do chemical and electrical work in the soil solution in equilibrium with the solid phases.<ref>{{Cite book |last=Essington |first=Michael E. |title=Soil and Water Chemistry |publisher=CRC Press |year=2004 |isbn=0-8493-1258-2 |location=Boca Raton, Florida |pages=474–482}}</ref> Clay and organic matter particles carry negative charge on their surfaces, and H<sup>+</sup> ions attracted to them are in equilibrium with H<sup>+</sup> ions in the soil solution. The measured pH is determined in the aqueous phase only, but the value obtained is affected by the presence and nature of soil colloids and the ionic strength of the aqueous phase. Changing the water-to-soil ratio in the mixture can alter the pH by disturbing the water-colloid equilibrium, particularly the ionic strength. Using 0.01 M CaCl<sub>2</sub> obviates this effect of water-to-soil ratio and gives a more consistent approximation of soil pH that relates to plant root growth, rhizosphere and microbial activity, drainage water acidity, and chemical processes in the soil. Using 0.01 M CaCl<sub>2</sub> brings all of the soluble ions in the aqueous phase closer to the colloidal surfaces, and allows the H<sup>+</sup> activity to be measured closer to them. This approach is especially useful for comparing soil samples from different locations and times.
===pH in nature===
===pH in nature===
[[File:Lemon- whole and split.jpg|thumb|[[Lemon juice]] tastes sour because it contains 5% to 6% [[citric acid]] and has a pH of 2.2 (high acidity).]]
[[File:Lemon_-_whole_and_split.jpg|thumb|[[Lemon juice]] tastes sour because it contains 5% to 6% [[citric acid]] and has a pH of 2.2 (high acidity).]]
pH-dependent [[plant pigment]]s that can be used as [[pH indicator]]soccurinmanyplants,including [[hibiscus]], [[red cabbage]] ([[anthocyanin]]), and grapes ([[red wine]]). The juice of [[citrus]] fruitsis acidicmainlybecauseitcontains [[citric acid]].Other [[carboxylic acid]]soccur inmany living systems. Forexample, [[lactic acid]]isproducedby [[muscle]] activity. The state of [[protonation]] of [[phosphate]] derivatives,such as [[Adenosine triphosphate|ATP]], is pH-dependent.Thefunctioning of the oxygen-transport enzyme[[hemoglobin]]is affected by pH in aprocess known as the [[Root effect]].
Plants containpH-dependent [[Plant pigment|pigments]] that can be used as [[PH indicator|pH indicators]],suchasthosefoundin [[hibiscus]], [[red cabbage]] ([[anthocyanin]]), and grapes ([[red wine]]). [[Citrus]] fruitshave acidicjiuiceprimarilydueto the presence of [[citric acid]], whileother [[Carboxylic acid|carboxylic acids]]can be found invarious living systems. Forinstance, [[muscle]]activityresultsin the production of [[lactic acid]]. The [[protonation]] state of [[phosphate]] derivatives,including [[Adenosine triphosphate|ATP]], is pH-dependent.[[Hemoglobin]],an oxygen-transport enzyme,isalso affected by pH in aphenomenon known as the [[Root effect]].
===Seawater===
=== pH inSeawater===
{{See also|Ocean acidification}}The pH of [[seawater]] is typically limited to a range between 7.4 and 8.5.<ref name="Chester Marine Geochem2">{{cite book |last=Chester, Jickells |first=Roy, Tim |title=Marine Geochemistry |date=2012 |publisher=Blackwell Publishing |isbn=978-1-118-34907-6}}</ref> It plays an important role in the ocean's [[Carbon cycle#Ocean|carbon cycle]], and there is evidence of ongoing [[ocean acidification]] caused by [[Carbon dioxide emission#Greenhouse gas emissions|carbon dioxide emissions]].<ref name="raven052">{{cite book |author=Royal Society |url=http://dge.stanford.edu/labs/caldeiralab/Caldeira%20downloads/RoyalSociety_OceanAcidification.pdf |title=Ocean acidification due to increasing atmospheric carbon dioxide |year=2005 |isbn=978-0-85403-617-2 |archive-url=https://web.archive.org/web/20100716000207/http://dge.stanford.edu/labs/caldeiralab/Caldeira%20downloads/RoyalSociety_OceanAcidification.pdf |archive-date=16 July 2010 |url-status=live}}</ref> However, pH measurement is complicated by the [[Chemical property|chemical properties]] of seawater, and several distinct pH scales exist in [[chemical oceanography]].<ref name="zeebe2">Zeebe, R. E. and Wolf-Gladrow, D. (2001) ''CO<sub>2</sub> in seawater: equilibrium, kinetics, isotopes'', Elsevier Science B.V., Amsterdam, Netherlands {{ISBN|0-444-50946-1}}</ref>
{{See also|Ocean acidification}}
The pH of [[seawater]] is typically limited to a range between 7.4 and 8.5.<ref name="Chester Marine Geochem">{{cite book|last=Chester, Jickells|first=Roy, Tim|title=Marine Geochemistry|date=2012|publisher=Blackwell Publishing|isbn=978-1-118-34907-6}}</ref> It plays an important role in the ocean's [[Carbon cycle#Ocean|carbon cycle]], and there is evidence of ongoing [[ocean acidification]] caused by [[Carbon dioxide emission#Greenhouse gas emissions|carbon dioxide emissions]].<ref name=raven05>{{cite book| author=Royal Society |url= http://dge.stanford.edu/labs/caldeiralab/Caldeira%20downloads/RoyalSociety_OceanAcidification.pdf|year=2005|title=Ocean acidification due to increasing atmospheric carbon dioxide|isbn=978-0-85403-617-2|url-status=live|archive-url= https://web.archive.org/web/20100716000207/http://dge.stanford.edu/labs/caldeiralab/Caldeira%20downloads/RoyalSociety_OceanAcidification.pdf|archive-date=16 July 2010}}</ref> However, pH measurement is complicated by the [[chemical property|chemical properties]] of seawater, and several distinct pH scales exist in [[chemical oceanography]].<ref name=zeebe>Zeebe, R. E. and Wolf-Gladrow, D. (2001) ''CO<sub>2</sub> in seawater: equilibrium, kinetics, isotopes'', Elsevier Science B.V., Amsterdam, Netherlands {{ISBN|0-444-50946-1}}</ref>
As part of its [[operational definition]] of the pH scale, the [[IUPAC]] defines a series of [[buffer solution]]s across a range of pH values (often denoted with [[National Bureau of Standards]] (NBS) or [[National Institute of Standards and Technology]] (NIST) designation). These solutions have a relatively low [[ionic strength]] (≈0.1) compared to that of seawater (≈0.7), and, as a consequence, are not recommended for use in characterizing the pH of seawater, since the ionic strength differences cause changes in [[standard electrode potential|electrode potential]]. To resolve this problem, an alternative series of buffers based on [[artificial seawater]] was developed.<ref>{{cite journal|doi=10.1016/0011-7471(73)90101-0|author=Hansson, I.|year=1973|title=A new set of pH-scales and standard buffers for seawater|journal=Deep-Sea Research|volume=20|pages=479–491|issue=5| bibcode=1973DSRA...20..479H}}</ref> This new series resolves the problem of ionic strength differences between samples and the buffers, and the new pH scale is referred to as the 'total scale', often denoted as pH<sub>T</sub>. The total scale was defined using a medium containing [[sulfate]] ions. These ions experience [[protonation]], {{chem2|H+}} + {{chem|SO|4|2-|↔ HSO|4|-}}, such that the total scale includes the effect of both [[proton]]s (free hydrogen ions) and hydrogen sulfate ions:
As part of its [[operational definition]] of the pH scale, the [[IUPAC]] defines a series of [[Buffer solution|buffer solutions]] across a range of pH values (often denoted with [[National Bureau of Standards]] (NBS) or [[National Institute of Standards and Technology]] (NIST) designation). These solutions have a relatively low [[ionic strength]] (≈0.1) compared to that of seawater (≈0.7), and, as a consequence, are not recommended for use in characterizing the pH of seawater, since the ionic strength differences cause changes in [[Standard electrode potential|electrode potential]]. To resolve this problem, an alternative series of buffers based on [[artificial seawater]] was developed.<ref>{{cite journal|author=Hansson, I.|year=1973|title=A new set of pH-scales and standard buffers for seawater|journal=Deep-Sea Research|volume=20|issue=5|pages=479–491|bibcode=1973DSRA...20..479H |doi=10.1016/0011-7471(73)90101-0}}</ref> This new series resolves the problem of ionic strength differences between samples and the buffers, and the new pH scale is referred to as the 'total scale', often denoted as pH<sub>T</sub>. The total scale was defined using a medium containing [[sulfate]] ions. These ions experience [[protonation]], {{chem2|H+}} + {{chem|SO|4|2-|↔ HSO|4|-}}, such that the total scale includes the effect of both [[Proton|protons]] (free hydrogen ions) and hydrogen sulfate ions:
An alternative scale, the 'free scale', often denoted 'pH<sub>F</sub>', omits this consideration and focuses solely on [{{chem2|H+}}]<sub>F</sub>, in principle making it a simpler representation of hydrogen ion concentration. Only [{{chem2|H+}}]<sub>T</sub> can be determined,<ref>{{cite journal| doi=10.1016/0016-7037(84)90225-4| author=Dickson, A. G.|year=1984|title=pH scales and proton-transfer reactions in saline media such as sea water|journal=Geochim. Cosmochim. Acta|volume=48|pages=2299–2308|issue=11|bibcode = 1984GeCoA..48.2299D }}</ref> therefore [{{chem2|H+}}]<sub>F</sub> must be estimated using the [{{chem|SO|4|2-}}] and the stability constant of {{chem|HSO|4|-}}, {{nowrap|1=K{{su|b=S|p=*}}}}:
An alternative scale, the 'free scale', often denoted 'pH<sub>F</sub>', omits this consideration and focuses solely on [{{chem2|H+}}]<sub>F</sub>, in principle making it a simpler representation of hydrogen ion concentration. Only [{{chem2|H+}}]<sub>T</sub> can be determined,<ref>{{cite journal |author=Dickson, A. G. |year=1984 |title=pH scales and proton-transfer reactions in saline media such as sea water |journal=Geochim. Cosmochim. Acta |volume=48 |issue=11 |pages=2299–2308 |bibcode=1984GeCoA..48.2299D |doi=10.1016/0016-7037(84)90225-4}}</ref> therefore [{{chem2|H+}}]<sub>F</sub> must be estimated using the [{{chem|SO|4|2-}}] and the stability constant of {{chem|HSO|4|-}}, {{nowrap|K{{su|b=S|p=*}}}}:
However, it is difficult to estimate K{{su|b=S|p=*}} in seawater, limiting the utility of the otherwise more straightforward free scale.
However, it is difficult to estimate K{{su|b=S|p=*}} in seawater, limiting the utility of the otherwise more straightforward free scale.
Another scale, known as the 'seawater scale', often denoted 'pH<sub>SWS</sub>', takes account of a further protonation relationship between hydrogen ions and [[fluoride]] ions, {{chem2|H+}} + {{chem2|F-}} ⇌ HF. Resulting in the following expression for [{{chem2|H+}}]<sub>SWS</sub>:
Another scale, known as the 'seawater scale', often denoted 'pH<sub>SWS</sub>', takes account of a further protonation relationship between hydrogen ions and [[fluoride]] ions, {{chem2|H+}} + {{chem2|F-}} ⇌ HF. Resulting in the following expression for [{{chem2|H+}}]<sub>SWS</sub>:
However, the advantage of considering this additional complexity is dependent upon the abundance of fluoride in the medium. In seawater, for instance, sulfate ions occur at much greater concentrations (>400 times) than those of fluoride. As a consequence, for most practical purposes, the difference between the total and seawater scales is very small.
However, the advantage of considering this additional complexity is dependent upon the abundance of fluoride in the medium. In seawater, for instance, sulfate ions occur at much greater concentrations (>400 times) than those of fluoride. As a consequence, for most practical purposes, the difference between the total and seawater scales is very small.
The following three equationssummarise the three scales of pH:
The following three equationssummarize the three scales of pH:
In practical terms, the three seawater pH scales differ in their values by up to 0.10 pH units, differences that are much larger than the accuracy of pH measurements typically required, in particular, in relation to the ocean's [[Total inorganic carbon|carbonate system]].<ref name=zeebe /> Since it omits consideration of sulfate and fluoride ions, the free scale is significantly different from both the total and seawater scales. Because of the relative unimportance of the fluoride ion, the total and seawater scales differ only very slightly.
In practical terms, the three seawater pH scales differ in their pH values up to 0.10, differences that are much larger than the accuracy of pH measurements typically required, in particular, in relation to the ocean's [[Total inorganic carbon|carbonate system]].<ref name="zeebe2" /> Since it omits consideration of sulfate and fluoride ions, the free scale is significantly different from both the total and seawater scales. Because of the relative unimportance of the fluoride ion, the total and seawater scales differ only very slightly.
===Living systems===
===Living systems===
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The pH ofdifferent cellular compartments, [[body fluid]]s, and organs is usually tightly regulatedin aprocesscalled [[acid–base homeostasis]].The most common disorderin acid–base[[homeostasis]]is[[acidosis]],whichmeans anacidoverload in the body,generallydefined by pH falling below 7.35. [[Alkalosis]] istheoppositecondition,with blood pH being excessively high.
In living organisms, the pH ofvarious [[Body fluid|body fluids]], cellular compartments, and organs is tightly regulatedto maintain astate of acid-base balance knownas [[acid–base homeostasis]].[[Acidosis]], defined by a pH below 7.35, is the most common disorderof acid–base homeostasisandoccurswhenthere is anexcessof acid in the body.Incontrast, [[alkalosis]] ischaracterizedbyexcessivelyhigh blood pH.
The pH of blood is usually slightly basic with a value of pH 7.365. This value is often referred to as physiological pH in biology and medicine. [[Dental plaque|Plaque]] can create a local acidic environment that can result in [[tooth decay]] by demineralization. [[Enzyme]]s and other [[protein]]s have an optimum pH range and can become inactivated or [[denaturation (biochemistry)|denatured]] outside this range.
<!-- <div>
[[File:Blood values sorted by mass and molar concentration.png|thumb|900px|[[Reference ranges for blood tests]], showing concentration of protons (purple) at left. It can be seen that the ranges are kept in a narrow range, and that free protons are among the compounds with the very smallest mass concentrations.]]
</div> -->
Blood pH is usually slightly basic, with a pH of 7.365, referred to as physiological pH in biology and medicine. [[Dental plaque|Plaque]] formation in teeth can create a local acidic environment that results in [[tooth decay]] through demineralization. [[Enzyme|Enzymes]] and other [[Protein|proteins]] have an optimal pH range for function and can become inactivated or [[Denaturation (biochemistry)|denatured]] outside this range.
==Calculations of pH==
The calculation of the pH of a solution containing acids and/or bases is an example of a [[Determination of equilibrium constants#Speciation calculations|chemical speciation calculation]], that is, a mathematical procedure for calculating the concentrations of all chemical species that are present in the solution. The complexity of the procedure depends on the nature of the solution. For strong acids and bases no calculations are necessary except in extreme situations. The pH of a solution containing a weak acid requires the solution of a [[quadratic equation]]. The pH of a solution containing a weak base may require the solution of a [[cubic equation]]. The general case requires the solution of a set of [[non-linear]] [[simultaneous equation]]s.
== pH Calculations ==
When calculating the pH of a solution containing acids and/or bases, a [[Determination of equilibrium constants#Speciation calculations|chemical speciation calculation]] is used to determine the concentration of all chemical species present in the solution. The complexity of the procedure depends on the nature of the solution. Strong acids and bases are compounds that are almost completely dissociated in water, which simplifies the calculation. However, for weak acids, a [[quadratic equation]] must be solved, and for weak bases, a cubic equation is required. In general, a set of [[non-linear]] [[Simultaneous equation|simultaneous equations]] must be solved.
Water itself is a weak acid and a weak base, so its dissociation must be takent into account at high pH and low solute concentration (see [[amphoterism]]). It [[Self-ionization of water|dissociates]] according to the equilibrium
: {{chem2|2 H2O <-> H3O+ (aq) + OH- (aq)}}
with a [[Acid dissociation constant|dissociation constant]], ''{{mvar|K<sub>w</sub>}}'' defined as
: <math chem="">K_w = \ce{[H+][OH^{-}]} </math>
A complicating factor is that water itself is a weak acid and a weak base (see [[amphoterism]]). It [[self-ionization of water|dissociates]] according to the equilibrium
:{{chem2|2 H2O <-> H3O+ (aq) + OH- (aq)}}
with a [[acid dissociation constant|dissociation constant]], {{mvar|K<sub>w</sub>}} defined as
where [H<sup>+</sup>] stands for the concentration of the aqueous [[hydronium ion]] and [OH<sup>−</sup>] represents the concentration of the [[hydroxide ion]]. This equilibrium needs to be taken into account at high pH and when the solute concentration is extremely low.
where [H<sup>+</sup>] stands for the concentration of the aqueous [[hydronium ion]] and [OH<sup>−</sup>] represents the concentration of the [[hydroxide ion]]. This equilibrium needs to be taken into account at high pH and when the solute concentration is extremely low.
===Strong acids and bases===
===Strong acids and bases===
[[Strong acid]]s and [[Strong base|bases]] are compounds that for practical purposes, arecompletely dissociated in water.Undernormalcircumstancesthismeansthat the concentration of hydrogen ionsin acidic solution can betaken to be equal to the concentration of the acid.ThepHisthenequal to minus thelogarithm oftheconcentrationvalue.[[Hydrochloricacid]](HCl)isanexample ofastrong acid. The pH of a 0.01M solution of HCl isequalto−log<sub>10</sub>(0.01),thatis,pH=2.[[Sodiumhydroxide]],NaOH, isanexample ofastrongbase.Thep[OH]value of a 0.01M solution ofNaOH is equal to−log<sub>10</sub>(0.01),that is, p[OH] = 2. From thedefinition ofp[OH]inthepOHsectionabove,this means that the pH is equal toabout12.Forsolutionsofsodiumhydroxideathigherconcentrationstheself-ionization equilibrium must be taken into account.
[[Strong acid|Strong acids]] and [[Strong base|bases]] are compounds that areessentially fully dissociated in water.Thismeansthatinanacidic solution, the concentration of hydrogen ions(H+) can beconsidered equal to the concentration of the acid.Similarly,inabasicsolution, theconcentration ofhydroxideions(OH-)canbeconsideredequaltothe concentration ofthebase. The pH of a solution isdefinedasthenegativelogarithmoftheconcentrationofH+,and the pOH isdefinedas the negative logarithm oftheconcentrationof OH-.Forexample,the pH of a 0.01M solution ofhydrochloric acid (HCl) is equal to2 (pH = −log10(0.01)),while thepOH ofa0.01Msolutionofsodiumhydroxide(NaOH) is equal to2(pOH=−log10(0.01)),whichcorrespondstoapHofabout12.
Self-ionization must also be considered when concentrationsareextremelylow.Consider,forexample,asolutionofhydrochloricacidat a concentration of 5×10<sup>−8</sup>M.Thesimpleprocedure given above wouldsuggestthatithas a pH of 7.3.Thisisclearlywrong asanacidsolution should have a pH of less than 7.Treating the system as a mixture ofhydrochloric acid andthe [[amphoteric]] substance water, a pH of 6.89results.<ref>{{cite web|last=Maloney|first=Chris|title=pH calculation of a very small concentration of a strong acid.|url=http://sinophibe.blogspot.com/2011/03/ph-calculation-of-very-small.html|access-date=13March 2011|url-status=live|archive-url=https://web.archive.org/web/20110708062942/http://sinophibe.blogspot.com/2011/03/ph-calculation-of-very-small.html|archive-date=8 July 2011}}</ref>
However, self-ionization of water must also be considered when concentrationsofastrongacidorbaseisveryloworhigh.For instance, a 5×10<sup>−8</sup>MsolutionofHCl wouldbeexpectedtohave a pH of 7.3basedontheabove procedure, which is incorrect asitisacidic and should have a pH of less than 7.In such cases, the system can be treated as a mixture ofthe acid or base andwater, which is an [[amphoteric]] substance. By accounting for the self-ionization of water, the true pH of the solution can be calculated. For example, a 5×10<sup>−8</sup>M solution of HCl would have a pH of 6.89when treated as a mixture of HCl and water. The self-ionization equilibrium of solutions of sodium hydroxide at higher concentrations must also be considered.<ref>{{cite web|last=Maloney|first=Chris|title=pH calculation of a very small concentration of a strong acid.|url=http://sinophibe.blogspot.com/2011/03/ph-calculation-of-very-small.html |url-status=live|archive-url=https://web.archive.org/web/20110708062942/http://sinophibe.blogspot.com/2011/03/ph-calculation-of-very-small.html|archive-date=8 July 2011 |access-date=13 March 2011}}</ref>
===Weak acids and bases===
===Weak acids and bases===
A [[Weak Acid|weak acid]] or the conjugate acid of a weak base can be treated using the same formalism.
A weak acid or the conjugate acid of a weak base can be treated using the same formalism.
* Acid HA: {{chem2|HA <-> H+ + A-}}
* Acid HA: {{chem2|HA <-> H+ + A-}}
* Base A: {{chem2|HA+ <-> H+ + A}}
* Base A: {{chem2|HA+ <-> H+ + A}}
First, an acid dissociation constant is defined as follows. Electrical charges are omitted from subsequent equations for the sake of generality
First, an acid dissociation constant is defined as follows. Electrical charges are omitted from subsequent equations for the sake of generality
and its value is assumed to have been determined by experiment. This being so, there are three unknown concentrations, [HA], [H<sup>+</sup>] and [A<sup>−</sup>] to determine by calculation. Two additional equations are needed. One way to provide them is to apply the law of [[mass conservation]] in terms of the two "reagents" H and A.
and its value is assumed to have been determined by experiment. This being so, there are three unknown concentrations, [HA], [H<sup>+</sup>] and [A<sup>−</sup>] to determine by calculation. Two additional equations are needed. One way to provide them is to apply the law of [[mass conservation]] in terms of the two "reagents" H and A.
C stands for [[analytical concentration]]. In some texts, one mass balance equation is replaced by an equation of charge balance. This is satisfactory for simple cases like this one, but is more difficult to apply to more complicated cases as those below. Together with the equation defining K<sub>a</sub>, there are now three equations in three unknowns. When an acid is dissolved in water C<sub>A</sub> = C<sub>H</sub> = C<sub>a</sub>, the concentration of the acid, so [A] = [H]. After some further algebraic manipulation an equation in the hydrogen ion concentration may be obtained.
C stands for [[analytical concentration]]. In some texts, one mass balance equation is replaced by an equation of charge balance. This is satisfactory for simple cases like this one, but is more difficult to apply to more complicated cases as those below. Together with the equation defining K<sub>a</sub>, there are now three equations in three unknowns. When an acid is dissolved in water C<sub>A</sub> = C<sub>H</sub> = C<sub>a</sub>, the concentration of the acid, so [A] = [H]. After some further algebraic manipulation an equation in the hydrogen ion concentration may be obtained.
Solution of this [[quadratic equation]] gives the hydrogen ion concentration and hence p[H] or, more loosely, pH. This procedure is illustrated in an [[ICE table]] which can also be used to calculate the pH when some additional (strong) acid or alkaline has been added to the system, that is, when C<sub>A</sub> ≠ C<sub>H</sub>.
Solution of this [[quadratic equation]] gives the hydrogen ion concentration and hence p[H] or, more loosely, pH. This procedure is illustrated in an [[ICE table]] which can also be used to calculate the pH when some additional (strong) acid or alkaline has been added to the system, that is, when C<sub>A</sub> ≠ C<sub>H</sub>.
For example, what is the pH of a 0.01M solution of [[benzoic acid]], pK<sub>a</sub> = 4.19?
For example, what is the pH of a 0.01M solution of [[benzoic acid]], pK<sub>a</sub> = 4.19?
For alkaline solutions an additional term is added to the mass-balance equation for hydrogen. Since addition of hydroxide reduces the hydrogen ion concentration, and the hydroxide ion concentration is constrained by the self-ionization equilibrium to be equal to <math chem>\frac{K_w}\ce{[H+]}</math>
For alkaline solutions, an additional term is added to the mass-balance equation for hydrogen. Since the addition of hydroxide reduces the hydrogen ion concentration, and the hydroxide ion concentration is constrained by the self-ionization equilibrium to be equal to <math chem="">\frac{K_w}\ce{[H+]}</math>, the resulting equation is:
In this case the resulting equation in [H] is a cubic equation.
Some systems, such as with polyprotic acids, are amenable to spreadsheet calculations.<ref>{{cite book |last1=Billo |first1=E.J. |title=EXCEL for Chemists|edition= 3rd |year=2011|publisher=Wiley-VCH|isbn=978-0-470-38123-6}}</ref> With three or more reagents or when many complexes are formed with general formulae such as A<sub>p</sub>B<sub>q</sub>H<sub>r</sub>,the following general method can be used to calculate the pH of a solution. For example, with three reagents, each equilibrium is characterized by an equilibrium constant, β.
Some systems, such as with[[polyprotic]] acids, are amenable to spreadsheet calculations.<ref>{{cite book |last1=Billo |first1=E.J. |title=EXCEL for Chemists|publisher=Wiley-VCH |year=2011 |isbn=978-0-470-38123-6 |edition=3rd}}</ref> With three or more reagents or when many complexes are formed with general formulae such as A<sub>p</sub>B<sub>q</sub>H<sub>r</sub>,the following general method can be used to calculate the pH of a solution. For example, with three reagents, each equilibrium is characterized by an equilibrium constant, β.
Note that there are no approximations involved in these equations, except that each stability constant is defined as a quotient of concentrations, not activities. Much more complicated expressions are required if activities are to be used.
Note that there are no approximations involved in these equations, except that each stability constant is defined as a quotient of concentrations, not activities. Much more complicated expressions are required if activities are to be used.
There are 3 [[non-linear]] [[simultaneous equation]]s in the three unknowns, [A], [B] and [H]. Because the equations are non-linear, and because concentrations may range over many powers of 10, the solution of these equations is not straightforward. However, many computer programs are available which can be used to perform these calculations. There may be more than three reagents. The calculation of hydrogen ion concentrations, using this formalism, is a key element in the [[determination of equilibrium constants]] by potentiometric titration.
There are three [[non-linear]] [[Simultaneous equation|simultaneous equations]] in the three unknowns, [A], [B] and [H]. Because the equations are non-linear and their concentrations may range over many powers of 10, the solution of these equations is not straightforward. However, many computer programs are available which can be used to perform these calculations. There may be more than three reagents. The calculation of hydrogen ion concentrations, using this approach, is a key element in the [[determination of equilibrium constants]] by [[potentiometric titration]].
== See also ==
== See also ==
Revision as of 01:39, 14 April 2023
Measure of the level of acidity or basicity of an aqueous solution
Inchemistry, pH (/piːˈeɪtʃ/), also referred to asacidity, historically denotes "potential ofhydrogen" (or "power of hydrogen").[1] It is a scale used to specify theacidity orbasicity of anaqueous solution. Acidic solutions (solutions with higher concentrations ofH+ions) are measured to have lower pH values than basic oralkaline solutions.
where [H+] is theequilibriummolar concentration (mol dm−3) of H+ in the solution. At 25 °C (77°F), solutions with a pH less than 7 are acidic, and solutions with a pH greater than 7 are basic. Solutions with a pH of 7 at this temperature are neutral (i.e. have the same concentration of H+ ions as OH− ions, i.e. the same aspure water). The neutral value of the pH depends on the temperature and is lower than 7 if the temperature increases above 25 °C. The pH value can be less than 0 for very concentratedstrong acids or greater than 14 for very concentratedstrong bases.[3]
In 1909, theDanish chemistSøren Peter Lauritz Sørensen introduced the concept of pH at theCarlsberg Laboratory[5], originally using the notation "pH•", with H• as a subscript to the lowercase p. The concept was later revised in 1924 to the modern pH to accommodate definitions and measurements in terms of electrochemical cells.
For the signp, I propose the name 'hydrogen ion exponent' and the symbol pH•. Then, for the hydrogen ion exponent (pH•) of a solution, the negative value of theBriggsian logarithm of the related hydrogen ionnormality factor is to be understood.[5]
Sørensen did not explain why he used the letter p, and the exact meaning of the letter is still disputed.[6] Sørensen described a way of measuring pH usingpotential differences, and it represents the negativepower of 10 in the concentration of hydrogen ions. The letterp could stand for the Frenchpuissance, GermanPotenz, or Danishpotens, all meaning "power", or it could mean "potential". All of these words start with the letterp inFrench,German, andDanish, which where the languages Sørensen published in (Carlsberg Laboratory was French-speaking, German was the dominant language of scientific publishing, and Sørensen was Danish). He also used the letterq in much the same way elsewhere in the paper, and he might have arbitrarily labelled the test solution "p" and the reference solution "q"; these letters are often paired.[7] Some literature sources suggest that "pH" stands for theLatin termpondus hydrogenii (quantity of hydrogen) orpotentia hydrogenii (power of hydrogen), although this is not supported by Sørensen's writings.[8][9][10]
BacteriologistAlice Catherine Evans, who influenceddairying andfood safety, credited William Mansfield Clark and colleagues, including herself, with developing pH measuring methods in the 1910s, which had a wide influence on laboratory and industrial use thereafter. In her memoir, she does not mention how much, or how little, Clark and colleagues knew about Sørensen's work a few years prior.[12] She said:
In these studies [of bacterial metabolism] Dr. Clark's attention was directed to the effect of acid on the growth of bacteria. He found that it is the intensity of the acid in terms of hydrogen-ion concentration that affects their growth. But existing methods of measuring acidity determined the quantity, not the intensity, of the acid. Next, with his collaborators, Dr. Clark developed accurate methods for measuring hydrogen-ion concentration. These methods replaced the inaccurate titration method of determining the acid content in use in biologic laboratories throughout the world. Also they were found to be applicable in many industrial and other processes in which they came into wide usage.[12]
The firstelectronic method for measuring pH was invented byArnold Orville Beckman, a professor at theCalifornia Institute of Technology in 1934.[13] It was in response to a request from the local citrus growerSunkist, which wanted a better method for quickly testing the pH of lemons they were picking from their nearby orchards.[14]
Definition
pH
The pH of a solution is defined as the decimallogarithm of the reciprocal of thehydrogen ionactivity,aH+.[15] Mathematically, pH is expressed as:
For example, for a solution with a hydrogen ion activity of 5×10−6 (i.e., the concentration of hydrogen ions inmoles per litre), the pH of the solution can be calculated as follows:
The concept of pH was developed becauseion-selective electrodes, which are used to measure pH, respond to activity. The electrode potential,E, follows theNernst equation for the hydrogen ion, which can be expressed as:
whereE is a measured potential,E0 is the standard electrode potential,R is thegas constant,T is the temperature inkelvins,F is theFaraday constant. ForH+, the number of electrons transferred is one. The electrode potential is proportional to pH when pH is defined in terms of activity.
The precise measurement of pH is presented in International StandardISO 31-8 as follows:[16] Agalvanic cell is set up to measure theelectromotive force (e.m.f.) between a reference electrode and an electrode sensitive to the hydrogen ion activity when they are both immersed in the same aqueous solution. The reference electrode may be asilver chloride electrode or acalomel electrode, and the hydrogen-ion selective electrode is astandard hydrogen electrode.
Reference electrode | concentrated solution of KCl || test solution | H2 | Pt
Firstly, the cell is filled with a solution of known hydrogen ion activity and the electromotive force,ES, is measured. Then the electromotive force,EX, of the same cell containing the solution of unknown pH is measured.
The difference between the two measured electromotive force values is proportional to pH. This method of calibration avoids the need to know thestandard electrode potential. The proportionality constant, 1/z, is ideally equal to, the "Nernstian slope".
In practice, aglass electrode is used instead of the cumbersome hydrogen electrode. A combined glass electrode has an in-built reference electrode. It is calibrated againstbuffer solutions of known hydrogen ion activity.IUPAC (International Union of Pure and Applied Chemistry) has proposed the use of a set of buffer solutions of knownH+ activity.[17] Two or more buffer solutions are used in order to accommodate the fact that the "slope" may differ slightly from ideal. To calibrate the electrode, it is first immersed in a standard solution, and the reading on apH meter is adjusted to be equal to the standard buffer's value. The reading from a second standard buffer solution is then adjusted using the "slope" control to be equal to the pH for that solution. Further details, are given in theIUPAC recommendations.[15] When more than two buffer solutions are used the electrode is calibrated by fitting observed pH values to a straight line with respect to standard buffer values. Commercial standard buffer solutions usually come with information on the value at 25 °C and a correction factor to be applied for other temperatures.
The pH scale is logarithmic and therefore pH is adimensionless quantity.[18] The pH scale ranges from 0 to 14, with a pH of 7 indicating neutrality, values less than 7 indicating acidity, and values greater than 7 indicating basicity. The pH scale is based on the hydrogen ion concentration, with each pH unit representing a tenfold difference in hydrogen ion concentration.
p[H]
This was the original definition of Sørensen in 1909,[19] which was superseded in favor of pH in 1924. [H] is the concentration of hydrogen ions, denoted [H+] in modern chemistry, which appears to have units of concentration. More correctly, thethermodynamic activity ofH+ in dilute solution should be replaced by [H+]/c0, where the standard state concentration c0 = 1 mol/L. This ratio is a pure number whose logarithm can be defined.
It is possible to measure the concentration of hydrogen ions directly using an electrode calibrated in terms of hydrogen ion concentrations. One common method is totitrate a solution of known concentration of a strong acid with a solution of known concentration of strong base in the presence of a relatively high concentration of background electrolyte. By knowing the concentrations of the acid and base, the concentration of hydrogen ions can be calculated and the measured potential can be correlated with concentrations. The calibration is usually carried out using aGran plot.[20] This procedure makes the activity of hydrogen ions equal to the numerical value of concentration.
The glass electrode (and otherion selective electrodes) should be calibrated in a medium similar to the one being investigated. For instance, if one wishes to measure the pH of a seawater sample, the electrode should be calibrated in a solution resembling seawater in its chemical composition.
The difference between p[H] and pH is quite small, and it has been stated that pH = p[H] + 0.04.[21] However, it is common practice to use the term "pH" for both types of measurement.
pOH
Relation between pH and pOH. Red represents the acidic region. Blue represents the basic region.
pOH is sometimes used as a measure of the concentration of hydroxide ions,OH−. pOH values are derived from pH measurements. The concentration of hydroxide ions in water is related to the concentration of hydrogen ions by
So, at room temperature, pOH ≈ 14 − pH. However this relationship is not strictly valid in other circumstances, such as in measurements ofsoil alkalinity.
pH can be measured using indicators, which change color depending on the pH of the solution they are in. By comparing the color of a test solution to a standard color chart, the pH can be estimated to the nearest whole number. For more precise measurements, the color can be measured using acolorimeter orspectrophotometer.Universal indicator is a mixture of several indicators that can provide a continuous color change over a range of pH values, typically from about pH 2 to pH 10. Universal indicator paper is made from absorbent paper that has been impregnated with universal indicator. An alternative method of measuring pH is using an electronicpH meter, which directly measures the voltage difference between a pH-sensitive electrode and a reference electrode.
Non-aqueous solutions
pH values can be measured in non-aqueous solutions, but they are based on a different scale from aqueous pH values, because thestandard states used for calculating hydrogen ion concentrations (activities) are different. The hydrogen ion activity,aH+, is defined[22][23] as:
whereμH+ is thechemical potential of the hydrogen ion, is its chemical potential in the chosen standard state,R is thegas constant andT is thethermodynamic temperature. Therefore, pH values on the different scales cannot be compared directly because of differences in the solvated proton ions, such as lyonium ions, which require an intersolvent scale which involves the transfer activity coefficient ofhydronium/lyonium ion.
In 2010, a new approach to measuring pH was proposed, called the "unified absolute pH scale". This approach allows for a common reference standard to be used across different solutions, regardless of their pH range. The unified absolute pH scale is based on the absolute chemical potential of the proton, as defined by theLewis acid–base theory. This scale is applicable to liquids, gases, and even solids.[24]
Extremes of pH measurements
The measurement of pH can become difficult at extremely acidic or alkaline conditions, such as below pH 2.5 (ca. 0.003 mol/dm3 acid) or above pH 10.5 (ca. 0.0003 mol/dm3 alkaline). This is due to the breakdown of theNernst equation in this conditions when using a glass electrode. There are several factors contribute to this problem. Firstly,liquid junction potentials may not be independent of pH.[25] Secondly, the highionic strength of concentrated solutions can affect the electrode potentials. At high pH the glass electrode may be affected by "alkaline error", because the electrode becomes sensitive to the concentration of cations such asNa+ andK+ in the solution.[26] To overcome these problems, specially constructed electrodes are available.
Runoff from mines or mine tailings can produce some extremely low pH values.[27]
Applications
The pH scale ranges from 0 to 14, with 7 being neutral. Pure water has a pH of 7 at 25°C, meaning it is neutral. When anacid is dissolved in water, the pH will be less than 7, while abase, oralkali, will have a pH greater than 7. A strong acid, such ashydrochloric acid, at concentration 1 mol dm−3 has a pH of 0, while a strong alkali likesodium hydroxide, at the same concentration, has a pH of 14. Since pH is a logarithmic scale, a difference of one in pH is equivalent to a tenfold difference in hydrogen ion concentration.
It's important to note that neutrality isn't exactly 7 at 25°C, although it's a good approximation in most cases. Neutrality occurs when the concentration of hydrogen ions ([H+]) equals the concentration of hydroxide ions ([OH−]), or when their activities are equal. Sinceself-ionization of water holds the product of these concentration [H+]/M×[OH−]/M = Kw, it can be seen that at neutrality [H+]/M = [OH−]/M =√Kw, or pH = pKw/2. pKw is approximately 14 but depends on ionic strength and temperature, and so the pH of neutrality does also. Pure water and a solution ofNaCl in pure water are both neutral, sincedissociation of water produces equal numbers of both ions. However the pH of the neutral NaCl solution will be slightly different from that of neutral pure water because the hydrogen and hydroxide ions' activity is dependent onionic strength, so Kw varies with ionic strength.
When pure water is exposed to air, it becomes mildly acidic. This is because water absorbscarbon dioxide from the air, which is then slowly converted intobicarbonate and hydrogen ions (essentially creatingcarbonic acid).
In Europe, topsoil pH is influenced by soil parent material, erosional effects, climate and vegetation. A recent map[29] of topsoil pH in Europe shows the alkaline soils in Mediterranean, Hungary, East Romania, North France. Scandinavian countries, Portugal, Poland and North Germany have more acid soils.
Measuring soil pH
Soil in the field is aheterogeneouscolloidal system that comprises sand, silt, clays, microorganisms, plant roots, and other living cells and decaying organic material. The pH of soil is a critical factor that affects many processes and properties, including those relevant to soil and environmental scientists, farmers, and engineers.[30] To measure the concentration of the H+ in soil, researchers typically take soil samples from a specific depth and bring them to the laboratory. The samples are then homogenized, sieved, and sometimes dried before analysis.
To determine the pH of the soil sample, a small amount of soil (typically 5 grams of field-moist soil) is mixed with distilled water or 0.01 M CaCl2 solution. The mixture is stirred vigorously and allowed to settle for 15–20 minutes, during which time the sand and silt particles settle out while the clays and other colloids remain suspended in the overlying water (aqueous phase). A pH electrode connected to a pH meter is calibrated with buffered solutions of known pH before being inserting into the upper portion of the aqueous phase, and the pH is measured. A combination pH electrode incorporates both the H+ sensing electrode (glass electrode) and a reference electrode that provides a pH-insensitive reference voltage and a salt bridge to the hydrogen electrode. In other configurations, the glass and reference electrodes are separate and attach to the pH meter in two ports. The pH meter measures the potential (voltage) difference between the two electrodes and converts it to pH. The separate reference electrode is usually thecalomel electrode, the silver-silver chloride electrode is used in the combination electrode.[30]
There are several uncertainties in measuring soil pH this way. Since an electrical potential difference between the glass and reference electrodes is measured, the activity of H+ is quantified, rather than concentration. The H+ activity is sometimes called the "effective H+ concentration" and is related to the chemical potential of the proton and its ability to do chemical and electrical work in the soil solution in equilibrium with the solid phases.[31] Clay and organic matter particles carry negative charge on their surfaces, and H+ ions attracted to them are in equilibrium with H+ ions in the soil solution. The measured pH is determined in the aqueous phase only, but the value obtained is affected by the presence and nature of soil colloids and the ionic strength of the aqueous phase. Changing the water-to-soil ratio in the mixture can alter the pH by disturbing the water-colloid equilibrium, particularly the ionic strength. Using 0.01 M CaCl2 obviates this effect of water-to-soil ratio and gives a more consistent approximation of soil pH that relates to plant root growth, rhizosphere and microbial activity, drainage water acidity, and chemical processes in the soil. Using 0.01 M CaCl2 brings all of the soluble ions in the aqueous phase closer to the colloidal surfaces, and allows the H+ activity to be measured closer to them. This approach is especially useful for comparing soil samples from different locations and times.
pH in nature
Lemon juice tastes sour because it contains 5% to 6%citric acid and has a pH of 2.2 (high acidity).
As part of itsoperational definition of the pH scale, theIUPAC defines a series ofbuffer solutions across a range of pH values (often denoted withNational Bureau of Standards (NBS) orNational Institute of Standards and Technology (NIST) designation). These solutions have a relatively lowionic strength (≈0.1) compared to that of seawater (≈0.7), and, as a consequence, are not recommended for use in characterizing the pH of seawater, since the ionic strength differences cause changes inelectrode potential. To resolve this problem, an alternative series of buffers based onartificial seawater was developed.[35] This new series resolves the problem of ionic strength differences between samples and the buffers, and the new pH scale is referred to as the 'total scale', often denoted as pHT. The total scale was defined using a medium containingsulfate ions. These ions experienceprotonation,H+ +SO2− 4↔ HSO− 4, such that the total scale includes the effect of bothprotons (free hydrogen ions) and hydrogen sulfate ions:
[H+]T = [H+]F + [HSO− 4]
An alternative scale, the 'free scale', often denoted 'pHF', omits this consideration and focuses solely on [H+]F, in principle making it a simpler representation of hydrogen ion concentration. Only [H+]T can be determined,[36] therefore [H+]F must be estimated using the [SO2− 4] and the stability constant ofHSO− 4,K* S:
However, it is difficult to estimate K* S in seawater, limiting the utility of the otherwise more straightforward free scale.
Another scale, known as the 'seawater scale', often denoted 'pHSWS', takes account of a further protonation relationship between hydrogen ions andfluoride ions,H+ +F− ⇌ HF. Resulting in the following expression for [H+]SWS:
[H+]SWS = [H+]F + [HSO− 4] + [HF]
However, the advantage of considering this additional complexity is dependent upon the abundance of fluoride in the medium. In seawater, for instance, sulfate ions occur at much greater concentrations (>400 times) than those of fluoride. As a consequence, for most practical purposes, the difference between the total and seawater scales is very small.
The following three equations summarize the three scales of pH:
pHF = −log [H+]F
pHT = −log([H+]F + [HSO− 4]) = −log[H+]T
pHSWS = −log(H+]F + [HSO− 4] + [HF]) = −log[v]SWS
In practical terms, the three seawater pH scales differ in their pH values up to 0.10, differences that are much larger than the accuracy of pH measurements typically required, in particular, in relation to the ocean'scarbonate system.[34] Since it omits consideration of sulfate and fluoride ions, the free scale is significantly different from both the total and seawater scales. Because of the relative unimportance of the fluoride ion, the total and seawater scales differ only very slightly.
In living organisms, the pH of variousbody fluids, cellular compartments, and organs is tightly regulated to maintain a state of acid-base balance known asacid–base homeostasis.Acidosis, defined by a pH below 7.35, is the most common disorder of acid–base homeostasis and occurs when there is an excess of acid in the body. In contrast,alkalosis is characterized by excessively high blood pH.
Blood pH is usually slightly basic, with a pH of 7.365, referred to as physiological pH in biology and medicine.Plaque formation in teeth can create a local acidic environment that results intooth decay through demineralization.Enzymes and otherproteins have an optimal pH range for function and can become inactivated ordenatured outside this range.
pH Calculations
When calculating the pH of a solution containing acids and/or bases, achemical speciation calculation is used to determine the concentration of all chemical species present in the solution. The complexity of the procedure depends on the nature of the solution. Strong acids and bases are compounds that are almost completely dissociated in water, which simplifies the calculation. However, for weak acids, aquadratic equation must be solved, and for weak bases, a cubic equation is required. In general, a set ofnon-linearsimultaneous equations must be solved.
Water itself is a weak acid and a weak base, so its dissociation must be takent into account at high pH and low solute concentration (seeamphoterism). Itdissociates according to the equilibrium
where [H+] stands for the concentration of the aqueoushydronium ion and [OH−] represents the concentration of thehydroxide ion. This equilibrium needs to be taken into account at high pH and when the solute concentration is extremely low.
Strong acids and bases
Strong acids andbases are compounds that are essentially fully dissociated in water. This means that in an acidic solution, the concentration of hydrogen ions (H+) can be considered equal to the concentration of the acid. Similarly, in a basic solution, the concentration of hydroxide ions (OH-) can be considered equal to the concentration of the base. The pH of a solution is defined as the negative logarithm of the concentration of H+, and the pOH is defined as the negative logarithm of the concentration of OH-. For example, the pH of a 0.01M solution of hydrochloric acid (HCl) is equal to 2 (pH = −log10(0.01)), while the pOH of a 0.01M solution of sodium hydroxide (NaOH) is equal to 2 (pOH = −log10(0.01)), which corresponds to a pH of about 12.
However, self-ionization of water must also be considered when concentrations of a strong acid or base is very low or high. For instance, a 5×10−8M solution of HCl would be expected to have a pH of 7.3 based on the above procedure, which is incorrect as it is acidic and should have a pH of less than 7. In such cases, the system can be treated as a mixture of the acid or base and water, which is anamphoteric substance. By accounting for the self-ionization of water, the true pH of the solution can be calculated. For example, a 5×10−8M solution of HCl would have a pH of 6.89 when treated as a mixture of HCl and water. The self-ionization equilibrium of solutions of sodium hydroxide at higher concentrations must also be considered.[40]
Weak acids and bases
Aweak acid or the conjugate acid of a weak base can be treated using the same formalism.
Acid HA:HA ⇌ H+ + A−
Base A:HA+ ⇌ H+ + A
First, an acid dissociation constant is defined as follows. Electrical charges are omitted from subsequent equations for the sake of generality
and its value is assumed to have been determined by experiment. This being so, there are three unknown concentrations, [HA], [H+] and [A−] to determine by calculation. Two additional equations are needed. One way to provide them is to apply the law ofmass conservation in terms of the two "reagents" H and A.
C stands foranalytical concentration. In some texts, one mass balance equation is replaced by an equation of charge balance. This is satisfactory for simple cases like this one, but is more difficult to apply to more complicated cases as those below. Together with the equation defining Ka, there are now three equations in three unknowns. When an acid is dissolved in water CA = CH = Ca, the concentration of the acid, so [A] = [H]. After some further algebraic manipulation an equation in the hydrogen ion concentration may be obtained.
Solution of thisquadratic equation gives the hydrogen ion concentration and hence p[H] or, more loosely, pH. This procedure is illustrated in anICE table which can also be used to calculate the pH when some additional (strong) acid or alkaline has been added to the system, that is, when CA ≠ CH.
For example, what is the pH of a 0.01M solution ofbenzoic acid, pKa = 4.19?
Step 1:
Step 2: Set up the quadratic equation.
Step 3: Solve the quadratic equation.
For alkaline solutions, an additional term is added to the mass-balance equation for hydrogen. Since the addition of hydroxide reduces the hydrogen ion concentration, and the hydroxide ion concentration is constrained by the self-ionization equilibrium to be equal to, the resulting equation is:
General method
Some systems, such as withpolyprotic acids, are amenable to spreadsheet calculations.[41] With three or more reagents or when many complexes are formed with general formulae such as ApBqHr, the following general method can be used to calculate the pH of a solution. For example, with three reagents, each equilibrium is characterized by an equilibrium constant, β.
Next, write down the mass-balance equations for each reagent:
Note that there are no approximations involved in these equations, except that each stability constant is defined as a quotient of concentrations, not activities. Much more complicated expressions are required if activities are to be used.
There are threenon-linearsimultaneous equations in the three unknowns, [A], [B] and [H]. Because the equations are non-linear and their concentrations may range over many powers of 10, the solution of these equations is not straightforward. However, many computer programs are available which can be used to perform these calculations. There may be more than three reagents. The calculation of hydrogen ion concentrations, using this approach, is a key element in thedetermination of equilibrium constants bypotentiometric titration.
^abSørensen, S. P. L. (1909)."Über die Messung und die Bedeutung der Wasserstoffionenkonzentration bei enzymatischen Prozessen"(PDF).Biochem. Z.21:131–304.Archived(PDF) from the original on 15 April 2021. Retrieved22 March 2021.Original German: Für die Zahl p schlage ich den Namen Wasserstoffionenexponent und die Schreibweise pH• vor. Unter dem Wasserstoffionexponenten (pH•) einer Lösungwird dann der Briggsche Logarithmus des reziproken Wertes des auf Wasserstoffionenbezagenen Normalitäts faktors de Lösungverstanden. Two other publications appeared in 1909, one in French and one in Danish.
^abEvans, Alice C. (1963)."Memoirs"(PDF).NIH Office of History. National Institutes of Health Office of History. Archived fromthe original(PDF) on 15 December 2017. Retrieved27 March 2018.
^Rossotti, F.J.C.; Rossotti, H. (1965). "Potentiometric titrations solution containing the background electrolyte".J. Chem. Educ.42.doi:10.1021/ed042p375.
^Mendham, J.; Denney, R. C.; Barnes, J. D.; Thomas, M. J. K. (2000),Vogel's Quantitative Chemical Analysis (6th ed.), New York: Prentice Hall,ISBN0-582-22628-7, Section 13.23, "Determination of pH"
^Himmel, Daniel; Goll, Sascha K.; Leito, Ivo; Krossing, Ingo (16 August 2010). "A Unified pH Scale for All Phases".Angewandte Chemie International Edition.49 (38):6885–6888.doi:10.1002/anie.201000252.ISSN1433-7851.PMID20715223.
^Feldman, Isaac (1956). "Use and Abuse of pH measurements".Analytical Chemistry.28 (12):1859–1866.doi:10.1021/ac60120a014.
^Mendham, J.; Denney, R. C.; Barnes, J. D.; Thomas, M. J. K. (2000),Vogel's Quantitative Chemical Analysis (6th ed.), New York: Prentice Hall,ISBN0-582-22628-7, Section 13.19 The glass electrode
^abZeebe, R. E. and Wolf-Gladrow, D. (2001)CO2 in seawater: equilibrium, kinetics, isotopes, Elsevier Science B.V., Amsterdam, NetherlandsISBN0-444-50946-1
