The pH scale is logarithmic and inversely indicates theactivity ofhydrogen ions in the solution
where [H+] is theequilibriummolar concentration of H+ (in M = mol/L) in the solution. At 25 °C (77 °F), solutions of which the pH is less than 7 are acidic, and solutions of which the pH is greater than 7 are basic. Solutions with a pH of 7 at 25 °C 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 range is commonly given as zero to 14, but a pH value can be less than 0 for very concentratedstrong acids or greater than 14 for very concentratedstrong bases.[2]
In 1909, theDanish chemistSøren Peter Lauritz Sørensen introduced the concept of pH at theCarlsberg Laboratory,[4] 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.[4]
Sørensen did not explain why he used the letter p, and the exact meaning of the letter is still disputed.[5][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 were the languages in which Sørensen published: Carlsberg Laboratory was French-speaking; German was the dominant language of scientific publishing; 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 with e4 then e5.[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, creditedWilliam 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]
The pH of a solution is defined as the decimallogarithm of the reciprocal of thehydrogen ionactivity,aH+.[3] Mathematically, pH is expressed as:
For example, for a solution with a hydrogen ion activity of5×10−6mol/L (i.e., the concentration of hydrogen ions), 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 themolar gas constant,T is the thermodynamic temperature,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:[15] 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 (H+) activity proposed by the International Union of Pure and Applied Chemistry (IUPAC).[3] 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.[16] 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.
This was the original definition of Sørensen in 1909,[18] which was superseded in favor of pH in 1924. [H] is the concentration of hydrogen ions, denoted [H+] in modern chemistry. More correctly, thethermodynamic activity ofH+ in dilute solution should be replaced by [H+]/c0, where the standard state concentrationc0 = 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.[19] 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.[20] However, it is common practice to use the term "pH" for both types of measurement.
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−. By definition, pOH is the negative logarithm (to the base 10) of the hydroxide ion concentration (mol/L). pOH values can be derived from pH measurements and vice-versa. 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. AUniversal 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 a 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.
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[21][22] as:
whereμH+ is thechemical potential of the hydrogen ion, is its chemical potential in the chosen standard state,R is themolar gas 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 insolvent scale that involves the transfer activity coefficient ofhydronium/lyonium ion.
In 2010, a new approach to measuring pH was proposed, called theunified 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 applies to liquids, gases, and even solids.[23] The advantages of the unified absolute pH scale include consistency, accuracy, and applicability to a wide range of sample types. It is precise and versatile because it serves as a common reference standard for pH measurements. However, implementation efforts, compatibility with existing data, complexity, and potential costs are some challenges.
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 (above ca. 0.0003 mol/dm3 alkaline). This is due to the breakdown of theNernst equation in such conditions when using a glass electrode. Several factors contribute to this problem. First,liquid junction potentials may not be independent of pH.[24] Second, 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.[25] To overcome these problems, specially constructed electrodes are available.
Runoff from mines or mine tailings can produce some extremely low pH values, down to −3.6.[26]
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.
Neutrality is not exactly 7 at 25 °C, but 7 serves as 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+] × [OH−] =Kw, it can be seen that at neutrality [H+] = [OH−] =√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, soKw 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).
Topsoil pH is influenced by soil parent material, erosional effects, climate and vegetation. A recent map[28] 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.
The pH ofseawater plays an important role in the ocean'scarbon cycle. There is evidence of ongoingocean acidification (meaning a drop in pH value): Between 1950 and 2020, the average pH of the ocean surface fell from approximately 8.15 to 8.05.[29]Carbon dioxide emissions from human activities are the primary cause of ocean acidification, withatmospheric carbon dioxide (CO2) levels exceeding 410 ppm (in 2020). CO2 from theatmosphere is absorbed by the oceans. This producescarbonic acid (H2CO3) which dissociates into abicarbonate ion (HCO− 3) and ahydrogen ion (H+). The presence of free hydrogen ions (H+) lowers the pH of the ocean.
The measurement of pH in seawater is complicated by thechemical properties of seawater, and three distinct pH scales exist inchemical oceanography.[30] 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.[30] Since it omits consideration of sulfate and fluoride ions, thefree 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.
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.[31] This new series resolves the problem of ionic strength differences between samples and the buffers, and the new pH scale is referred to as thetotal 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, thefree 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,[32] therefore [H+]F must be estimated using the [SO2− 4] and the stability constant ofHSO− 4,K* S:
However, it is difficult to estimateK* S in seawater, limiting the utility of the otherwise more straightforward free scale.
Another scale, known as theseawater 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:
The pH level of food influences its flavor, texture, andshelf life.[33] Acidic foods, such ascitrus fruits, tomatoes, andvinegar, typically have a pH below 4.6[34] with sharp and tangy taste, while basic foods taste bitter or soapy.[35] Maintaining the appropriate pH in foods is essential for preventing the growth of harmfulmicroorganisms.[34] The alkalinity of vegetables such asspinach andkale can also influence their texture and color during cooking.[36] The pH also influences theMaillard reaction, which is responsible for the browning of food during cooking, impacting both flavor and appearance.[37]
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 blood 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 alkaline, 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.
When calculating the pH of a solution containing acids 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 taken 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 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 0.01 inmoles per litreM solution of hydrochloric acid (HCl) is equal to 2 (pH = −log10(0.01)), while the pOH of a 0.01 M 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, a5×10−8 M 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, a5×10−8 M 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.[43]
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 definingKa, there are now three equations in three unknowns. When an acid is dissolved in waterCA =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, whenCA ≠CH.
For example, what is the pH of a 0.01 M 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:
Some systems, such as withpolyprotic acids, are amenable to spreadsheet calculations.[44] 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:
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 threesimultaneous 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
^Akdas, Zelal; Bakkalbasi, Emre (2017). "Influence of different cooking methods on color, bioactive compounds, and antioxidant activity of kale".International Journal of Food Properties.20 (4):877–887.doi:10.1080/10942912.2016.1188308.
