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Chemical thermodynamics

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From Wikipedia, the free encyclopedia

Study of chemical reactions within the laws of thermodynamics

Potassium reacting with water, producing heat, hydrogen gas, and a lilac flame. — Anexothermic reaction betweenpotassium andwater. The release ofchemical potential energy asheat andlight produces the lilacflame.

Chemical thermodynamics is the study of the interrelation ofheat andwork withchemical reactions or with physical changes ofstate within the confines of thelaws of thermodynamics. Chemical thermodynamics involves not only laboratory measurements of various thermodynamic properties, but also the application of mathematical methods to the study of chemical questions and thespontaneity of processes.

The structure of chemical thermodynamics is based on the first twolaws of thermodynamics. Starting from the first and second laws of thermodynamics, four equations called the "fundamental equations of Gibbs" can be derived. From these four, a multitude of equations, relating the thermodynamic properties of thethermodynamic system can be derived using relatively simple mathematics. This outlines the mathematical framework of chemical thermodynamics.^[1]

History

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J. Willard Gibbs - founder ofchemical thermodynamics

In 1865, the German physicistRudolf Clausius, in hisMechanical Theory of Heat, suggested that the principles ofthermochemistry, e.g. theheat evolved incombustion reactions, could be applied to the principles ofthermodynamics.^[2] Building on the work of Clausius, between the years 1873-76 the American mathematical physicistWillard Gibbs published a series of three papers, the most famous one being the paperOn the Equilibrium of Heterogeneous Substances. In these papers, Gibbs showed how the first two laws of thermodynamics could be measured graphically and mathematically to determine both thethermodynamic equilibrium of chemical reactions as well as their tendencies to occur or proceed. Gibbs' collection of papers provided the first unified body of thermodynamic theorems from the principles developed by others, such as Clausius andSadi Carnot.^{[citation needed]}

During the early 20th century, two major publications successfully applied the principles developed by Gibbs to chemical processes and thus established the foundation of the science of chemical thermodynamics. The first was the 1923 textbookThermodynamics and the Free Energy of Chemical Substances byGilbert N. Lewis andMerle Randall. This book was responsible for supplanting thechemical affinity with the termfree energy in the English-speaking world. The second was the 1933 bookModern Thermodynamics by the methods of Willard Gibbs written byE. A. Guggenheim. In this manner, Lewis, Randall, and Guggenheim are considered as the founders of modern chemical thermodynamics because of the major contribution of these two books in unifying the application ofthermodynamics tochemistry.^[1]

Overview

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The primary objective of chemical thermodynamics is the establishment of a criterion for determination of the feasibility orspontaneity of a given transformation.^[3] In this manner, chemical thermodynamics is typically used to predict theenergy exchanges that occur in the following processes:^{[citation needed]}

The followingstate functions are of primary concern in chemical thermodynamics:^{[citation needed]}

Mostidentities in chemical thermodynamics arise from application of the first and second laws of thermodynamics, particularly thelaw of conservation of energy, to these state functions.

The threelaws of thermodynamics (global, unspecific forms):

The energy of the universe is constant.
In any spontaneous process, there is always an increase in entropy of the universe.
The entropy of a perfect crystal (well ordered) at 0 Kelvin is zero.

Chemical energy

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Main article:Chemical energy

Chemical energy is the energy that can be released whenchemical substances undergo a transformation through achemical reaction. Breaking and making chemical bonds involvesenergy release or uptake, often as heat that may be either absorbed by or evolved from the chemical system.^{[citation needed]}

Energy released (or absorbed) because of a reaction between chemical substances ("reactants") is equal to the difference between the energy content of the products and the reactants. This change in energy is called the change ininternal energy of a chemical system. It can be calculated from $\Delta _{\rm {f}}U_{\mathrm {reactants} }^{\rm {o}}$ , theinternal energy of formation of the reactant molecules related to thebond energies of the molecules under consideration, and $\Delta _{\rm {f}}U_{\mathrm {products} }^{\rm {o}}$ , the internal energy of formation of the product molecules. The change in internal energy is equal to the heat change if it is measured under conditions of constant volume (at STP condition), as in a closed rigid container such as abomb calorimeter. However, at constant pressure, as in reactions in vessels open to the atmosphere, the measured heat is usually not equal to the internal energy change, because pressure-volume work also releases or absorbs energy. (The heat change at constant pressure is called theenthalpy change; in this case the widely tabulatedenthalpies of formation are used.)^{[citation needed]}

A related term is theheat of combustion, which is the chemical energy released due to acombustion reaction and of interest in the study offuels. Food is similar to hydrocarbon and carbohydrate fuels, and when it is oxidized, its energy release is similar (though assessed differently than for a hydrocarbon fuel — seefood energy).^{[citation needed]}

In chemical thermodynamics, the term used for the chemical potential energy ischemical potential, and sometimes theGibbs-Duhem equation is used.

Chemical reactions

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Main article:Chemical reaction

In most cases of interest in chemical thermodynamics there are internaldegrees of freedom and processes, such aschemical reactions andphase transitions, which createentropy in the universe unless they are at equilibrium or are maintained at a "running equilibrium" through "quasi-static" changes by being coupled to constraining devices, such aspistons orelectrodes, to deliver and receive external work. Even for homogeneous "bulk" systems, the free-energy functions depend on thecomposition, as do all theextensive thermodynamic potentials, including the internal energy. If the quantities { N_i }, the number ofchemical species, are omitted from the formulae, it is impossible to describe compositional changes.^{[citation needed]}

Gibbs function or Gibbs Energy

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For an unstructured, homogeneous "bulk" system, there are still variousextensive compositional variables { N_i } thatG depends on, which specify the composition (the amounts of eachchemical substance, expressed as the numbers of molecules present or the numbers ofmoles). Explicitly,

$G=G(T,P,\{N_{i}\})\,.$

For the case where onlyPV work is possible,

$\mathrm {d} G=-S\,\mathrm {d} T+V\,\mathrm {d} P+\sum _{i}\mu _{i}\,\mathrm {d} N_{i}\,$

a restatement of thefundamental thermodynamic relation, in whichμ_i is thechemical potential for thei-thcomponent in the system

$\mu _{i}=\left({\frac {\partial G}{\partial N_{i}}}\right)_{T,P,N_{j\neq i},etc.}\,.$

The expression for dG is especially useful at constantT andP, conditions, which are easy to achieve experimentally and which approximate the conditions inliving creatures

$(\mathrm {d} G)_{T,P}=\sum _{i}\mu _{i}\,\mathrm {d} N_{i}\,.$

Chemical affinity

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Main article:Chemical affinity

While this formulation is mathematically defensible, it is not particularly transparent since one does not simply add or remove molecules from a system. There is always aprocess involved in changing the composition; e.g., a chemical reaction (or many), or movement of molecules from one phase (liquid) to another (gas or solid). We should find a notation which does not seem to imply that the amounts of the components ( N_i ) can be changed independently. All real processes obeyconservation of mass, and in addition, conservation of the numbers ofatoms of each kind.

Consequently, we introduce an explicit variable to represent the degree of advancement of a process, a progressvariable ξ for theextent of reaction (Prigogine & Defay, p. 18; Prigogine, pp. 4–7; Guggenheim, p. 37.62), and to the use of thepartial derivative ∂G/∂ξ (in place of the widely used "ΔG", since the quantity at issue is not a finite change). The result is an understandableexpression for the dependence of dG onchemical reactions (or other processes). If there is just one reaction $(\mathrm {d} G)_{T,P}=\left({\frac {\partial G}{\partial \xi }}\right)_{T,P}\,\mathrm {d} \xi .\,$

If we introduce thestoichiometric coefficient for thei-th component in the reaction

$\nu _{i}=\partial N_{i}/\partial \xi \,$

(negative for reactants), which tells how many molecules ofi are produced or consumed, we obtain an algebraic expression for the partial derivative

$\left({\frac {\partial G}{\partial \xi }}\right)_{T,P}=\sum _{i}\mu _{i}\nu _{i}=-\mathbb {A} \,$

where we introduce a concise and historical name for this quantity, the "affinity", symbolized byA, as introduced byThéophile de Donder in 1923.(De Donder; Progogine & Defay, p. 69; Guggenheim, pp. 37, 240) The minus sign ensures that in a spontaneous change, when the change in the Gibbs free energy of the process is negative, the chemical species have a positive affinity for each other. The differential ofG takes on a simple form that displays its dependence on composition change

$(\mathrm {d} G)_{T,P}=-\mathbb {A} \,d\xi \,.$

If there are a number of chemical reactions going on simultaneously, as is usually the case,

$(\mathrm {d} G)_{T,P}=-\sum _{k}\mathbb {A} _{k}\,d\xi _{k}\,.$

with a set of reaction coordinates { ξ_j }, avoiding the notion that the amounts of the components ( N_i ) can be changed independently. The expressions above are equal to zero atthermodynamic equilibrium, while they are negative when chemical reactions proceed at a finite rate, producing entropy. This can be made even more explicit by introducing the reactionrates dξ_j/dt. For everyphysically independentprocess (Prigogine & Defay, p. 38; Prigogine, p. 24)

$\mathbb {A} \ {\dot {\xi }}\leq 0\,.$

This is a remarkable result since the chemical potentials are intensive system variables, depending only on the local molecular milieu. They cannot "know" whether temperature and pressure (or any other system variables) are going to be held constant over time. It is a purely local criterion and must hold regardless of any such constraints. Of course, it could have been obtained by taking partial derivatives of any of the other fundamental state functions, but nonetheless is a general criterion for (−T times) the entropy production from that spontaneous process; or at least any part of it that is not captured as external work. (SeeConstraints below.)

We now relax the requirement of a homogeneous "bulk" system by letting thechemical potentials and the affinity apply to any locality in which a chemical reaction (or any other process) is occurring. By accounting for theentropy production due to irreversible processes, the equality for dG is now replaced by

$\mathrm {d} G=-S\,\mathrm {d} T+V\,\mathrm {d} P-\sum _{k}\mathbb {A} _{k}\,\mathrm {d} \xi _{k}+\mathrm {\delta } W'\,$

$\mathrm {d} G_{T,P}=-\sum _{k}\mathbb {A} _{k}\,\mathrm {d} \xi _{k}+\mathrm {\delta } W'.\,$

Any decrease in theGibbs function of a system is the upper limit for anyisothermal,isobaric work that can be captured in thesurroundings, or it may simply bedissipated, appearing asT times a corresponding increase in the entropy of the system and its surrounding. Or it may go partly toward doing external work and partly toward creating entropy. The important point is that theextent of reaction for a chemical reaction may be coupled to the displacement of some external mechanical or electrical quantity in such a way that one can advance only if the other also does. The coupling may occasionally berigid, but it is often flexible and variable.

Solutions

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In solutionchemistry andbiochemistry, theGibbs free energy decrease (∂G/∂ξ, in molar units, denoted cryptically by ΔG) is commonly used as a surrogate for (−T times) the global entropy produced by spontaneouschemical reactions in situations where no work is being done; or at least no "useful" work; i.e., other than perhaps ± P dV. The assertion that allspontaneous reactions have a negative ΔG is merely a restatement of thesecond law of thermodynamics, giving it thephysical dimensions of energy and somewhat obscuring its significance in terms of entropy. When no useful work is being done, it would be less misleading to use theLegendre transforms of the entropy appropriate for constantT, or for constantT andP, the Massieu functions −F/T and −G/T, respectively.

Non-equilibrium

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Main article:non-equilibrium thermodynamics

Generally the systems treated with the conventional chemical thermodynamics are either at equilibrium or near equilibrium.Ilya Prigogine developed the thermodynamic treatment ofopen systems that are far from equilibrium. In doing so he has discovered phenomena and structures of completely new and completely unexpected types. His generalized, nonlinear and irreversible thermodynamics has found surprising applications in a wide variety of fields.

The non-equilibrium thermodynamics has been applied for explaining how ordered structures e.g. the biological systems, can develop from disorder. Even if Onsager's relations are utilized, the classical principles of equilibrium in thermodynamics still show that linear systems close to equilibrium always develop into states of disorder which are stable to perturbations and cannot explain the occurrence of ordered structures.

Prigogine called these systemsdissipative systems, because they are formed and maintained by the dissipative processes which take place because of the exchange of energy between the system and its environment and because they disappear if that exchange ceases. They may be said to live insymbiosis with their environment.

The method which Prigogine used to study the stability of the dissipative structures to perturbations is of very great general interest. It makes it possible to study the most varied problems, such as city traffic problems, the stability of insect communities, the development of ordered biological structures and the growth of cancer cells to mention but a few examples.

System constraints

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In this regard, it is crucial to understand the role of walls and otherconstraints, and the distinction betweenindependent processes andcoupling. Contrary to the clear implications of many reference sources, the previous analysis is not restricted tohomogeneous,isotropic bulk systems which can deliver onlyPdV work to the outside world, but applies even to the most structured systems. There are complex systems with many chemical "reactions" going on at the same time, some of which are really only parts of the same, overall process. Anindependent process is one thatcould proceed even if all others were unaccountably stopped in their tracks. Understanding this is perhaps a "thought experiment" inchemical kinetics, but actual examples exist.

A gas-phase reaction at constant temperature and pressure which results in an increase in the number of molecules will lead to an increase in volume. Inside a cylinder closed with a piston, it can proceed only by doing work on the piston. The extent variable for the reaction can increase only if the piston moves out, and conversely if the piston is pushed inward, the reaction is driven backwards.

Similarly, aredox reaction might occur in anelectrochemical cell with the passage ofcurrent through awire connecting theelectrodes. The half-cell reactions at theelectrodes are constrained if no current is allowed to flow. The current might be dissipated asJoule heating, or it might in turn run an electrical device like amotor doingmechanical work. Anautomobile lead-acid battery can be recharged, driving the chemical reaction backwards. In this case as well, the reaction is not an independent process. Some, perhaps most, of the Gibbs free energy of reaction may be delivered as external work.

Thehydrolysis ofATP toADP andphosphate can drive theforce-times-distance work delivered by livingmuscles, and synthesis of ATP is in turn driven by a redox chain inmitochondria andchloroplasts, which involves the transport ofions across the membranes of thesecellular organelles. The coupling of processes here, and in the previous examples, is often not complete. Gas can leak slowly past a piston, just as it can slowly leak out of arubber balloon. Some reaction may occur in a battery even if no external current is flowing. There is usually a couplingcoefficient, which may depend on relative rates, which determines what percentage of the driving free energy is turned into external work, or captured as "chemical work", a misnomer for the free energy of another chemical process.

References

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^^a ^bOtt, Bevan J.; Boerio-Goates, Juliana (2000).Chemical Thermodynamics – Principles and Applications. Academic Press.ISBN 0-12-530990-2.
^Clausius, R. (1865).The Mechanical Theory of Heat – with its Applications to the Steam Engine and to Physical Properties of Bodies. London: John van Voorst, 1 Paternoster Row. MDCCCLXVII.
^Klotz, I. (1950).Chemical Thermodynamics. New York: Prentice-Hall, Inc.

External links

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Chemical Thermodynamics - University of North Carolina
Chemical energetics (Introduction to thermodynamics and the First Law)
Thermodynamics of chemical equilibrium (Entropy, Second Law and free energy)

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