Thermodynamics Can Be Used to Determine All of the Following Except

Study of chemical reactions within the laws of thermodynamics

Chemical thermodynamics is the study of the interrelation of heat and work with chemical reactions or with physical changes of land within the confines of the laws of thermodynamics. Chemic thermodynamics involves not just laboratory measurements of various thermodynamic properties, merely also the application of mathematical methods to the study of chemical questions and the spontaneity of processes.

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

History [edit]

In 1865, the German language physicist Rudolf Clausius, in his Mechanical Theory of Heat, suggested that the principles of thermochemistry, e.m. the heat evolved in combustion reactions, could exist applied to the principles of thermodynamics.^[2] Building on the work of Clausius, between the years 1873-76 the American mathematical physicist Willard Gibbs published a serial of iii papers, the most famous one being the paper On 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 the thermodynamic equilibrium of chemical reactions as well as their tendencies to occur or continue. Gibbs' collection of papers provided the start unified torso of thermodynamic theorems from the principles adult by others, such as Clausius and Sadi Carnot.

During the early 20th century, 2 major publications successfully applied the principles adult past Gibbs to chemic processes and thus established the foundation of the scientific discipline of chemical thermodynamics. The first was the 1923 textbook Thermodynamics and the Complimentary Energy of Chemical Substances past Gilbert N. Lewis and Merle Randall. This volume was responsible for supplanting the chemical affinity with the term complimentary energy in the English language-speaking earth. The second was the 1933 volume Modernistic Thermodynamics past the methods of Willard Gibbs written by E. A. Guggenheim. In this way, Lewis, Randall, and Guggenheim are considered equally the founders of modernistic chemical thermodynamics because of the major contribution of these two books in unifying the awarding of thermodynamics to chemistry.^[one]

Overview [edit]

The main objective of chemical thermodynamics is the establishment of a benchmark for determination of the feasibility or spontaneity of a given transformation.^[iii] In this manner, chemical thermodynamics is typically used to predict the energy exchanges that occur in the following processes:

1. Chemical reactions
2. Phase changes
3. The germination of solutions

The post-obit state functions are of primary concern in chemical thermodynamics:

• Internal energy (U)
• Enthalpy (H)
• Entropy (Southward)
• Gibbs gratis free energy (G)

Most identities in chemic thermodynamics arise from awarding of the first and second laws of thermodynamics, peculiarly the police of conservation of energy, to these state functions.

The 3 laws of thermodynamics (global, unspecific forms):

ane. The energy of the universe is constant.

two. In any spontaneous process, at that place is ever an increment in entropy of the universe.

3. The entropy of a perfect crystal (well ordered) at 0 Kelvin is nada.

Chemical energy [edit]

Chemical energy is the energy released when chemic substances undergo a transformation through a chemic reaction. Breaking and re-making of chemical bonds involves energy release or uptake,^[four] frequently as oestrus that may be either captivated or evolved from the chemic arrangement.

Energy released (or captivated) because of a reaction betwixt chemic substances ("reactants") is equal to the departure between the energy content of the products and the reactants. This change in energy is called the change in internal free energy of a chemical system. It could be calculated from ${\displaystyle \Delta _{\rm {f}}U_{\mathrm {reactants} }^{\rm {o}}}$ , the internal energy of formation of the reactant molecules related to the bond energies of the molecules under consideration,^[4] and ${\displaystyle \Delta _{\rm {f}}U_{\mathrm {products} }^{\rm {o}}}$ , the internal energy of formation of the production molecules. The change in internal energy is equal to the heat change if it is measured under weather of constant volume (at STP condition), equally in a closed rigid container such as a bomb calorimeter. However, at constant pressure level, as in reactions in vessels open to the atmosphere, the measured estrus is commonly not equal to the internal energy change, because pressure-volume work likewise releases or absorbs energy. (The heat alter at constant pressure is called the enthalpy alter; in this instance the widely tabulated enthalpies of germination are used.)

A related term is the heat of combustion, which is the energy (mostly of O_two ^[iv]) released due to a combustion reaction and of interest in the report of fuels. Nutrient is similar to hydrocarbon and carbohydrate fuels, and when information technology is oxidized, its energy release is like (though assessed differently than for a hydrocarbon fuel — see nutrient energy).

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

Chemical reactions [edit]

In nigh cases of interest in chemical thermodynamics there are internal degrees of freedom and processes, such as chemical reactions and stage transitions, which create entropy 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 equally pistons or electrodes, to deliver and receive external work. Fifty-fifty for homogeneous "bulk" systems, the free-free energy functions depend on the composition, every bit do all the extensive thermodynamic potentials, including the internal free energy. If the quantities {N _i  }, the number of chemical species, are omitted from the formulae, it is impossible to depict compositional changes.

Gibbs function or Gibbs Energy [edit]

For an unstructured, homogeneous "majority" system, there are still various all-encompassing compositional variables {N _i  } that G depends on, which specify the composition (the amounts of each chemical substance, expressed as the numbers of molecules present or the numbers of moles). Explicitly,

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

For the case where only PV piece of work is possible,

${\displaystyle \mathrm {d} G=-S\,\mathrm {d} T+5\,\mathrm {d} P+\sum _{i}\mu _{i}\,\mathrm {d} N_{i}\,}$

a restatement of the cardinal thermodynamic relation, in which μ_i is the chemical potential for the i-th component in the arrangement

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

The expression for dG is especially useful at constant T and P, atmospheric condition, which are easy to achieve experimentally and which approximate the weather condition in living creatures

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

Chemical affinity [edit]

While this formulation is mathematically defensible, information technology is non particularly transparent since i does not simply add or remove molecules from a system. At that place is always a process involved in changing the limerick; e.one thousand., a chemical reaction (or many), or movement of molecules from one stage (liquid) to another (gas or solid). We should find a notation which does not seem to imply that the amounts of the components (North _i  ) can be changed independently. All existent processes obey conservation of mass, and in addition, conservation of the numbers of atoms of each kind.

Consequently, we introduce an explicit variable to represent the degree of advancement of a process, a progress variableξ for the extent of reaction (Prigogine & Defay, p. eighteen; Prigogine, pp. 4–7; Guggenheim, p. 37.62), and to the apply of the partial derivative ∂1000/∂ξ (in place of the widely used "ΔG", since the quantity at effect is not a finite alter). The result is an understandable expression for the dependence of dG on chemical reactions (or other processes). If there is merely one reaction

${\displaystyle (\mathrm {d} G)_{T,P}=\left({\frac {\partial G}{\fractional \xi }}\right)_{T,P}\,\mathrm {d} \xi .\,}$

If we innovate the stoichiometric coefficient for the i-th component in the reaction

${\displaystyle \nu _{i}=\partial N_{i}/\fractional \11 \,}$

(negative for reactants), which tells how many molecules of i are produced or consumed, nosotros obtain an algebraic expression for the fractional derivative

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

where nosotros introduce a concise and historical name for this quantity, the "affinity", symbolized past A, as introduced by Théophile 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 accept a positive analogousness for each other. The differential of Yard takes on a simple class that displays its dependence on limerick change

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

If there are a number of chemical reactions going on simultaneously, as is ordinarily the example,

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

with a fix 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 at thermodynamic equilibrium, while they are negative when chemical reactions proceed at a finite rate, producing entropy. This tin be fabricated fifty-fifty more explicit past introducing the reaction rates dξ _j /dt. For every physically independent process (Prigogine & Defay, p. 38; Prigogine, p. 24)

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

This is a remarkable issue since the chemic potentials are intensive system variables, depending only on the local molecular milieu. They cannot "know" whether temperature and pressure (or whatsoever other system variables) are going to exist held abiding over fourth dimension. It is a purely local criterion and must agree regardless of any such constraints. Of form, it could have been obtained past taking partial derivatives of any of the other fundamental state functions, but still is a full general criterion for (−T times) the entropy product from that spontaneous process; or at to the lowest degree whatsoever part of it that is not captured as external work. (Meet Constraints below.)

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

${\displaystyle \mathrm {d} G=-S\,\mathrm {d} T+Five\,\mathrm {d} P-\sum _{m}\mathbb {A} _{grand}\,\mathrm {d} \xi _{thousand}+\mathrm {\delta } West'\,}$

or

${\displaystyle \mathrm {d} G_{T,P}=-\sum _{thousand}\mathbb {A} _{k}\,\mathrm {d} \11 _{k}+\mathrm {\delta } W'.\,}$

Any subtract in the Gibbs function of a system is the upper limit for any isothermal, isobaric piece of work that tin be captured in the surroundings, or it may simply be dissipated, appearing as T times a corresponding increase in the entropy of the system and its surrounding. Or information technology may go partly toward doing external work and partly toward creating entropy. The important point is that the extent of reaction for a chemical reaction may be coupled to the displacement of some external mechanical or electric quantity in such a way that one can advance only if the other also does. The coupling may occasionally be rigid, but information technology is often flexible and variable.

Solutions [edit]

In solution chemistry and biochemistry, the Gibbs costless free energy decrease (∂G/∂ξ, in molar units, denoted cryptically by ΔM) is commonly used as a surrogate for (−T times) the global entropy produced by spontaneous chemic reactions in situations where no work is being washed; or at to the lowest degree no "useful" piece of work; i.eastward., other than mayhap ±P d5. The assertion that all spontaneous reactions have a negative ΔGis merely a restatement of the second law of thermodynamics, giving it the physical dimensions of energy and somewhat obscuring its significance in terms of entropy. When no useful work is beingness washed, information technology would be less misleading to use the Legendre transforms of the entropy advisable for abiding T, or for abiding T and P, the Massieu functions −F/T and −K/T, respectively.

Not-equilibrium [edit]

Generally the systems treated with the conventional chemic thermodynamics are either at equilibrium or well-nigh equilibrium. Ilya Prigogine adult the thermodynamic treatment of open systems that are far from equilibrium. In doing and so he has discovered phenomena and structures of completely new and completely unexpected types. His generalized, nonlinear and irreversible thermodynamics has institute surprising applications in a wide variety of fields.

The non-equilibrium thermodynamics has been applied for explaining how ordered structures e.grand. the biological systems, tin can develop from disorder. Fifty-fifty if Onsager'southward relations are utilized, the classical principles of equilibrium in thermodynamics yet show that linear systems close to equilibrium always develop into states of disorder which are stable to perturbations and cannot explicate the occurrence of ordered structures.

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

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

Organisation constraints [edit]

In this regard, it is crucial to understand the function of walls and other constraints, and the distinction between independent processes and coupling. Contrary to the clear implications of many reference sources, the previous assay is not restricted to homogeneous, isotropic bulk systems which tin evangelize only Pd5 work to the exterior globe, just applies fifty-fifty to the near structured systems. At that place 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. An contained process is one that could keep even if all others were unaccountably stopped in their tracks. Understanding this is mayhap a "thought experiment" in chemical kinetics, but actual examples exist.

A gas-phase reaction at abiding temperature and force per unit area which results in an increase in the number of molecules volition lead to an increase in volume. Inside a cylinder closed with a piston, information technology tin can continue only by doing work on the piston. The extent variable for the reaction tin can increment merely if the piston moves out, and conversely if the piston is pushed inward, the reaction is driven backwards.

Similarly, a redox reaction might occur in an electrochemical cell with the passage of current through a wire connecting the electrodes. The one-half-jail cell reactions at the electrodes are constrained if no current is allowed to menstruation. The current might be dissipated as Joule heating, or it might in plough run an electrical device similar a motor doing mechanical piece of work. An automobile lead-acrid battery tin can be recharged, driving the chemical reaction backwards. In this example likewise, the reaction is non an independent process. Some, maybe most, of the Gibbs complimentary energy of reaction may be delivered as external work.

The hydrolysis of ATP to ADP and phosphate can drive the force-times-distance work delivered by living muscles, and synthesis of ATP is in plow driven past a redox concatenation in mitochondria and chloroplasts (powered by O₂ ^[4] and light, respectively) which involves the transport of ions across the membranes of these cellular organelles. The coupling of processes here, and in the previous examples, is often non consummate. Gas can leak slowly past a piston, only every bit it can slowly leak out of a rubber balloon. Some reaction may occur in a battery even if no external current is flowing. There is usually a coupling coefficient, which may depend on relative rates, which determines what percentage of the driving free free energy is turned into external work, or captured as "chemical work", a misnomer for the free energy of another chemic process.

See also [edit]

• Thermodynamic databases for pure substances

References [edit]

1. ^ ^{a b} Ott, Bevan J.; Boerio-Goates, Juliana (2000). Chemical Thermodynamics – Principles and Applications. Academic Press. ISBN0-12-530990-ii.
2. ^ Clausius, R. (1865). The Mechanical Theory of Oestrus – with its Applications to the Steam Engine and to Physical Backdrop of Bodies. London: John van Voorst, 1 Paternoster Row. MDCCCLXVII.
3. ^ Klotz, I. (1950). Chemic Thermodynamics. New York: Prentice-Hall, Inc.
4. ^ ^{a b c d} Schmidt-Rohr, K. (2015). "Why Combustions Are Always Exothermic, Yielding Nearly 418 kJ per Mole of O_ii", J. Chem. Educ. 92: 2094-2099. http://dx.doi.org/10.1021/acs.jchemed.5b00333

Further reading [edit]

• Herbert B. Callen (1960). Thermodynamics . Wiley & Sons. The clearest account of the logical foundations of the field of study. ISBN0-471-13035-4. Library of Congress Itemize No. 60-5597
• Ilya Prigogine & R. Defay, translated by D.H. Everett; Chapter IV (1954). Chemical Thermodynamics. Longmans, Green & Co. Uncommonly clear on the logical foundations equally practical to chemistry; includes non-equilibrium thermodynamics. {{cite book}}: CS1 maint: multiple names: authors list (link)
• Ilya Prigogine (1967). Thermodynamics of Irreversible Processes, tertiary ed. Interscience: John Wiley & Sons. A elementary, concise monograph explaining all the basic ideas. Library of Congress Catalog No. 67-29540
• E.A. Guggenheim (1967). Thermodynamics: An Advanced Treatment for Chemists and Physicists, fifth ed. North The netherlands; John Wiley & Sons (Interscience). A remarkably astute treatise. Library of Congress Catalog No. 67-20003
• Th. De Donder (1922). "L'affinite. Applications aux gaz parfaits". Bulletin de la Classe des Sciences, Académie Royale de Belgique. Serial five. 8: 197–205.
• Thursday. De Donder (1922). "Sur le theoreme de Nernst". Bulletin de la Classe des Sciences, Académie Royale de Belgique. Serial 5. viii: 205–210.

External links [edit]

• Chemic Thermodynamics - University of Due north Carolina
• Chemical energetics (Introduction to thermodynamics and the First Police force)
• Thermodynamics of chemic equilibrium (Entropy, Second Law and gratuitous energy)

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Source: https://en.wikipedia.org/wiki/Chemical_thermodynamics

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