Entropy change of chemical reactions

However, using entropy as a criterion of whether a biochemical process can occur spontaneously is difficult, as the entropy changes of chemical reactions are not readily measured, and the entropy change of both the system and its surroundings must be known. These difficulties are overcome by using a different thermodynamic function, free energy (G), proposed by Josiah Willard Gibbs which combines the first and second laws of thermodynamics ... 

Using the procedure of Eq. (7), the entropy change of chemical reaction (2) can be written as... 

The third law of thermodynamics was first stated by Nernst For certain isothermal chemical reactions between solids, the entropy changes approach zero as the thermodynamic temperature approaches zero. Nernst based this statement on his analysis of experimental data obtained by T. W. Richards, who studied the entropy changes of chemical reactions between solids as the temperature was made lower and lower. The statement of Nernst was sometimes called Nernst s heat theorem, although it is a statement of experimental fact and not a mathematical theorem. 

Entropy Changes of Chemical Reactions at Various Temperatures... 

As mentioned earlier, there are some substances such as carbon monoxide that do not obey the third law of thermodynamics in their ordinary forms. The absolute entropy of these substances determined by an integration such as in Eq. (3.5-1) turned out to be too small to agree with values inferred from entropy changes of chemical reactions and absolute entropies of other substances. Carbon monoxide molecules have only a small dipole moment (small partial charges at the ends of the molecule) and the two ends of the molecule are nearly the same size, so a carbon monoxide molecule fits into the crystal lattice almost as well with its ends reversed as in its equilibrium position. Metastable crystals can easily form with part of the molecules in the reversed position. If we assume that the occurrence of reversed molecules is independent of the rest of the state of the crystal, we can write... 

Tabulated entropy changes of formation could be used to calculate entropy changes of chemical reactions instead of absolute entropies. 

The third law of thermodynamics asserts that if the entropies of all samples of pure perfect crystalline elements are taken as zero, the entropies of all samples of pure perfect crystalline compounds can also consistently be taken as zero. Entropies relative to the entropy at zero temperature are called absolute entropies. The values of these absolute entropies can be used to calculate entropy changes of chemical reactions. 

There is no correspondingly direct way of measuring the entropy changes of chemical reactions. There is no experimental device like a calorimeter that provides such information. However, if for some reaction A + B C + Dwe can measure the equilibrium constant (by measuring the concentrations of aU four species at equilibrium), then from Eq. 12.15 we can compute Ag° for the reaction, at some known temperature T. If we have the enthalpy data to compute Ah° for the reaction, then we can compute... 

When a chemical reaction is proceeding, it is, by definition, not at equilibrium and thus not reversible. Thus, entropy changes in chemical reactions cannot be obtained from heat effects in calorimetric experiments. Entropy changes can be obtained by studying chemical equilibrium (Chapter 7) or by opposing the tendency of the reaction to proceed with an applied electric potential (Chapter 10). 

First we will consider the entropy changes accompanying chemical reactions that occur under conditions of constant temperature and pressure. As for the other types of processes we have considered, the entropy changes in the surroundings are determined by the heat flow that occurs as the reaction takes place. However, the entropy changes in the system (the reactants and products of the reaction) can be predicted by considering the change in positional probability. 

Tabulated standard molar entropies are used to calculate entropy changes in chemical reactions at 25°C and 1 atm, just as standard enthalpies of formation are combined to obtain enthalpies of reaction according to Hess s law (see Section 12.3). 

The third law of thermodynamics states that the entropy of any pure substance in equilibrium approaches zero at the absolute zero of temperature. Consequently, the entropy of every pure substance has a fixed value at each temperature and pressure, which can be calculated by starting with the low-temperature values and adding the results of all phase transitions that occur at intervening temperatures. This leads to tabulations of standard molar entropy S° at 298.15 K and 1 atm pressure, which can be used to calculate entropy changes for chemical reactions in which the reactants and products are in these standard states. 

Describe measurements of absolute entropy, and calculate standard-state entropy changes for chemical reactions (Section 13.6, Problems 23-30). 

Unlike enthalpies for which values at absolute zero are important, hard to measure, and must be tabulated carefully, entropies of most pure compounds can be taken to be zero at absolute zero. Tabulations of entropy are thus simpler than tables of enthalpies, and finding entropy changes for chemical reactions from tables is often more precise than finding the comparable enthalpy change because there is no comparable law for enthalpies. 

Thus the absolute entropies of elements and compounds can be. established. These can be used to determine the entropy changes accompanying chemical reactions. 

We can extend these observations about the entropy changes of a pure substance to provide some generalizations about the expected entropy changes for chemical reactions. In general, the entropy is expected to increase for processes in which... 

Our treatment of engines will suggest a new state function, called entropy. Using its initial definition as a start, we will derive some equations that allow us to calculate the entropy changes for various processes. After considering a different way of defining entropy, we will state the third law of thermodynamics, which makes entropy a unique state function in thermodynamics. Finally, we will consider entropy changes for chemical reactions. 

About 150 years ago, many scientists thought that all chemical reactions gave off heat to the surroundings. They thought that all chemical reactions were exothermic. We now know this not true. Many chemical reactions and processes are endothermic. Enthalpy changes alone cannot help us predict whether or not a reaction will occur. If we want to predict this, we need to consider the entropy change of the reaction. 

Transient, or time-resolved, techniques measure tire response of a substance after a rapid perturbation. A swift kick can be provided by any means tliat suddenly moves tire system away from equilibrium—a change in reactant concentration, for instance, or tire photodissociation of a chemical bond. Kinetic properties such as rate constants and amplitudes of chemical reactions or transfonnations of physical state taking place in a material are tlien detennined by measuring tire time course of relaxation to some, possibly new, equilibrium state. Detennining how tire kinetic rate constants vary witli temperature can further yield infonnation about tire tliennodynamic properties (activation entlialpies and entropies) of transition states, tire exceedingly ephemeral species tliat he between reactants, intennediates and products in a chemical reaction. 

Chemistry can be divided (somewhat arbitrarily) into the study of structures, equilibria, and rates. Chemical structure is ultimately described by the methods of quantum mechanics equilibrium phenomena are studied by statistical mechanics and thermodynamics and the study of rates constitutes the subject of kinetics. Kinetics can be subdivided into physical kinetics, dealing with physical phenomena such as diffusion and viscosity, and chemical kinetics, which deals with the rates of chemical reactions (including both covalent and noncovalent bond changes). Students of thermodynamics learn that quantities such as changes in enthalpy and entropy depend only upon the initial and hnal states of a system consequently thermodynamics cannot yield any information about intervening states of the system. It is precisely these intermediate states that constitute the subject matter of chemical kinetics. A thorough study of any chemical reaction must therefore include structural, equilibrium, and kinetic investigations. 

The entropy of any chemical substance increases as temperature increases. These changes in entropy as a function of temperature can be calculated, but the techniques require calculus. Fortunately, temperature affects the entropies of reactants and products similarly. The absolute entropy of every substance increases with temperature, but the entropy of the reactants often changes with temperature by almost the same amount as the entropy of the products. This means that the temperature effect on the entropy change for a reaction is usually small enough that we can consider A Sj-eaction he independent of temperature. 

So knowing the states of the reactants and products in a chemical reaction should allow us to predict whether the reaction is accompanied by an increase or a decrease in entropy. Consider, for example, the reaction 2Na(s) + Cl fg) -> 2NaCl(s). We know that the entropies of solids are very much smaller than the entropies of gases and, because this reaction results in a decrease in the number of moles of gaseous molecules (from 1 to 0), the entropy will decrease. Similarly, we would predict an increase in entropy for the reaction CaCOjfs) -> CaO(s) + CO g) because there is an increase in the number of moles of gaseous molecules (from 0 to if However, the entropy change for the reaction CaSiOjfs) CaO(s) + SiO s) is difficult to predict because the reactants and products are solids and are likely to have very similar entropy values. All we can say is that the entropy change is likely to be small. 

The free energy of a substance, like its enthalpy and entropy, depends on temperature, pressure, the physical state of the substance (solid, liquid, or gas), and its concentration (in the case of solutions). As a result, free-energy changes for chemical reactions must be compared under a well-defined set of standard-state conditions ... 

One such process that we could consider is the chemical reaction A + B —> C + D, with ( = , the extent of the reaction, which will be introduced in Chapter 7. Equation (3) then indicates that the entropy change of every... 

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