Entropy absolute value

The chemical potential, plays a vital role in both phase and chemical reaction equiUbria. However, the chemical potential exhibits certain unfortunate characteristics which discourage its use in the solution of practical problems. The Gibbs energy, and hence is defined in relation to the internal energy and entropy, both primitive quantities for which absolute values are unknown. Moreover, p approaches negative infinity when either P or x approaches 2ero. While these characteristics do not preclude the use of chemical potentials, the appHcation of equiUbrium criteria is faciUtated by the introduction of a new quantity to take the place of p but which does not exhibit its less desirable characteristics. 

The problem which the classical thermodynamics leaves over for consideration, the solution of which would be a completion of that system, is therefore the question as to the possibility of fixing the absolute values of the energy and entropy of a system of bodies. 

With the entropy, however, the case is quite otherwise, and we shall now go on to show that as soon as we are in possession of a method of determining the absolute value of the entropy of a system, all the lacunae of the classical thermodynamics can be completed. The required information is furnished by a hypothesis put forward in 1906 by W. Nernst, and usually called by German writers das Nernstsche Wdrmetheorem. We can refer to it without ambiguity as Nernsfs Theorem. ... 

The integral does not furnish the absolute value of, the entropy, because the lower limit is undetermined. If this is regarded as fixed, the integral with various upper limits gives the values of the entropies referred to this arbitrary standard state, and the differences between these values and any one of them referred to this arbitrary standard state will be the values of the entropies referred to the new standard state (cf. 42). 

A note on good practice Avoid the error of setting the standard entropies of elements equal to zero, as you would for AH° the entropies to use are the absolute values for the given temperature and are zero only at T = 0. 

This is an expression of Nernst s postulate which may be stated as the entropy change in a reaction at absolute zero is zero. The above relationships were established on the basis of measurements on reactions involving completely ordered crystalline substances only. Extending Nernst s result, Planck stated that the entropy, S0, of any perfectly ordered crystalline substance at absolute zero should be zero. This is the statement of the third law of thermodynamics. The third law, therefore, provides a means of calculating the absolute value of the entropy of a substance at any temperature. The statement of the third law is confined to pure crystalline solids simply because it has been observed that entropies of solutions and supercooled liquids do not approach a value of zero on being cooled. 

The fact that the water molecules forming the hydration sheath have limited mobility, i.e. that the solution is to certain degree ordered, results in lower values of the ionic entropies. In special cases, the ionic entropy can be measured (e.g. from the dependence of the standard potential on the temperature for electrodes of the second kind). Otherwise, the heat of solution is the measurable quantity. Knowledge of the lattice energy then permits calculation of the heat of hydration. For a saturated solution, the heat of solution is equal to the product of the temperature and the entropy of solution, from which the entropy of the salt in the solution can be found. However, the absolute value of the entropy of the crystal must be obtained from the dependence of its thermal capacity on the temperature down to very low temperatures. The value of the entropy of the salt can then yield the overall hydration number. It is, however, difficult to separate the contributions of the cation and of the anion. 

More accurately, we can determine free energy and entropy differences, since their absolute value remains unspecified. 

The absolute value of the entropy of a compound is obtained directly by integration of the heat capacity from 0 K. The main contributions to the heat capacity and thus to the entropy are discussed in this chapter. Microscopic descriptions of the heat capacity of solids, liquids and gases range from simple classical approaches to complex lattice dynamical treatments. The relatively simple models that have been around for some time will be described in some detail. These models are, because of their simplicity, very useful for estimating heat capacities and for relating the heat capacity to the physical and chemical... 

As was the case with energy, the definition of entropy permits only a calculation of differences, not an absolute value. Integration of Equation (6.48) provides an expression for the finite difference in entropy between two states ... 

Figure 7. Comparison between the absolute value of the electron correlation = Exact and the von Neumann entropy (S) as a function of the internuclear distance R for the H2 molecule using two Gaussian basis sets STO-3G and 3-21G.

Absolute values lor the enthalpies and entropies of hydration of ions were discussed in terms of their sizes and chai ses. 

The absolute values of the intermolecular change of the internal energy and entropy associated with the volume dilation may be written as... 

In D/8 T)P is always negative and its absolute value nearly always exceeds unity. Hence AHd is nearly always negative and dissociation therefore, more often than not, exothermic. The entropy term arises solely from changes in the degree of physical solvation. It does not account for the fact that one particle, the ion pair, dissociates into two free ions. Formation of two species from one increases the entropy of the system by an extra term A S, whose value is determined mainly by the greater translational freedom of the two free ions relative to the ion pair. Thus A Gd is given by the modified equation... 

For comparison, % vs 1/T curves for the same NIPA network with some alcohols as solvents [19] are also shown in Fig. 4, and the values of Ah and As determined are included in Table 1. It is seen that these quantities are all negative for the systems studied, and that the absolute values of these quantities in NIPA-water system are far larger than those in other systems. In fact, Ah in NIPA-water system is much larger than kBT, which explains the strong temperature dependence of the volume in this gel. Similarly, T As is much larger than kBT, which drives the transition to the phase with larger entropy as temperature rises. 

So far, we have been able to calculate only changes in the entropy of a substance. Can we determine the absolute value of the entropy of a substance We have seen that it is not possible to determine absolute values of the enthalpy. However, entropy is a measure of disorder, and it is possible to imagine a perfectly orderly state of matter with no disorder at all, corresponding to zero entropy an absolute zero of entropy. This idea is summarized by the third law of thermodynamics ... 

Values of AG°f at 25°C for some common substances are listed in Table 17.3, and additional values are given in Appendix B. Note that AG°f for an element in its most stable form at 25°C is defined to be zero. Thus, solid graphite has AG°f = 0 kj/mol, but diamond, a less stable form of solid carbon at 25°C, has AG°f = 2.9kJ/mol. As with standard enthalpies of formation, AH°f, a zero value of AG°f for elements in their most stable form establishes a thermochemical "sea level," or reference point, with respect to which the standard free energies of other substances are measured. We can t measure the absolute value of a substance s free energy (as we can the entropy), but that s not a problem because we are interested only in free-energy differences between reactants and products. 

---