Exceptions to the Third Law

The Third Law requires that a perfectly crystalline solid of a pure material be present at 0 Kelvin for So to equal zero. Exceptions to the Third Law occur when this is not the case. For example, AgCl(s) and AgBr(s) mix to form a 

JThis calculation is one of the most satisfying in science. The values of the thermodynamic properties of the ideal gas calculated from molecular parameters are usually more accurate than the same thermodynamic results obtained from experimental measurements. 

They used electrochemical cell measurements to determine AmixGm, and solution calorimetric measurements to determine Am x//m. The results they obtained at T = 298.15 K are AmjXGm = 1060 J-mol 1 and Amjx//m = 340 J mol 1. 

From these results AmjXSm for the mixing process can be calculated. To do so, we start with equation (4.16), 

The conclusion is that AmjxSm =4.66 J K I mol 1 for the solution process at 0 Kelvin. If one assumes that the entropies of the AgBr and AgCl are zero at 0 Kelvin, then the solid solution must retain an amount of entropy that will give this entropy of mixing. 

---

Each listed type of randomization (orientional, hydrogen-bonding network, nuclear spin statistics, isotopes, impurities, defects, and others that could be cited) makes independent contributions to S0 0. Hence, it seems safe to conclude that no macroscopic sample of real substance that ever appeared on Earth satisfies S0 = 0, i.e., that every real substance represents an imperfect exception to the third law as commonly stated. 

Sometimes molecules get frozen in to other states so that the perfect crystal state, the true equilibrium state, is not attained at low temperatures. Then So as measured is not zero. Such cases are often, but misleadingly, called exceptions to the Third Law . Thus a number of substances form glassy solids which remain apparently stable at low temperatures despite the fact that the crystalline state is the one of lowest free energy. This is because it would take an extremely long time, at low temperatures, for the molecules of the glass to rearrange themselves to the pattern required for crystallization. 

Finally, we should point out that, while the exceptions to the Third Law noted above may be a headache for scientists who measiue calorimetric properties of materials, they pose no practical problems in most chemical applications. Chemical reactions alone do not change nuclear spin, and in many cases do not alter isotope ratios significantly, so that configurational contributions to the entropy of reactants are normally balanced by those of the products in a reaction. In most cases these effects are thermodynamically minor or insignificant. 

The third law of thermodynamics lacks the generality of the other laws, since it applies only to a special class of substances, namely pure, crystalline substances, and not to all substances. In spite of this restriction the third law is extremely useful. The reasons for exceptions to the law can be better understood after we have discussed the statistical interpretation of the entropy the entire matter of exceptions to the third law will be deferred until then. 

The validity of the third law is tested by comparing the change in entropy of a reaction computed from the third-law entropies with the entropy change computed from equilibrium measurements. Discrepancies appear whenever one of the substances in the reaction does not follow the third law. A few of these exceptions to the third law were described in Section 9.17. 

Experience indicates that the Third Law of Thermodynamics not only predicts that So — 0, but produces a potential to drive a substance to zero entropy at 0 Kelvin. Cooling a gas causes it to successively become more ordered. Phase changes to liquid and solid increase the order. Cooling through equilibrium solid phase transitions invariably results in evolution of heat and a decrease in entropy. A number of solids are disordered at higher temperatures, but the disorder decreases with cooling until perfect order is obtained. Exceptions are... 

An exceptional case of a very different type is provided by helium [15], for which the third law is valid despite the fact that He remains a liquid at 0 K. A phase diagram for helium is shown in Figure 11.5. In this case, in contrast to other substances, the solid-liquid equilibrium line at high pressures does not continue downward at low pressures until it meets the hquid-vapor pressure curve to intersect at a triple point. Rather, the sohd-hquid equilibrium line takes an unusual turn toward the horizontal as the temperature drops to near 2 K. This change is caused by a surprising... 

The third law of thermodynamics says that the entropy of pure, perfect crystalline substance is zero at absolute zero. But, in actual practice, it has been found that certain chemical reactions between crystalline substance, do not have DS = 0 at 0°K, which indicates that exceptions to third law exist. Such exceptional reactions involve either ice, CO, N2O or H2. It means that in the crystalline state these substances do not have some definite value of entropy even at absolute zero. This entropy is known as Residual Entropy. At 0°K the residual entropies of some crystalline substances are... 

Over the years, many experiments have been carried out which confirm the third law. The experiments have generally been of two types. In one type the change of entropy for a change of phase of a pure substance or for a standard change of state for a chemical reaction has been determined from equilibrium measurements and compared with the value determined from the absolute entropies of the substances based on the third law. In the other type the absolute entropy of a substance in the state of an ideal gas at a given temperature and pressure has been calculated on the basis of statistical mechanics and compared with those based on the third law. Except for well-known, specific cases the agreement has been within the experimental error. The specific cases have been explained on the basis of statistical mechanics or further experiments. Such studies have led to a further understanding of the third law as it is applied to chemical systems. 

It is of importance to note that, except for hydrogen and deuterium molecules, the entropy derived from heat capacity measurements, i.e., the thermal entropy, as it is frequently called, is equivalent to the practical entropy in other words, the nuclear spin contribution is not included in the former. The reason for this is that, down to the lowest temperatures at which measurements have been made, the nuclear spin does not affect the experimental values of the heat capacity used in the determination of entropy by the procedure based on the third law of thermodynamics ( 23b). Presumably if heat capacities could be measured right down to the absolute zero, a temperature would be reached at which the nuclear spin energy began to change and thus made a contribution to the heat capacity. The entropy derived from such data would presumably include the nuclear spin contribution of R In (2i + 1) for each atom. Special circumstances arise with molecular hydrogen and deuterium to which reference will be made below ( 24n). 

The entropy crisis described in the preceding paragraph is the result of an extrapolation. With the exception of He and " He (Wilks, 1967)," there is no known substance for which a Kauzmann temperature is actually reached. Nevertheless, the extrapolation needed to provoke a conflict with the Third Law is indeed modest for many substances (Angell, 1997), and what intervenes to thwart the imminent crisis is a kinetic phenomenon, the laboratory glass transition. This suggests a connection between the kinetics and... 

However, as new approaches or new theories are developed, the solution of problems insoluble within the framework of traditional concepts is accompanied by appearance of new problems and enigmas. This approach is not an exception. In particular, the mechanism of the transfer of the condensation energy of the low-volatility product to the reactant and the effect of the S3mi-metry of the reactant crystal-lattice on the composition of the gaseous decomposition products remain unclear. To solve these problems on the basis of the new mechanistic and kinetic concepts discussed in this book, it would be appropriate to use the experience accumulated in solid-state physical chemistry and in crystal chemistry. The systematic differences between the enthalpies measured by the third-law method and those measured by the second-law and Arrhenius plot methods undoubtedly deserves a more thorough study. This problem is especially important for successful application to reactions involving the formation of solid products. 

We cannot measure the absolute internal energy U or enthalpy H because the zero of energy is arbitrary. As a result, we are usually only interested in determining changes in these properties (At/ and A.H) during a process. However, it is possible to determine the absolute entropy of a substance. This is because of the third law of thermodynamics, which states that the entropy of a pure substance in its thermodynamically most stable form is zero at the absolute zero of temperature, independent of pressure. For the vast majority of substances, the thermodynamically most stable form at 0 K is a perfect crystal. An important exception is helium, which remains liquid, due to its large quantum zero-point motion, at 0 K for pressures below about 10 bar. 

The Asubkf°(298, HI law) values are characterized by a fairly large spread (see Table 32). A pairwise comparison of the AsubPf°(298, III law) and Asubff°(298, n law) values showed that the enthalpy of sublimation foimd by the second law was, as a rule, smaller than that calculated by the third law. This was evidence of the occurrence of side decomposition reactions. An exception to this finding are calculations from the estimated temperature dependence of vapor pressure above the melting point (Polyachenok, 1972). The value 315.0 3.0 kJ/mol recommended by Chervonnyi and Chervonnaya (2004e) is the mean of the AsubPf° (298, in law) values. 

---