Tests of the Third Law

There are two ultimate experimental tests of the third law. The first might compare the entropies in the limit as T — 0 if of perfectly and poorly crystalline forms of the 

crystalline glycerol must be melted at T, which involves the heat of fusion AmH and the entropy change 

Finally, liquid glycerol is frozen to glass (hence no heat of fusion), and cooled from Tto to 0 K, and for this, 

The entropy change for this whole cycle A B — C — D must be identical to the direct process A - D (since S is a function of state). The experimental result is Aa-+dS = 4.6 calK mol . As expected, the glass has a higher entropy than the crystal because it is more disordered. If the Third Law is correct, and the crystal truly perfect, it will have zero entropy at 0 K, and the glass will have a residual entropy S() = 4.6 cal K mol due to frozen-in defects or randomness. 

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C. C. Stephenson and W. F. Giauque. "A Test of the Third Law of Thermodynamics by Means of Two Crystalline Forms of Phosphine. The Heat Capacity. Heat of Vaporization and Vapor Pressure of Phosphine. Entropy of the Gas". J. Chem. Phys.. 5. 149-158 (1937). 

An interesting test of the third law is possible when a solid is capable of existing in two or more modifications, i.e., enantiotropic forms, with a definite transition point. The entropy of the high temperature form (a) at some temperature above the transition point may, in some cases, be obtained in two independent ways. First, heat capacity measurements can be made on the form (/3) stable below the transition point, and the entropy at this temperature may then be determined in the usual manner. To this is then added the entropy of transition, thus giving the entropy of the o-f orm at the transition point (cf. first three lines of Table XVI). The entropy contribution of the a-form from the transition temperature to the chosen temperature is then obtained from heat capacity measurements on the o-form. The second procedure is to cool the ot-form rapidly below the transition point so that it remains in a metastable state. Its heat capacity can then be determined from very low temperatures up to temperatures above the normal transition point, and the entropy of the a-form is then obtained directly from these data. Measurements of this kind have been made with a number of substances, e.g., sulfur, tin, cyclohexanol and phosphine, and the entropies obtained by the two method have been found to be in close agreement. ... 

From the figures given in Table IV the increase of entropy during the reaction is 8.5 units. As a test of the third law of thermodynamics this value may be compared with a determination of the entropy change of this reaction made by Gerke,21 from the potentials of galvanic cells, in a research already referred to. He measured the potential, E, and the change of the potential with temperature, AE/AT, of cells of the type... 

The second common example, depicted in Figure 6.7b, is less obvious, but really a better test of the Third Law. Here we wish to know if there really is no entropy... 

If water or some other compound with a simple molecular structure has been studied, it is possible to combine the entropy of vaporization, A5 = AHyl T, with the third-law calorimetric entropy of the liquid to obtain a thermodynamic value for the entropy of the vapor. The statistical mechanical value of Sg can be calculated using the known molar mass and the spectroscopic parameters for the rotation and vibration of the gas-phase molecule. A comparison of Sg (thermodynamic) with Sg (spectroscopic) provides a test of the validity of the third law of thermodynamics. The case of H2O is particularly interesting, since ice has a nonzero residual entropy at 0 K due to frozen-in disorder in the proton positions. ... 

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. 

Rhombic sulphur transforms to monoclinic sulphur at 95.5°C (368.5 K) with an enthalpy change of 96 cal/mole (401.7 j/mol). Test the validity of the third law of thermodynamics for this transition from the following data ... 

Lord Kelvin s close associate, the expert experimentalist J. P. Joule, set about to test the former s theoretical relationship and in 1859 published an extensive paper on the thermoelastic properties of various solids—metals, woods of different kinds, and, most prominent of all, natural rubber. In the half century between Gough and Joule not only was a suitable theoretical formula made available through establishment of the second law of thermodynamics, but as a result of the discovery of vulcanization (Goodyear, 1839) Joule had at his disposal a more perfectly elastic substance, vulcanized rubber, and most of his experiments were carried out on samples which had been vulcanized. He confirmed Gough s first two observations but contested the third. On stretching vulcanized rubber to twice its initial length. Joule ob-... 

Since the publication of the third edition, additional data have been critically reviewed. New or additional data included in this edition are bioconcentration factors, aquatic mammalian toxicity values, degradation rates, corresponding half-lives in various environmental compartments, ionization potentials, aqueous solubility of miscellaneous compounds, Henry s law constants, biological, chemical, and theoretical oxygen demand values for various organic compounds. Five additional tables have been added Test Method Number Index, Dielectric Values of Earth Materials and Fluids, Lowest Odor Threshold Concentrations of Organic Compoimds in Water, and Lowest Threshold Concentrations of Organic Compounds in Water. 

Another procedure for testing the third law of thermodynamics is to combine heat content with entropy data for a given reaction, and so to determine the free energy change, the value of which is known from direct measurement. The standard free energy change for the formation of silver oxide, i.e., for the reaction 2Ag(s) + = Ag20(s), can be derived from... 

Furthermore, in many cases the effect of the third component, namely the solvent, is decisive. For example, the measured Henry s law constant for the system aromatic substance-HCl, only reflects the difference between the chemical potential of HCl in solution, and in the vapour phase, p% (Kortiim and Vogel, 1955). The values obtained therefore do not permit a quantitative interpretation and only give qualitatively the relative order of the basicity of unsaturated compounds. This is also true for partition measurements between an acid and an organic phase, if in such a case the necessary thermodynamic assumptions have not been tested or established by separate investigations. 

This was first demonstrated ia 1862 by Berthelot and Saint-Gibes (32), who found that when equivalent quantities of ethyl alcohol and acetic acid were abowed to react, the esterification stopped when two-thirds of the acid had reacted. Sinularly, when equal molar proportions of ethyl acetate and water were heated together, hydrolysis of the ester stopped when about one-third of the ester was hydroly2ed. By varyiag the molar ratios of alcohol to acid, yields of ester >66% were obtained by displacement of the equbibrium. The results of these tests were ia accordance with the mass action law shown ia equation 5. 

Then if any two phases are separately in equilibrium with a third phase, they are also in equilibrium when placed in contact, so that if any one phase (e.y., the vapour) is taken as a test-phase, and the other phases are separately in equilibrium with this, the whole system will be in equilibrium. Under the conditions imposed, it is sufficient that the vapour pressure, or osmotic pressure, of each component has the same value at all the interfaces, for we may consider each component separately by intruding across the interface a diaphragm permeable to that compo- -nent alone. Then if the vapour, or osmotic pressures, are not equal at the third interface to their values at the first and second interfaces, i.e., at the interfaces on the test-phase, we could carry out a reversible isothermal cycle in which any quantity of a specified component is taken from the test-phase to the phase of higher pressure, then across the interface to the phase of lower pressure, and then back to the test-phase. In this cycle, work would be obtained, which however is impossible. Hence the two phases which are separately in equilibrium with the test-phase are also in equilibrium with each other. This may be called the Law of the Mutual Compatibility of Phases (cf. 106). 

An interesting, but controversial, article on the analysis of equilibrium data has appeared (94). The establishment of true equilibrium is tested by concordance between enthalpies derived from second and third law treatments. 

Critical Assessment of Third Law Statements Each statement of the purported third law may be critically tested in terms of three criteria ... 

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