Lewis and Randall

Because it is necessary to exclude some substances, including some crystals, from the Nemst heat theorem, Lewis and Gibson (1920) introduced the concept of a perfect crystal and proposed the following modification as a definitive statement of the third law of themiodynamics (exact wording due to Lewis and Randall (1923)) ... 

With sufficient data, equation (6.47) can be integrated to give o,. However, adequate data are available for only a few mixtures, and approximate relationships are used to estimate o,. The simplest approximation uses the Lewis and Randall rule given by11... 

Note the similarity between the Lewis and Randall rule... 

Dalton s law is based on the assumption of ideal gases so that each behaves independently and exerts the same partial pressure as it would il alone in the container. The Lewis and Randall rule assumes that the fugacitv of the gases is independent so that the gas has the same fugacity coefficient as it would have at the same total pressure when other gases were not present. 

Thus, with the Lewis and Randall approximation, o, has the same value as the pure gas would have at the same temperature and total pressure. 

Lewis and Randall stated that in dilute solutions the activity coefficient of a strong electrolyte is the same in all solutions of the same ionic strength this statement was confirmed in thermodynamic deductions of activity coefficients. The molality version of 7 can be applied in a fully analogous way and allows a more straightforward treatment of solution properties. [Conversion of molality into molarity requires the solution densities e.g., for a solute of molar mass M and a solution of density q we have... 

The fugacity of species B in an ideal solution of gases is given by the Lewis and Randall rule... 

Activity coefficient vary with the concentration especially in the presence of added electrolyte. Lewis and Randall introduced the quantity called ionic strength which is a measure of the intensity of the electric field due to the ions in a solution. It is defined as the sum of the terms obtained by multiplying the molarity (concentration) of each ion present in solution by the square of its valence... 

In 1920, Bom wrote to G. N. Lewis about the reprint he had received of Lewis s 1916 paper on the "atom and the molecule." The "cubic" distribution of electrons, Born cautioned, had no general usefulness, and Lewis should look at how Born treated the problem in his new work, which he had sent Lewis. 3 Born expressed some humility about his knowledge of chemistry, confessing to Lewis a few years later, with respect to the new Lewis and Randall textbook on chemical thermodynamics, that he could not speak as well to the chemical side as to the physical side.4... 

Lewis and Randall s Thermodynamics and the Free Energy of Chemical Substances used a notation different from Continental notation, necessitating a standardization in notation by a committee set up jointly by the Faraday Society, the Chemical Society, and the Physical Society. See Slater, Introduction, v. 

Lewis and Gibson [3] also emphasized the positive entropy of solutions at 0 K and pointed out that supercooled liquids, such as glasses, even when composed of a single element (such as sulfur), probably retain a positive entropy as the temperamre approaches absolute zero. For these reasons Lewis and Randall [4] proposed the following statement of the third law of thermodynamics ... 

Lewis and Randall [3] have recalculated some of Thomsen s data on the heat absorbed when 2 moles of gaseous HCl is dissolved in lOOOg of H2O. A plot of A// as a function of 2 at constant is shown in Figure 18.5. 

In the case of ternary or higher-order mixtures, solution of the Gibbs-Duhem equation is again based on application of the properties of the exact differentials (Lewis and Randall, 1970) ... 

The solution of the problem requires integration procedures along pseudo-binary lines that result in the combination of integral forms of the type in equation 2.101. In this context it is unnecessary to proceed further with detailed treatment, for which reference may be made to Lewis and Randall (1970). 

The concept of ionic strength, which allows individual ionic activity coefficients to be estimated, was developed by Lewis and Randall (1921). The ionic strength of a solution is given by... 

The mean salt method derives implicitly from the concept of ionic strength, as expressed by Lewis and Randall (1921). It is assumed that, within the range of the ionic strength of interest, for a standard uni-univalent electrolyte such as KCl, the following assumption is valid ... 

Of particular practical interest are the general energy conversion factors (Lewis and Randall, 1970) presented in table A1.4. 

S (c, monoclinic). The heat of transformation of monoclinic to rhombic sulfur was measured by Bronsted,3 Mitscherlich,2 Tammann,2, 3 Lewis and Randall,1 Wigand,1 and Mondain-Monval.1, 4 Using Lewis and Randall s5 values for the heat capacities, we have found that Bron-sted s3 data yield, for the transformation, T=0.120— 0.0005 (i+273.1) -0.00000125 (t+273.1)2 whence, at 18°, T= -0.080, and at 95°, the normal transition temperature, T=—0.088. Mondain-Monval1,4 found T= —0.087. 

Lewis and Randall also evoke the imagery of Gibbs paper as a thermodynamic gold mine, in a section entitled The Modem Stage of Thermodynamics ... 

Nevertheless, as noted by Lewis and Randall, certain post-Gibbsian addenda appeared, which will be discussed in the present section. Some of these innovations, such as activity and fugacity (Section 5.8.1), were designed primarily to satisfy practical needs of representing experimental thermochemical data, with no deeper claims on the underlying structure of the theory. In contrast, the developments initiated by Nemst s heat theorem, culminating in what became widely known as the third law of thermodynamics, appear to call into question the structural completeness of the Gibbsian formalism. These developments will be critically discussed in Section 5.8.2. 

The most important post-Gibbsian addenda alluded to by Lewis and Randall (1923) are introduced in their section entitled The Third Law of Thermodynamics as follows ... 

Lewis and Randall (1923) If the entropy of each element in some crystalline state be taken as zero at T = 0, then every substance has a finite positive entropy but at T= 0, the entropy may be zero, and is for the case of perfect crystalline substances. 

Eventually, the rather tentative and confusing language of Lewis and Randall was replaced by the form of the third law that is quoted in nearly all textbooks today, namely... 

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