annual review
BRUCE CASWELL JOE M. SMITH
Thermodynamics Constant development of new products by the chemical indust? is reflected in the continuing increase in thermodynamic datu available us well as new uppyoaches to attainment of same hermodynamics, based as it is on the unchanging a firm standard in a rapidly expanding technology. The concept of equilibrium still offers the basis of comparison for rate processes. Hence, there is a continual need for compositions of phases in equilibrium, compositions of reaction mixtures in equilibrium, and equilibrium thermal properties. As new products are discovered and processes are designed to produce them, thermodynamic data for the new materials are measured and reported. The type of information does not change, but the materials do. This is why there seems to be a constant or even slowly increasing number of papers on the same subjects each year. Nevertheless, emphasis shifts from time to time, as it now has to an increasing emphasis on multicomponent systems, and as it did a few years ago to inorganic substances reflecting the needs of the space industries to develop materials stable at extreme temperatures. As in the previous review ( 7 I A ) , the present summary i s not exhaustive. The references were selected for their interest to chemical engineers and chemists.
Tand second laws, is
Books and Special Topics
Highly controlled atmosfiheres permit Drs. John Stringer and Raymond Dodds of Battelle to study the energetics and mechanisms of tantalum oxidation. The apfiaratus, shown here, functions in the ranges ,5001000’ C., and oxygen partial presmres of 100-760 torr
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INDUSTRIAL A N D E N G I N E E R I N G CHEMISTRY
A survey of the thermal data on light elements was the subject of a meeting in December 1963. Papers were presented and are now published (7A) on thermodynamic properties including heats of formation and reaction on boron, beryllium, and fluorine compounds, and on refractory materials. Of the books published recently, two of interest to chemical engineering are Van Kess’s (72A) book, “The Classical Thermodynamics of Non-Electrolyte Solutions,” and Hill’s (8A) two-part work “The Thermodynamics of Small Systems.” The Van Ness book treats the classical thermodynainics of solutions in a concise and clearly written manner, and should be of
Equations of State
great use to both research workers and students, although it contains no problems. Hill’s work, which was overlooked in the previous review, introduces an entirely new branch of thermodynamics. Small systems are those which lie somewhere between the macroscopic world and the world of individual molecules. Those interested in the fields of colloidal particles, polymers and macromolecules, nucleation phenomena associated with drops, bubbles, and crystals should find this new branch of thermodynamics most interesting. This is primarily a work on thermodynamics and not statistical mechanics, although some acquaintance with the latter area will be helpful to the reader. Because of its generality, thermodynamics occasionally gives rise to controversies over interpretation of its laws. The polemical letters dealing with these matters are interesting and not infrequently amusing. The possibility of negative degrees of freedom among coexisting phases has been put forth by Halliwell and Nyburg ( 7 A ) . The specific system is a binary mixture with two liquid phases, two solid phases, and a vapor: five phases and 1 degrees of freedom. To have this situation, it is necessary for the triple points of the substances to be close enough so that when placed in the same vessel their limited miscibility will bring the triple points into exact coincidence. A “near miss” example is mercury (m.p. = 38.9’ C.) and diethylaniline (m.p. = 38.8’ (2.). Brynestad ( Z A ) , however, has denied the possibility of such negative degrees of freedom. A long polemic on the proof of the Onsager reciprocal relations continues, and Duda and Vrentas (5A) published the latest contribution. Several years ago Sliepcevich and Finn (70A) proposed a proof of the celebrated Onsager relations based only on macroscopic considerations. The attacks which followed have tried to establish that this proof is vacuous or, at best, highly restricted. I t would appear that a truly macroscopic proof of the Onsager relations will require an as yet undiscovered new principle of continuum physics. That such a principle will prove elusive is indicated by the known special cases, such as that dealt with by Hill and Plesner (QA), where reciprocal relations do not hold. A solidly based approach to continuum thermodynamics is provided by Coleman (3A, 4A) and Green ( 6 4 ) .
Advances in thermodynamics are clearly dependent on the development of suitable equations of state. This applies especially to the liquid state. During the past year, Flory (4B)has obtained a three-parameter equation for liquid normal paraffins by treating them as hard sphere, repulsive linear segments. While the model was originally intended for linear polymers, it presents reasonable agreement with experiment for hexane. The model has been generalized to nonpolar mixtures without hydrogen bonding (70H). Because of its simplicity, the hard sphere model continues to receive considerable attention in theoretical studies of the liquid state. The properties of binary mixtures of hard spheres have been computed from the radial distribution function by Lebowitz and Rowlinson (7B). No separation into two liquid phases is predicted. Yosim and Owens (73B) have shown that the hard sphere theory of fused salts gives good agreement with experiment. The LennardJones and Devonshire quantum cell model has been applied to liquid hydrogen (QB). By treating the volume elements of a gas as particles in a continuum force field, Erdos (3B) has rederived the virial equation of state. The force field is that derived from the intermolecular potential. A new statistical mechanical study of the critical region has been given by Zhil’kov (14B). Panchenkov suggested (8B) that the equation of state for a pure liquid should be of the form f(P-V-T, 7) = 0 where y is the coordination number. This idea is not new; however, it has never gained much favor because of the difficulty of determining y. Elgeti (2B) has treated water vapor as a van der Waals gas in which complexes are formed and, by choosing appropriate values of 7,has obtained good agreement with experimental P-V-T data over a wide range. The most serious objection to this concept lies in the assumptions, such as Elgeti’s, which are necessary to determine y from experimental data. The older established equations continue to find application in a wide variety of situations : the virial ( I B ) , Strobridge (6B),Benedict-WebbRubin (IOB), and Redlich-Kwong (72B). Gyorog and Obert (5B) have presented a generalized correlation for the virial coefficients of pure gases. The limitations of two-parameter equations of state have long been understood in terms of molecular concepts. For this reason, those interested in improved generalized correlations have sought a third parameter, and the only major disagreement between various workers would appear to lie in the choice of this third parameter. Viswanath and Su ( 7 7B) have overlooked these rather basic facts and presented yet another twoparameter generalized compressibility chart. Their correlation naturally shows a marginal improvement of The Lydersen-Greenkorn-Hougen correlation for 2, = 0.27, and this is the justification for the new work. Anyone using generalized correlations accepts inherent limitations on the accuracy to be expected. If he uses the Lydersen-Greenkorn-Hougen correlation for Z, = 0.27, an answer is obtained which can be improved, if necessary, with the aid of the third parameter 2,. VOL. 5 7
NO.
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DECEMBER 1 9 6 5
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TABLE I.
P-V-T DATA Propel lies and Conditions
System IlzO-methyl cellosolve; ethyl cellosolve; ethylene glycoldioxane n-Hexane, n-heptane, n-octane Biphenyl, G-, m-terphenyl KC1-KPiO s H z O trans-%Butene CCL. CCla, CHa, CCh(CHs)z, CCI(CHa)s, C(CHa)a Ethane-n-heptane-n-pentane Ethylene Binaries of CoHs, CCla, CSz, p - , m- o-xylene, toluene dioxane, t e h i n in cyclohexane Hz0 Benzoic acid-toluene Sea ice p-Hz
P-V-T, critical region B, 20" to 60' C. u,
I34 c
P-V-T critical region t' (liq.), l 2 j 0 to 240° C. C u, -26'to - l o C.C u , critical region u = specifc or
VAPOR PRESSURE AND HEATS OF PHASE CHANGE
AH,, (371' to 451' K . ) P,, AHv (
