RESEARCH

Thermo Yields Better P-V-T Figures Improved correlation from theory of corresponding states gives development engineers more data for their money

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Improved corresponding states correlation relates organics of widely differing structures to each other. With it, you can calculate thermodynamic properties of many new chemicals from molecular structure plus one density measurement

A o DEVELOP manufacturing processes, chemical engineers must have sonic idea of the thermodynamic properties of the chemicals they will be handling. They can measure these properties or-more cheaply—they can calculate them. Now, Arnold Bondi of Shell Develop­ment, Emeryville, Calif., has come up with an improved calculation based on the long-standing theory of correspond­ing states ( two substances at the same reduced pressure and reduced tempera­ture will be at the same reduced volume ).

Thermodynamic calculations are, at best, educated guesses based on some correlation which has proved to be true to some extent for known chemicals and is assumed to be true for t h e chemical in question. Such guesses can easily be inaccurate.

With his correlation, you need only one density measurement and the moleoular structure of the new com­pound t o calculate the thermodynamic properties you need, Mr. Bondi says. And the calculations hold within \c/c for a host of structurally-different hydro­carbons, b" adds.

Mr. Hondi's correlation does away with measurements of critical volume, pressure, and temperature—a plus, be­cause these properties are difficult, if not impossible, to measure for hydro­carbons of higher molecular weight than C12. THe correction replaces the criti­cal volume with the so-called van der Waals v/olume ( Vw )—calculated from x-ray diffraction data—and replaces the critical temperature with the "standard energy of vaporization" (E°)— calcu­lated from vapor pressure data.

The beauty of these two parameters is that they can be calculated from the molecular structure, Mr. Bondi told the American Institute of Chemical Engi­neers, meeting in St. Paul, Minn. Each constituent group in a molecule has a van der Waals volume and a standard energy of vaporization associated with it. Mr. Bondi has calculated these values for most common organic groups, using x-iay data and vapor pressure-temperature data on known compounds. To get Vw and E° for the new com­pound, you merely add up the values for each group within the molecule.

Once you have calculated Vw and E° for the new compound, you can plot reduced density (p* = V w / V ) against temperature between the melting point and the atmospheric pressure boiling point. From this, you can get curves for surface tension, for heat capacity difference between liquid and vapor phases, and for internal pressure, all as functions of p*. And from internal pressure, you can calculate P-V-T properties at high pressures and at tem­peratures from the melting point to close to the boiling point at atmospheric pressure. Result: almost complete ther­modynamic identification of the new compound from only one density measurement.

Mr. Bondi has shown that this cor­relation is valid for liquid hydrocarbons from Cxo to C(}4 and for some poly­ethylene, polypropylene, and polysty­rene melts. It holds reasonably well for mildly polar compounds such as ethers, but it does not apply to polar materials such as alcohols.

And he has noted one other interest­ing feature: For 100 of the 124 com­pounds he has put through this correla­tion, the critical reduced density comes out to be 0.19 i t 0.01. This, he says, corresponds to the packing density you would expect for a continuous network with a coordination number of three.

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