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Additional info for AB INITIO Methods in Quantum Chemistry 2 (Advances in Chemical Physics) (Vol 67)
Eq. 32) Hence, h = @ ( T exp ) [-w(o)/kT]Zna3g (36) In this expression both w(o)/kT and g are completely determined by the values of the two dimensionless parameters ze/kT and ct: the first is given by Eq. 31, while the function g cannot be expressed in analytical form but has to be evaluated by numerical integration of Eq. 35. The expression 36 for h evidently enables one to calculate the vapor pressure and energy of formation of a clathrate once the values of the two parameters have been determined.
Accordingly, a cross section through the P-T-x diagram at constant temperature below 0°C would reveal a two-phase area G+H in which the composition of the latter is less sensitive to pressure than found in the corresponding case for the hydroquinone clathrates (cf. Fig. 4). Since the composition of a hydrate is not constant the method for its determination first suggested by de Forcrand12 and improved by Scheffer and Meyer38 gives the composition in the quadruple point only. In this method, which has also been used by von Sta~kelberg,~" the heats of formation per mole of solute of the hydrate from pure gas and pure liquid water as well as from pure gas and ice are required.
35. Reamer, H . , Selleck, F. , and Sage, B. , T r a n s . Am. I n s t . M i n i n g M e t . Engrs. 195,Tech. Pub. No. 3376 (in J . Petrol. Technol. 4, No. 8, 197 (1952)). 36. Roberts, 0. , Brownscombe, E. , and Howe, L. , Oil Gas J . 39, No. 30, 37 (1940). 37. Rushbrooke, G. , Introduction to Statistical Mechanics, Clarendon Press, Oxford, 1949, pp. 277-278. 38. Scheffer, F. E. , Proc. A c a d . S c i . A m s t e r d a m 21, 1204, 1338 (1919). CLATHIWTE SOLUTIONS 57 39. , Svensk Kem. T i d s k r .