Branched-chain organic compounds. Part 11: Validation of a new method for determination of the potential energy of cohesion of an organic crystal and deduction of the heat capacity of the vapour

Abstract

The cohesion energy of ethyl 3-cyano-3-(3,4-dimethyloxyphenyl)-2,2,4-trimethylpentanoate, as obtained from the change of kinetic and potential energies in the heat of sublimation of the crystal, E _p,coh = −46.7 kJ mol⁻¹ (78.6 °C), has been validated. A safe physicomathematic test based on the balance of entropy for the sublimation and Planck’s equation for changes of state, extended to entropy, was devised to ascertain the kinetic energies of the crystal and the gas molecule. Entropic equations were developed for the phase equilibrium to find precisely and with simplicity the vibrational energy of the crystal by using the vapour pressure exclusively and independently from the internal rotational and vibrational motion of the gas molecule. The heat capacity of the vapour was determined in this way, which in this case releases the solid allowing vibrational movement in the gas phase to meet the pressure of sublimation, C _p (T)/J K⁻¹ mol⁻¹ = 1.268 T/K + 58.62 (71.1–86.1 °C). An independent variational method of deducing the vibrational entropy, energy, or heat capacity of the gas molecule from each other was compared with the equations and was shown to yield the quantities with high accuracy. Values of the Nernst–Lindemann functions are tabulated.

Graphical abstract