Second Virial Coefficients and the Forces Between Complex Molecules

Abstract

The second virial coefficients of ethane, propane, n-butane, n-heptane, ammonia, methyl chloride, and the freons are computed from available experimental data. The causes for sizeable errors in second virial coefficients are considered. At temperatures above the critical, the second virial agrees with the theorem of corresponding states. Below the critical temperature, molecules with dipoles have unusually large virials and the values of their reduced dipole moment, μ/(TcVc)½, determine the discrepancy. The data for isomeric hydrocarbons show that the second virial is not sensitive to the shape of the molecule. This makes it impossible to determine the exact laws of intermolecular interaction from the temperature variation of the second virial. The imperfections of a gas are considered to arise from the presence of double molecules which exist for the duration of a collision. The equilibrium constant for the formation of double molecules is related to the second virial and its temperature variation gives the entropy ΔS and the energy ΔE of their formation. These may be interpreted qualitatively in terms of the intermolecular forces. The second virial coefficient for all substances fits the equation: B(T) = ba(1 — c exp (—ΔE/RT)) where ba, c, and ΔE are taken as constants. Here bac=exp (ΔS/R). A corresponding states equation is given for estimating second virials when no experimental data are available.

Proton Transfer in the K-Channel Analog of B-Type Cytochrome c Oxidase from Thermus thermophilus

“…Whereas entropy is only indirectly accessible by the conformational variability, enthalpy relies on the interplay between kinetic and potential energies. Based on the second viral theorem (27), the average kinetic energy is proportional to the number of degrees of freedom of the molecular system and therefore does not change in a proton transfer process.…”

Second virial cross coefficients for (ammonia + water) derived from gas phase excess enthalpy measurements

“…(19) The best of these data (20)(21)(22) and some more recent measurements (23,24) are well fitted by •, table 1. The curve through the measurements was calculated from the association model described in Section 6.…”

Dimerization Degree of Water Molecules, Their Effective Polarizability, and Heat Capacity of Saturated Water Vapor

“…Автори використовують рiзнi методи для дослiдження: 1) визначення концентрацiї ди-мерiв d за допомогою другого вiрiального коефiцi-єнта [10][11][12]; 2) прямий розрахунок [13][14][15], що ви-магає знання коливальних i обертальних спектрiв збуджень димерiв; 3) визначення концентрацiї за допомогою дослiдження теплопровiдностi водяної пари. На жаль, результати суттєво вiдрiзняються один вiд одного.…”

“…Ми розгляне-мо 1) специфiку нормальних координат для диме-ра води; 2) тепловi коливання дипольного момен-ту димера; 3) внесок теплових збуджень у вiль-ну енергiю; 4) узагальнення int ( ) для ансамблю мономерiв та димерiв та 5) їх спiльний вплив на поведiнку ефективної поляризовностi молекули та теплоємностi водяної пари. Ми також детально порiвняємо температурну залежнiсть концентрацiї димерiв, отриману в [10][11][12][13][14].…”