Modified van der Waals equation for liquids

Abstract

The van der Waals equation is modified for application to the liquid state by (a) using the conventional Hildebrand term for the internal pressure; (b) introducing an interaction constant B to describe external kinetic degrees of freedom; (c) introducing a quantity β₀ for the residual compressibility of the molecules themselves. At high volumes β₀ can be neglected and the proposed form of the van der Waals equation reduced to β_T/α=(V—b₀)/BR, where b₀ is the molar volume at 0°K. Good linearity is observed when β_T/α is plotted against volume for simple liquids; the number of “apparent degrees of freedom” 3B is for argon 4, for nitrogen 5.3, oxygen 5.8 and methane 6.5. Values of b₀ are extrapolated from the same plots and reasonable values are obtained. For straight chain hydrocarbons with r carbon atoms, 3B=(r+5) and the above equation predict the internal pressure successfully. At low volumes, and pressures of 0–10,000 atm, polyatomic liquids may be treated successfully if (β₀) is taken into account, and values of β₀ may be estimated. The moduli 1/β₀for methanol, diethyl ether, n-octane and acetone are 1–2 × 10¹¹dynes/cm².