van der Waals equation (redirected from Van der Waals equation of state)

van der Waals equation: see gas laws.

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van der Waals equation [′van dər ‚wȯlz i‚kwā·zhən]

(physical chemistry)

An empirical equation of state which takes into account the finite size of the molecules and the attractive forces between them:p= [RT/(v-b)] - (a/v²), wherepis the pressure,vis the volume per mole,Tis the absolute temperature,Ris the gas constant, andaandbare constants.

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Van der Waals equation

An equation of state of gases and liquids proposed by J. D. van der Waals in 1873 that takes into account the nonzero size of molecules and the attractive forces between them. He expressed the pressure p as a function of the absolute temperature T and the molar volume V_m = V/n, where n is the number of moles of gas molecules in a volume V (see equation below).

Here R = 8.3145 J K^-1 mol^-1 is the universal gas constant, and a and b are parameters that depend on the nature of the gas. Parameter a is a measure of the strength of the attractive forces between the molecules, and b is approximately equal to four times the volume of the molecules in one mole, if those molecules can be represented as elastic spheres. The equation has no rigorous theoretical basis for real molecular systems, but is important because it was the first to take reasonable account of molecular attractions and repulsions, and to emphasize the fact that the intermolecular forces acted in the same way in both gases and liquids. It is accurate enough to account for the fact that all gases have a critical temperature T_c above which they cannot be condensed to a liquid. The expression that follows from this equation is T_c= 8a/27 Rb. See Critical phenomena, Intermolecular forces

In a gas mixture, the parameters a and b are taken to be quadratic functions of the mole fractions of the components since they are supposed to arise from the interaction of the molecules in pairs. The resulting equation for a binary mixture accounts in a qualitative but surprisingly complete way for the many kinds of gas-gas, gas-liquid, and liquid-liquid phase equilibria that have been observed in mixtures.

The equation is too simple to represent quantitatively the behavior of real gases, and so the parameters a and b cannot be determined uniquely; their values depend on the ranges of density and temperature used in their determination. For this reason, the equation now has little practical value, but it remains important for its historical interest and for the concepts that led to its derivation. See Thermodynamic principles