An analytical equation of state based on the statistical-mechanical perturbation theory has been applied to calculate the liquid density and the vapour-pressure curve for long-chain n-alkane systems from C_(9) up to C_(20). The equation of state consists of three temperature-dependent parameters: the second virial coefficient, a constant for scaling the softness of repulsive forces, and an effective hard-sphere diameter equivalent to the van der Waals covolume. The second virial coefficients of these n-alkanes are scarce and there is no accurate potential energy function to allow their theoretical calculation. In this work, the second virial coefficients have been calculated by using two corresponding-states correlations—one based on the critical constants and another based on the heat of vaporisation and liquid density at the freezing point. The other two temperature-dependent parameters of the equation of state can be calculated by using a scaling rule. The resulting equation of state derived from the critical constants is more accurate than that based on the heat of vaporisation for the prediction of the saturated liquid densities, but is less accurate in the compressed state.
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