Calculus can be used to derive a relation between the critical constants and the van der Waals parameters of a gas. The critical point of a van der Waals gas occurs where the isotherm has a flat inflexion, which is where dp/dVm = 0 (zero slope) and d2p/dVm2 = 0 (zero curvature). (a) Derive expressionsfor these first and second derivatives by differentiating the van derWaals equation of state. Hence find expressions for the critical constants in terms of the van derWaals parameters. (b) Show that the value of the compression factor at the critical point is (3)/(8) . (c) The values of the van der Waals parameters of nitrogen dioxide, N02, are a = 5.354 dm6 bar mol-1 and b= 0.04424 dm3 mol-1. Calculate the values of the criticalconstants and confirm that the compression factor does indeedhave a value of (3)/(8) at the critical point.
Calculus can be used to derive a relation between the critical constants and the van der Waals parameters of a gas. The critical point of a van der Waals gas occurs where the isotherm has a flat inflexion, which is where dp/dVm = 0 (zero slope) and d2p/dVm2 = 0 (zero curvature). (a) Derive expressions
for these first and second derivatives by differentiating the van derWaals equation of state. Hence find expressions for the critical constants in terms of the van derWaals parameters. (b) Show that the value of the compression factor at the critical point is (3)/(8) . (c) The values of the van der Waals parameters of nitrogen dioxide, N02, are a = 5.354 dm6 bar mol-1 and b= 0.04424 dm3 mol-1. Calculate the values of the critical
constants and confirm that the compression factor does indeed
have a value of (3)/(8) at the critical point.
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