The van der Waals equation is given as:
[tex](P+a(\frac{n}{V})^{^{2}})(V-nb) = nRT[/tex] -(1)
where, P is pressure, T is temperature, V is volume, R is universal gas constant, n is number of moles, and a and b are van der Waals constant.
Given values are:
Volume, V = 0.470 L
Number of moles, n = 1 mol
Temperature, T = 295 K
van der Waals constant, a = [tex]1.355 bar dm^{6}mol^{-2}[/tex] and b = [tex]0.320 dm^{3}mol^{-1}[/tex]
Substituting the values in equation (1):
[tex](P+1.355(\frac{1}{0.470})^{^{2}})(0.470-1\times 0.0320) = 1\times 0.08314\times 295[/tex]
[tex]P = \frac{1\times 0.08314\times 295}{(0.470-1\times 0.0320)} - 1.355(\frac{1}{0.470})^{^{2}}[/tex]
[tex]P = 49.682 atm[/tex]
Hence, the pressure exerted by [tex]Ar[/tex] using the van der Waals equation is [tex]49.682 atm[/tex].
