Question

According to the ideal gas law, a 10.08 mol sample of krypton gas in a 0.8488 L container at 496.7 K should exert a pressure of 484.0 atm. By what percent does the pressure calculated using the van der Waals' equation differ from the ideal pressure? For Kr gas, a = 2.318 L²atm/mol² and b = 3.978×10^-2 L/mol.

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Hint: % difference = 100 × (P _ideal - P_{van der Waals}) / P _ideal

Answer 1

PV = nRT

P = nRT/V

     = 10.08*0.0821*496.7/0.8488   = 484atm

(P+an^2/V^2)(v-nb) = nRT

(P + 2.318*(10.08)^2/(0.8488)^2)(0.8488-10.08*0.03978) = 10.08*0.0821*496

(p + 326.9)(0.4478)= 410.4737

(P+326.9)                 = 916.64

P                                = 916.64-326.9 = 589.74

   P = 589.74atm

% difference = 100 × (P _VAN- P_IDEAL) / P _VAN

                            = 100*(589.74-484)/589.74 = 17.92%