[Single-digit Integer] The van der Waal's constants a and b for a gas of molar mass 164.2 g/mol are 4.105 atm-L^2/mol^2 and 0.1 L/mol, respectively. The density (in kg/m^3) of the gas at 2 atm and 500

Question

[Single-digit Integer] The van der Waal's constants a and b for a gas of molar mass 164.2 g/mol are 4.105 atm-L^2/mol^2 and 0.1 L/mol, respectively. The density (in kg/m^3) of the gas at 2 atm and 500 K is

Prashant Kotian · Accepted Answer

Correct answer: 8. Using the van der Waals equation: (P + a/Vm^2)(Vm - b) = RT. Substituting the given values: (2 + 4.105/Vm^2)(Vm - 0.1) = 0.0821 × 500 = 41.05. Solving this cubic equation for Vm yields Vm ≈ 20.6 L/mol. Density d = M / Vm = 164.2 g/mol / 20.6 L/mol = 7.97 g/L = 7.97 kg/m^3 ≈ 8 kg/m^3. Thus, the integer answer is 0008.

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