Question #162450

Estimate the molar volume of Argon at 100 and 100 atm by treating it is as ideal gas and a van der Waals gas. Give your conclusion based on the result. Given a/(atm dm^{6} mol^{-2}) and b/(10^{-2} dm^{3} mol^{-1}) for Argon are 1.337 and 3.20 respectively.

Expert's answer

( P + "\\frac{a}{V_m^2}" ) (V_{m }-b) = RT

(100 + "\\frac{1.337}{V_m^2}" )( V_{m }- 3.20 ) = 0.0821 × 100

(100V"_m^2" + 1.337)(V_{m }- 3.20 ) = V"_m^2" 8.21

(100V"_m^3" + 1.337V_{m } - 320 V"_m^2" - 4.2784 - 8.21 V"_m^2" ) = 0

100V"_m^3" - 311.79 V"_m^2" + 1.337V_{m }- 4.2784 = 0

V_{m = }3.118 L_{ /mol}

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