Question

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 dm⁶ mol^-2) and b/(10^-2 dm³ mol^-1) for Argon are 1.337 and 3.20 respectively.

Answer 1

( 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