Question

The compression actor(compressibility factor) for 1 mole of avander Waals' gas at $0^{\circ }C$ and 100 atmosphere pressure is found to' be 0.5. Assuming: that the volume of gas molecule is negligible, calculate the vander Waals constant a.

• A. $1.253Litr{e}^{2}mol{e}^{2}atm$
• B. $7.5L^{2}mo{l}^{-2}atm$
• C. $8.6mo{l}^{-2}atm$
• D. $5.5mo{l}^{-2}atm$

Answer 1

The correct option is A $1.253Litr{e}^{2}mol{e}^{2}atm$

Compression factor $Z=\frac{PV}{nRT}=0.5\Rightarrow V=\frac{0.5nRT}{P}$

When volume is negligible Vander waal's equation $P=\frac{n^{2}a}{V^2}=\frac{n^{2}a}{(0.5nRT/P{)}^2}=\frac{a{P}^2}{0.25R^2{T}^2}$

$a=\frac{0.25R^2{T}^2}{P}=\frac{0.25\times {\left(0.082\right)}^2\times {\left(273\right)}^2}{100}=\frac{125.3}{100}=1.253l^{2}mol{e}^{2}atm$