Question

What is the compressibility factor $\left(Z\right)$ for $0.02$ mole of a van der waal's gas at pressure of $0.1atm$. Assume the size of gas molecule is negligible.
(Given: $RT=20Latmmo{l}^{-1}$ and $a=1000atm{L}^{-2}mo{l}^{-1}$)

• A. $2$
• B. $1$
• C. $0.02$
• D. $0.5$

Answer 1

The correct option is D $0.5$

As the size of the gas molecule is negligble, then the volume correction $b$ is also neglible.
$(0.1+\frac{1000\times (0.02{)}^2}{V^2})V=20\times 0.02=0.1V^2-0.4V+0.4=0\Rightarrow V^2-4V+4=0\Rightarrow V=2LZ=\frac{PV}{nRT}=\frac{0.1\times 2}{0.02\times 20}=0.5$