Question

$2\text{mol}$ of ammonia occupied a volume of $5\text{L}$ at $27{}^{\circ }C$. Calculate the pressure if the gas obeyed van der Waals equation. $(a=4.17{\text{atm L}}^2{\text{mol}}^{-2},b=0.0371{\text{L mol}}^{-1})$.

• A. $9.33\text{atm}$
• B. $18.66\text{atm}$
• C. $4.66\text{atm}$
• D. $12.32\text{atm}$

Answer 1

The correct option is A $9.33\text{atm}$

Given:
$n=2\text{mol},V=5\text{L}$
$T=273+27=300\text{K}$
$a=4.17{\text{atm L}}^2{\text{mol}}^{-2},b=0.0371{\text{L mol}}^{-1}$.
$R=0.082\text{atm L}{\text{mol}}^{-1}{\text{K}}^{-1}$
Applying van der Waals equation for n moles
$(P+\frac{a{n}^2}{V^2})(V-nb)=nRT$
$\Rightarrow (P+\frac{4.17\times 2^2}{5^2})(5-2\times 0.0371)=2\times 0.082\times 300P=\frac{2\times 0.082\times 300}{4.92}-0.667$
on solving we get :
$P=9.33\text{atm}$