Question

Calculate the pressure exerted by 5 mol of $C{O}_2$ in 1 L vessel at ${47}^{\circ }C$ using van der Waals equation. Also, calculate the pressure for an ideal gas. Given $a=3.592atm{L}^{2}mo{l}^{-2}$, b = 0.0427 L $mo{l}^{-1}$ .

• A. 131.2 , 77.01
• B. 69.83, 126.22
• C. 77.01, 131.2
• D. 114 , 122

Answer 1

The correct option is C

77.01, 131.2

From the Van der Waals equation, we have $⟮p+\frac{an}{V^2}⟯⟮V-nb⟯=nRT$
Substituting $n=5,V=1L,T=320K,a=3.592atm{L}^{2}mo{l}^{-2}andb=0.0427mo{l}^{-1}$ ,we get

$p=\frac{nRT}{V-nb}-\frac{a{n}^2}{V^2}=\frac{5\times 0.082\times 320}{1-5\times 0.0427}-\frac{3.592\times 25}{1}$

$=166.81-89.8=77.01atm$

For an ideal gas , we have

$P=\frac{nRT}{V}=\frac{5\times 0.082\times 320}{1}=131.2atm$