Question

If volume occupied by $C{O}_2$ molecules is negligible, then what will be the pressure $\left(\frac{p}{5.277}\right)$ exerted by one mole of $C{O}_2$ gas at $300K$? $\left(a=3.592atm{L}^{2}mo{l}^2\right)$

• A. $7$
• B. $8$
• C. $9$
• D. $3$

Answer 1

Answer: (B)

$\left(p+\frac{a{n}^2}{V^2}\right)$ $\left(V-nb\right)=nRT$
$\left(p+\frac{a}{V^2}\right)\left(V-b\right)=RT$ $\left(\because n=1\right)$
If b is negligible p $=\frac{RT}{V}-\frac{a}{V^2}$
The equation is quadratic in $V$ , thus
$V=\frac{+RT\pm \sqrt{R^2{T}^2-4ap}}{2p}$
Since $V$ has one value at given $P$ and $T$, thus numericalvalue of discriminant = $0$
$R^2{T}^2=4ap$
$p=\frac{R^2{T}^2}{4a}$ $=\frac{{\left(0.0821\right)}^2{\left(300\right)}^2}{4\times 3.592}$ $\therefore$ $\frac{p}{5.277}=8$