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 $300K?(a=3.592atm{L}^{2}mo{l}^{-2})$.

• A. $7$
• B. $8$
• C. $9$
• D. $3$

Answer 1

The correct option is B $8$

$(P+\frac{a{n}^2}{V^2})(V-nb)=nRT$
$(P+\frac{a}{V^2})(V-b)=RT(\because n=1)$
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 numerical value of discriminant $=0$
$R^2{T}^2=4aP$
$P=\frac{R^2{T}^2}{4a}=\frac{\left(0.0821{)}^2\right(300{)}^2}{4\times 3.592}\therefore \frac{P}{5.277}=8$.