Question

Calculate the pressure (in atm as nearest integer) exerted by one mole of $C{O}_2$ gas at 273 K, if the van der Waal's constant ${}^{\prime }{a}^{\prime }=3.592d{m}^{6}atmmo{l}^{-2}$. Assume that the volume occupied by $C{O}_2$ molecules is negligible.

Answer 1

According to van der Waal's equation:
$[P+(a/V^2\left)\right][V-b]=RT$ (for 1 mol)
If b is negligible, then
$[P+(a/V^2\left)\right]\left[V\right]=RT$
$PV=RT-\left(a/V\right)$
$P=\frac{RT}{V}-\frac{a}{V^2}$
$V^{2}P-RTV+a=0$
$V=\frac{+RT\pm \sqrt{(-RT{)}^2-4Pa}}{2P}$
Since, volume of gas is constant P and T, thus, V can have only one value or discriminant $=0$
$R^2{T}^2-04Pa=0$
$P=\frac{R^2{T}^2}{4a}=\frac{(0.0821{)}^2\times (273{)}^2}{4\times 3.592}$
$=34.98atm$
nearest integer value is 35 atm.