Question

The density of vapours of a substance at 1 atm pressure and 400 K is 0.4 kg m${}^{-3}$. These vapours effuse through a pin at a rate of 2 times faster than $S{O}_2$ under the same conditions. Is it attractive or repulsive forces operating in the given gas molecule?
(Given 1 atm = 101325 Nm${}^{-2}$)

Answer 1

$\frac{r_v}{r_{so}}=\sqrt{\frac{M_{so}}{M_v}}$
$2=\sqrt{\frac{64}{M_v}};4=\frac{64}{M_v},M_v=16$
Molar volume $\overline{V}=\frac{16\times {10}^{-3}}{0.4}=40\times {10}^{-3}{m}^3$
Compressibility factor $Z=\frac{PV}{RT}=\frac{101325\times 40\times {10}^{-3}}{8.314\times 400}$
$=1218.9\times {10}^{-3}=1.219$
Since $Z>1$, repulsive forces do operate.