Question

At room temperature ${NH}_3$ gas at one atm & HCl gas at P Atm are allowed to effuse through identical pin holes to the opposite ends of a glass tube 1 m long & uniform cross-section. A white deposit is observed at a distance of 60 cm from the HCl end. What is P?

Answer 1

Since the pressure of gases are different, and the temperature is constant, the rate at which molecules of the two gases diffuse is directly proportional to the pressure. This rate of diffusion is also directly proportional to the distance traveled by the gas.

Hence by using Graham's law of diffusion

$\frac{r_1}{r_2}=\sqrt{\frac{M_{N{H}_3}}{M_{HCl}}}\times \frac{P_{HCl}}{P_{N{H}_3}}$

$r_1$ of $HCl$ at pressure $P_{HCl}=60cm$

$r_2$ of $N{H}_3$ at pressure $P_{N{H}_3}=40cm$

$\frac{60}{40}=\sqrt{\frac{17}{36.5}}\times \frac{P}{1}$

$\frac{3}{2}=\sqrt{\frac{17}{36.5}}\times P$

Squaring both side

$\frac{9}{4}=\frac{17}{36.5}\times P^2$

$p^2=\frac{9\times 36.5}{4\times 17}$

$p=\sqrt{\frac{146}{68}}$

$P=2.197atm$