Question

At room temperature, ammonia gas at 1 atm pressure and HCl gas at pressure P atm is allowed to effuse through identical pinholes from opposite ends of a glass tube of 1-meter length and uniform area of cross $-$ section. $N{H}_{4}Cl$ is first formed at a distance of 60 cm from the end through which HCl gas was sent in. Calculate the value of P (in atm).

(Write your answer to the nearest integer).

Answer 1

Since the pressures 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 travelled by the gas.

$r_1$ (of HCI gas) at pressure $P=60=k_P/\sqrt{36.5}$ ……(i)

and $r_2$ (of $N{H}_3$) at 1 atm. Pressure $P=40=k\times 1/\sqrt{17}$ ….(ii)

From (i) and (ii):

$r_1/r_2=60/40=\frac{k_P}{\sqrt{36.5}}\times \frac{\sqrt{17}}{k\times 1}$

$P=\frac{60}{40}\times \sqrt{\frac{36.5}{17}}=2.197$ atm

Nearest integer value answer is 2