Calculate the distance from the HCL inlet to the point where the gases meet?

Question

A glass tube, 100cm long, is fitted at each end by stoppers that have small holes of identical diameters. Gaseous HCL is allowed to effuse into the tube from one end and gaseous NH3 is allowed to effuse from the other end. when these gases meet, they react and form NH4CL. calculate the distance (cm) from the HCL inlet to the point where the gases meet.

Answer 1

The molar masses of HCl and NH3 are: 36.4606 g/mol and 17.0306 g/mol, respectively.  

Let the distance (cm) from the HCL inlet to the point where the gases meet is x cm.  Since the effusion time is the same for two gases, the effusion rate must proportional to the effusion distances.  Since the effuse rate is also inversely proportional to the square root of the molar masses.  we have:

x(36.4606/17.0306)^0.5 = 100-x, or:

x = 100/(1+(36.4606/17.0306)^0.5) = 40.6 (cm)