Question

X and Y are two volatile liquids with molar weights of 10 $gmo{l}^{-1}$and 40 $gmo{l}^{-1}$ respectively. Two cotton plugs, one soaked in X and the other soaked in Y, are simultaneously placed at the ends of a tube of length L = 24 cm, as shown in the figure. The tube is filled with an inert gas at 1 atmosphere pressure and a temperature of 300 K. Vapours of X and Y react to form a product which is first observed at a distance d cm from the plug soaked in X. Take X and Y to have equal molecular diameters and assume ideal behaviour for the inert gas and the two vapours.

The value of d in cm (shown in the figure as estimated from Graham’s law, is

• A. 8
• B. 12
• C. 16
• D. 20

Answer 1

The correct option is C 16

Remember
$v_x/v_y=\sqrt{(}{M}_y/M_x)=\sqrt{(}4/1)$
So the velocities are in the ratio 2:1.

Since the time taken must be the same for both the gases, the distance travelled will be in the ratio 2:1. We divide the tube into 3 parts, each part has a length of 8 cm. Hence, the distance d = 16 cm (because of the ratio of distances/velocities being 2:1).