X and Y are two volatile liquids with molar weights of `10g mol^(-1) and 40g mol^(-1)` respectively. Two cotton plugs, one soaked in X and the other soaked in Y, are simultaneously placed at the ends of the tube of length L=24cm, 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 from the plug soaked in X. Take X and Y to have equal molecular diameters and assume ideal behavior 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:

Options

A. larger mean free path for X as compared to that of Y
B. larger mean free path for Y as compared to that of X
C. increased collision frequency of Y with the inert gas as compared to that of X with the inert gas
D. increased collision frequency of X with the inert gas as compared to that of Y with the inert gas

Answer

B, D

Explanation

x is a lighter gas than y, hence x has greater molecular speed. Due to greater molecular speed of x, it will have smaller mean free path and greater collision frequency with the inert gas molecules. As a result, x will take more time to travel a given distance along a straight line. Hence x and y will meet at a distance smaller than one calculated from Graham’s law.