X and Y are two volatile liquids with molar weights of 10gmol−1 and 40gmol−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=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 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✓ Correct
(D)20
Answer: (C)
Solution
According to Graham's law of diffusion, the rate of diffusion is inversely proportional to the square root of molar mass:
rYrX=MXMY=1040=4=2
The vapors meet when they have traveled distances that are in the ratio of their rates. If X travels distance d and Y travels distance (24−d):
24−dd=rYrX=2
d=2(24−d)
d=48−2d
3d=48
d=16 cm
JEE Advanced · 2014 · 25 May 2014 · Paper 2 · Single correct option
