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X and Y are two volatile liquids with molar weights of 10 gmol1and 40 gmol1 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 


  1. 8
  2. 12
  3. 16
  4. 20


Solution

The correct option is C 16
Remember
vx/vy=(My/Mx)=(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/velocites being 2:1).

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