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Question

A straight glass tube has 2 inlets X and Y at the two ends of a 200 cm long tube as shown in the figure. HCl gas through inlet X and NH3 gas through inlet Y are allowed to enter in the tube at the same time and under identical conditions. At a point P inside the tube, both the gases meet first. The distance of point P from X is:

A
118.9 cm
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B
81.1 cm
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C
150.1 cm
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D
108.9 cm
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Solution

The correct option is B 81.1 cm
Let x cm be the distance travelled by the gas from HCl side. So, the distance from NH3 side is (200x) cm. Consider at time 't' both the gases meet.

Rate of diffusion =distance travelledtime taken
r1r2=x200x….(i)

Consider r1 to be the rate of diffusion for HCl and r2 to be the rate of diffusion for NH3.

So, according to Graham's law of diffusion,
r1r2 = Molar Mass of NH3 (M2)Molar Mass of HCl (M1)..(ii)

r1r2=1736.5
Using (i) and (ii)
x200x=1736.5
= 1.46x=200x
x=81.13 cm

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