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50 ml of hydrogen diffuses out through a small hole of a vessel in 20 minutes.

The time taken by 40 ml of oxygen to diffuse out is:

A. 8 min
B. 32 min
C. 12 min
D. 64 min

Answer :

Using Graham's Law of Effusion and the given diffusion rates, we find that 40 ml of oxygen will take 64 minutes to diffuse out through a small hole of a vessel.Therefore correct option is D

The time taken by 40 ml of oxygen to diffuse out can be determined using Graham's Law of Effusion, which states that the rate of effusion for a gas is inversely proportional to the square root of its molar mass. Given that hydrogen effuses four times as rapidly as oxygen, we can set up a ratio of their rates of effusion (RateH2 / RateO2 = 4/1), since the square root of the mass ratio is equal to their rate ratio (sqrt(MO2)/sqrt(MH2) = 4). Knowing that 50 ml of hydrogen diffuses out in 20 minutes, we can set up a proportion to find the time it takes for 40 ml of oxygen to effuse. If 50 ml of hydrogen takes 20 minutes, then, by the inverse proportion, 40 ml would take 16 minutes (since 16 minutes is the time that 50 ml of hydrogen would take to effuse if it followed Oxygen's slower rate). From there, we need to adjust the time for the difference in the rates of effusion of hydrogen and oxygen, which is a factor of 4. Therefore, 16 minutes imes 4 gives us 64 minutes for 40 ml of oxygen to diffuse out.

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