Question

Equal moles of hydrogen and oxygen gases are placed in a container with a pin-hole through which both can escape. What fraction of the oxygen escapes in the time required for one-half of the hydrogen to escape?

Options

• `3/8`

• `1/2`

• `1/8`

• `1/4`

Answer 1

`1/8`

Explanation:

Graham's law of diffusion states that the rate of diffusion/effusion of a gas is inversely related to its molar mass squared.

∴ `r_(O_2)/r_(H_2) = sqrt((M_(H_2))/(M_(O_2))`

= `sqrt(2/32) = 1/4`

The diffusion rate = `"Volume of gas diffused"/"Time required for diffusion"`

∴ `V_(O_2)/V_(H_2) = 1/4`  ......(∵ Time is same)

∴ `n_(O_2)/n_(H_2) = 1/4` ......(∵ P and Tare constant)

∴ `n_(O_2) = 1/4 xx n_(H_2) = 1/4 xx 1/2 = 1/8`