Given:

Let us assume 1 mole of hydrogen and 1 mole of oxygen gases are placed in a container with a pin-hole through which both can escape.

$$\frac{n_{o}t_{H}}{n_{H}t_{o}} = \sqrt{\frac{M_{H}}{M_{o}}}$$

Here

$$n_{o}$$ is the number of moles of oxygen effused in time $$t_{o}$$ $$n_{H}$$ is the number of moles of hydrogen effused in time $$t_{H}$$ $$M_{o}$$ is the molar mass of oxygen

$$M_{H}$$ is the molar mass of hydrogen

$$\frac{n_{o}}{\frac{1}{2}} = \sqrt{\frac{2}{32}}$$

since $$t_{o} = t_{Ho} and n_{H} = \frac{1}{2}$$ $$n_{o} = \frac{1}{2} * \frac{1}{4} = \frac{1}{8}$$

The fraction of the oxygen that escapes in the time required for one-half of the hydrogen to escape is = $$\frac{1}{8}$$

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