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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