Question

Equal moles of hydrogen and oxygen gases are placed in a container with a pin-hole through which both can escape. How many moles of Oxygen gas escape in the time required for half a mole of the hydrogen to escape?

• A. $\frac{1}{4}$
• B. $\frac{3}{8}$
• C. $\frac{1}{2}$
• D. $\frac{1}{8}$

Answer 1

Answer: (D)

Step 1:

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.

By using Graham's Law:

$\frac{n_{O_2}}{n_{H_2}}=\sqrt{\frac{M_{H_2}}{M_{O_2}}}$

Step 2:

$\Rightarrow \frac{n_{O_2}}{0.5}=\sqrt{\frac{2}{32}}$

$\therefore n_{O_2}=\frac{1}{8}$

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

Hence, option (D) is correct.