Equal masses of helium and oxygen are mixed in a container at `25 C^(@)` . The fraction of the total pressure exerted by oxygen in the mixture of gases is

Options

A. (a) 1/3
B. (b) 2/3
C. (c) 1/9
D. (d) 4/9

Explanation

To solve the problem of finding the fraction of the total pressure exerted by oxygen in a mixture of equal masses of helium and oxygen, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Molar Masses**:
- The molar mass of helium (He) is 4 g/mol.
- The molar mass of oxygen (O₂) is 32 g/mol (since O has an atomic mass of 16 g, and O₂ = 2 × 16 g).

2. **Assume Equal Masses**:
- Let’s assume we have 32 grams of each gas for easier calculations.

3. **Calculate the Number of Moles**:
- For helium:
\[ \text{Number of moles of He} = \frac{\text{mass}}{\text{molar mass}} = \frac{32 \text{ g}}{4 \text{ g/mol}} = 8 \text{ moles} \]
- For oxygen:
\[ \text{Number of moles of O₂} = \frac{\text{mass}}{\text{molar mass}} = \frac{32 \text{ g}}{32 \text{ g/mol}} = 1 \text{ mole} \]

4. **Calculate the Total Number of Moles**:
- Total moles in the mixture:
\[ \text{Total moles} = \text{moles of He} + \text{moles of O₂} = 8 + 1 = 9 \text{ moles} \]

5. **Calculate the Mole Fraction of Oxygen**:
- The mole fraction of oxygen (χO₂) is given by:
\[ \chi_{O₂} = \frac{\text{moles of O₂}}{\text{total moles}} = \frac{1}{9} \]

6. **Find the Fraction of Total Pressure Exerted by Oxygen**:
- According to Dalton's Law of Partial Pressures, the fraction of total pressure exerted by a gas is equal to its mole fraction:
\[ \frac{P_{O₂}}{P_{T}} = \chi_{O₂} = \frac{1}{9} \]

### Final Answer:
The fraction of the total pressure exerted by oxygen in the mixture is \( \frac{1}{9} \).

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