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. 1/3
B. 2/3
C. 1/9
D. 4/9

Explanation

To solve the problem of finding the fraction of the total pressure exerted by oxygen when equal masses of helium and oxygen are mixed in a container at 25°C, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Information**:
- Equal masses of helium and oxygen are mixed. Let's denote the mass of each gas as \( W \).
- The molar mass of helium (He) is approximately 4 g/mol.
- The molar mass of oxygen (O₂) is approximately 32 g/mol.

2. **Calculate the Number of Moles**:
- The number of moles of helium can be calculated using the formula:
\[ n_{He} = \frac{W}{M_{He}} = \frac{W}{4} \]
- The number of moles of oxygen can be calculated similarly:
\[ n_{O_2} = \frac{W}{M_{O_2}} = \frac{W}{32} \]

3. **Calculate the Total Number of Moles**:
- The total number of moles in the mixture is the sum of the moles of helium and oxygen:
\[ n_{total} = n_{He} + n_{O_2} = \frac{W}{4} + \frac{W}{32} \]
- To add these fractions, find a common denominator (which is 32):
\[ n_{total} = \frac{8W}{32} + \frac{W}{32} = \frac{9W}{32} \]

4. **Calculate the Mole Fraction of Oxygen**:
- The mole fraction of oxygen (\( X_{O_2} \)) is given by:
\[ X_{O_2} = \frac{n_{O_2}}{n_{total}} = \frac{\frac{W}{32}}{\frac{9W}{32}} = \frac{1}{9} \]

5. **Calculate the Fraction of Total Pressure Exerted by Oxygen**:
- According to Dalton's Law of Partial Pressures, the partial pressure of a gas in a mixture is equal to the mole fraction of that gas multiplied by the total pressure:
\[ P_{O_2} = P_{total} \times X_{O_2} \]
- Therefore, the fraction of the total pressure exerted by oxygen is:
\[ \text{Fraction of total pressure by } O_2 = X_{O_2} = \frac{1}{9} \]

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