Equal masses of methane and oxygen are mixed in an empty container at `25^(@)C`. The fraction of the total pressure exerted by oxygen is:

Options

A. `(2)/(3)`
B. `(1)/(3)xx(273)/(298)`
C. `(1)/(3)`
D. `(1)/(2)`

Explanation

To solve the problem of finding the fraction of the total pressure exerted by oxygen when equal masses of methane (CH₄) and oxygen (O₂) are mixed in a container at 25°C, we can follow these steps:

### Step-by-Step Solution:

1. **Define the Masses:**
Let the mass of methane (CH₄) be \( W \) grams. Since equal masses are used, the mass of oxygen (O₂) will also be \( W \) grams.

2. **Calculate the Number of Moles:**
- The molar mass of methane (CH₄) is 16 g/mol.
- The number of moles of methane (\( n_{CH₄} \)) can be calculated using the formula:
\[ n_{CH₄} = \frac{W}{\text{Molar mass of CH₄}} = \frac{W}{16} \]
- The molar mass of oxygen (O₂) is 32 g/mol.
- The number of moles of oxygen (\( n_{O₂} \)) can be calculated as:
\[ n_{O₂} = \frac{W}{\text{Molar mass of O₂}} = \frac{W}{32} \]

3. **Calculate Total Moles:**
The total number of moles (\( n_{total} \)) in the container is the sum of the moles of methane and oxygen:
\[ n_{total} = n_{CH₄} + n_{O₂} = \frac{W}{16} + \frac{W}{32} \]

4. **Finding a Common Denominator:**
To add these fractions, we need a common denominator. The least common multiple of 16 and 32 is 32:
\[ n_{total} = \frac{2W}{32} + \frac{W}{32} = \frac{3W}{32} \]

5. **Calculate the Mole Fraction of Oxygen:**
The mole fraction of oxygen (\( X_{O₂} \)) is given by the ratio of the moles of oxygen to the total moles:
\[ X_{O₂} = \frac{n_{O₂}}{n_{total}} = \frac{\frac{W}{32}}{\frac{3W}{32}} = \frac{1}{3} \]

6. **Determine the Fraction of Total Pressure:**
According to Dalton's Law of Partial Pressures, the fraction of the total pressure exerted by a gas is equal to its mole fraction. Thus, the fraction of total pressure exerted by oxygen is:
\[ \text{Fraction of total pressure by } O₂ = X_{O₂} = \frac{1}{3} \]

### Final Answer:
The fraction of the total pressure exerted by oxygen is \( \frac{1}{3} \).