A gas mixture contains oxygen and nitrogen in `1 : 2` mole ratio . Ratio of the partial pressures of nitrogen and oxygen in the mixture is

Options

A. `1 : 2`
B. `2 : 1`
C. `7 : 8`
D. `8 : 7`

Answer

To solve the problem of finding the ratio of the partial pressures of nitrogen (N₂) and oxygen (O₂) in a gas mixture with a mole ratio of 1:2, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Mole Ratio**:
- The mole ratio of oxygen to nitrogen is given as 1:2.
- Let's denote the moles of oxygen as \(1x\) and the moles of nitrogen as \(2x\).

2. **Calculate Total Moles**:
- The total moles in the mixture can be calculated as:
\[ \text{Total moles} = \text{moles of O}_2 + \text{moles of N}_2 = 1x + 2x = 3x \]

3. **Determine Mole Fractions**:
- The mole fraction of nitrogen (\(X_{N_2}\)) is given by:
\[ X_{N_2} = \frac{\text{moles of N}_2}{\text{total moles}} = \frac{2x}{3x} = \frac{2}{3} \]
- The mole fraction of oxygen (\(X_{O_2}\)) is given by:
\[ X_{O_2} = \frac{\text{moles of O}_2}{\text{total moles}} = \frac{1x}{3x} = \frac{1}{3} \]

4. **Calculate Partial Pressures**:
- The partial pressure of nitrogen (\(P_{N_2}\)) is calculated using the formula:
\[ P_{N_2} = X_{N_2} \times P_{\text{total}} = \frac{2}{3} \times P_{\text{total}} \]
- The partial pressure of oxygen (\(P_{O_2}\)) is calculated as:
\[ P_{O_2} = X_{O_2} \times P_{\text{total}} = \frac{1}{3} \times P_{\text{total}} \]

5. **Find the Ratio of Partial Pressures**:
- The ratio of the partial pressures of nitrogen to oxygen is:
\[ \frac{P_{N_2}}{P_{O_2}} = \frac{\frac{2}{3} P_{\text{total}}}{\frac{1}{3} P_{\text{total}}} \]
- Simplifying this gives:
\[ \frac{P_{N_2}}{P_{O_2}} = \frac{2}{1} = 2 \]

6. **Final Answer**:
- Therefore, the ratio of the partial pressures of nitrogen to oxygen is:
\[ P_{N_2} : P_{O_2} = 2 : 1 \]