A closed vessel contains `8 g` of oxygen and ` 7 g` of nitrogen. The total pressure is 10 atm at a given temperature. If now oxygen is absorbed by introducing a suitable absorbent, the pressure of the remaining gas in atm will be

Options

A. 2
B. 10
C. 4
D. 5

Explanation

To solve the problem step by step, we can use Dalton's Law of Partial Pressures and the ideal gas law. Here’s how we can approach it:

### Step 1: Calculate the number of moles of each gas
We need to find the number of moles of oxygen (O₂) and nitrogen (N₂) in the vessel.

- **Molecular mass of O₂** = 32 g/mol
- **Molecular mass of N₂** = 28 g/mol

Using the formula:
\[ n = \frac{\text{mass}}{\text{molecular mass}} \]

For oxygen:
\[ n_{O_2} = \frac{8 \text{ g}}{32 \text{ g/mol}} = 0.25 \text{ mol} \]

For nitrogen:
\[ n_{N_2} = \frac{7 \text{ g}}{28 \text{ g/mol}} = 0.25 \text{ mol} \]

### Step 2: Calculate the total number of moles
The total number of moles in the vessel before the absorption of oxygen is:
\[ n_{\text{total}} = n_{O_2} + n_{N_2} = 0.25 \text{ mol} + 0.25 \text{ mol} = 0.5 \text{ mol} \]

### Step 3: Use Dalton's Law of Partial Pressures
According to Dalton's Law, the total pressure (P_total) is the sum of the partial pressures of each gas:
\[ P_{\text{total}} = P_{O_2} + P_{N_2} \]

Given that \( P_{\text{total}} = 10 \text{ atm} \).

### Step 4: Calculate the partial pressures
The partial pressure of each gas can be calculated using the formula:
\[ P_i = \frac{n_i}{n_{\text{total}}} \times P_{\text{total}} \]

For oxygen:
\[ P_{O_2} = \frac{n_{O_2}}{n_{\text{total}}} \times P_{\text{total}} = \frac{0.25}{0.5} \times 10 \text{ atm} = 5 \text{ atm} \]

For nitrogen:
\[ P_{N_2} = \frac{n_{N_2}}{n_{\text{total}}} \times P_{\text{total}} = \frac{0.25}{0.5} \times 10 \text{ atm} = 5 \text{ atm} \]

### Step 5: Determine the pressure after oxygen is absorbed
After the oxygen is absorbed, only nitrogen remains in the vessel. Therefore, the pressure of the remaining gas (nitrogen) will be equal to its partial pressure before the absorption of oxygen:
\[ P_{N_2} = 5 \text{ atm} \]

### Final Answer
The pressure of the remaining gas (nitrogen) in the vessel after the oxygen is absorbed is **5 atm**.

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