A mixture of one mole of each of `O_2(g), H_2(g)`, He(g) exists in a container of volume V at temperatureT in which partial pressure of `H_2` (g) is 2atm. the total pressure in the container is:

Options

A. 6atm
B. 18atm
C. 33atm
D. 24atm

Answer

To solve the problem, we need to find the total pressure in a container that holds a mixture of gases: O₂, H₂, and He. We know the partial pressure of H₂ is 2 atm, and we have one mole of each gas in the container.

### Step-by-Step Solution:

1. **Identify the Given Information:**
- One mole of O₂, H₂, and He.
- Partial pressure of H₂ (P_H₂) = 2 atm.
- Total number of moles (n) = 3 moles (1 mole of each gas).

2. **Use Dalton's Law of Partial Pressures:**
- According to Dalton's Law, the total pressure (P_total) in a mixture of gases is the sum of the partial pressures of each individual gas:
\[ P_{\text{total}} = P_{H_2} + P_{O_2} + P_{He} \]

3. **Find the Partial Pressure of O₂:**
- Since we have one mole of each gas and the gases behave ideally, we can use the ideal gas law (PV = nRT) to find the partial pressure of O₂.
- Rearranging the ideal gas law gives us:
\[ P = \frac{nRT}{V} \]
- For O₂, since the number of moles (n) is 1:
\[ P_{O_2} = \frac{1 \cdot RT}{V} \]

4. **Find the Partial Pressure of He:**
- Similarly, for He:
\[ P_{He} = \frac{1 \cdot RT}{V} \]

5. **Relate Partial Pressures:**
- Since P_H₂ is given as 2 atm, we can express the partial pressures of O₂ and He in terms of P_H₂.
- We know that the total pressure is the sum of the partial pressures:
\[ P_{O_2} = P_{H_2} = 2 \text{ atm} \]
\[ P_{He} = P_{H_2} = 2 \text{ atm} \]

6. **Calculate the Total Pressure:**
- Now substituting the values into the equation for total pressure:
\[ P_{\text{total}} = P_{H_2} + P_{O_2} + P_{He} = 2 \text{ atm} + 2 \text{ atm} + 2 \text{ atm} = 6 \text{ atm} \]

### Final Answer:
The total pressure in the container is **6 atm**.

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