A gaseous mixture contains 1 g of `H_(2)` , 4 g of He , 7 g of `N_(2)` and 8 g of `O_(2)` . The gas having the highest partial pressure is :-

Options

A. `H_(2)`
B. `O_(2)`
C. He
D. `N_(2)`

Answer

To determine which gas in the mixture has the highest partial pressure, we need to follow these steps:

### Step 1: Calculate the number of moles of each gas.
The number of moles can be calculated using the formula:
\[ \text{Number of moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} \]

1. **For Hydrogen (H₂)**:
- Mass = 1 g
- Molar mass of H₂ = 2 g/mol
\[ \text{Moles of H₂} = \frac{1 \text{ g}}{2 \text{ g/mol}} = 0.5 \text{ moles} \]

2. **For Helium (He)**:
- Mass = 4 g
- Molar mass of He = 4 g/mol
\[ \text{Moles of He} = \frac{4 \text{ g}}{4 \text{ g/mol}} = 1 \text{ mole} \]

3. **For Nitrogen (N₂)**:
- Mass = 7 g
- Molar mass of N₂ = 28 g/mol
\[ \text{Moles of N₂} = \frac{7 \text{ g}}{28 \text{ g/mol}} = 0.25 \text{ moles} \]

4. **For Oxygen (O₂)**:
- Mass = 8 g
- Molar mass of O₂ = 32 g/mol
\[ \text{Moles of O₂} = \frac{8 \text{ g}}{32 \text{ g/mol}} = 0.25 \text{ moles} \]

### Step 2: Summarize the number of moles.
- Moles of H₂ = 0.5
- Moles of He = 1
- Moles of N₂ = 0.25
- Moles of O₂ = 0.25

### Step 3: Identify the gas with the highest number of moles.
From the calculations:
- The highest number of moles is for Helium (He) with 1 mole.

### Step 4: Determine the gas with the highest partial pressure.
Since the partial pressure of a gas is directly proportional to its mole fraction, and Helium has the highest number of moles, it will also have the highest partial pressure.

### Conclusion:
The gas having the highest partial pressure in the mixture is **Helium (He)**.

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