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 will follow these steps:

### Step 1: Calculate the number of moles of each gas.
To find the number of moles, we use the formula:
\[ \text{Moles} = \frac{\text{Mass (g)}}{\text{Molar Mass (g/mol)}} \]

- For \( H_2 \):
\[ \text{Moles of } H_2 = \frac{1 \text{ g}}{2 \text{ g/mol}} = 0.5 \text{ moles} \]

- For \( He \):
\[ \text{Moles of } He = \frac{4 \text{ g}}{4 \text{ g/mol}} = 1 \text{ mole} \]

- For \( N_2 \):
\[ \text{Moles of } N_2 = \frac{7 \text{ g}}{28 \text{ g/mol}} = 0.25 \text{ moles} \]

- For \( O_2 \):
\[ \text{Moles of } O_2 = \frac{8 \text{ g}}{32 \text{ g/mol}} = 0.25 \text{ moles} \]

### Step 2: Calculate the total number of moles in the mixture.
\[ \text{Total moles} = \text{Moles of } H_2 + \text{Moles of } He + \text{Moles of } N_2 + \text{Moles of } O_2 \]
\[ \text{Total moles} = 0.5 + 1 + 0.25 + 0.25 = 2 \text{ moles} \]

### Step 3: Calculate the mole fraction of each gas.
The mole fraction (\(X\)) is given by:
\[ X = \frac{\text{Moles of gas}}{\text{Total moles}} \]

- For \( H_2 \):
\[ X_{H_2} = \frac{0.5}{2} = 0.25 \]

- For \( He \):
\[ X_{He} = \frac{1}{2} = 0.5 \]

- For \( N_2 \):
\[ X_{N_2} = \frac{0.25}{2} = 0.125 \]

- For \( O_2 \):
\[ X_{O_2} = \frac{0.25}{2} = 0.125 \]

### Step 4: Determine the partial pressure of each gas.
The partial pressure (\(P_i\)) can be calculated using:
\[ P_i = X_i \times P_{\text{total}} \]
Assuming \(P_{\text{total}} = 1\) atm for simplicity (the actual value will not change the comparison):
- For \( H_2 \):
\[ P_{H_2} = 0.25 \times P_{\text{total}} = 0.25 \text{ atm} \]

- For \( He \):
\[ P_{He} = 0.5 \times P_{\text{total}} = 0.5 \text{ atm} \]

- For \( N_2 \):
\[ P_{N_2} = 0.125 \times P_{\text{total}} = 0.125 \text{ atm} \]

- For \( O_2 \):
\[ P_{O_2} = 0.125 \times P_{\text{total}} = 0.125 \text{ atm} \]

### Conclusion:
The gas with the highest partial pressure is **Helium (He)**, with a partial pressure of \(0.5 \text{ atm}\).