A gaseous mixture contains 4.0g of `H_(2)` and 56.0g of `N_(2)`. The mole fraction of `H_(2)` in the mixture is

Options

A. `0.1`
B. `0.2`
C. `0.5`
D. `0.8`

Explanation

To find the mole fraction of \( H_2 \) in the gaseous mixture containing \( 4.0 \, \text{g} \) of \( H_2 \) and \( 56.0 \, \text{g} \) of \( N_2 \), we will follow these steps:

### Step 1: Calculate the number of moles of \( H_2 \)
The formula to calculate the number of moles is given by:
\[ \text{Moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} \]
For \( H_2 \):
- Mass of \( H_2 = 4.0 \, \text{g} \)
- Molar mass of \( H_2 = 2.0 \, \text{g/mol} \)

Calculating the moles of \( H_2 \):
\[ \text{Moles of } H_2 = \frac{4.0 \, \text{g}}{2.0 \, \text{g/mol}} = 2.0 \, \text{mol} \]

### Step 2: Calculate the number of moles of \( N_2 \)
For \( N_2 \):
- Mass of \( N_2 = 56.0 \, \text{g} \)
- Molar mass of \( N_2 = 28.0 \, \text{g/mol} \)

Calculating the moles of \( N_2 \):
\[ \text{Moles of } N_2 = \frac{56.0 \, \text{g}}{28.0 \, \text{g/mol}} = 2.0 \, \text{mol} \]

### Step 3: Calculate the total number of moles in the mixture
The total number of moles in the mixture is the sum of the moles of \( H_2 \) and \( N_2 \):
\[ \text{Total moles} = \text{Moles of } H_2 + \text{Moles of } N_2 = 2.0 \, \text{mol} + 2.0 \, \text{mol} = 4.0 \, \text{mol} \]

### Step 4: Calculate the mole fraction of \( H_2 \)
The mole fraction of \( H_2 \) is given by the formula:
\[ X_{H_2} = \frac{\text{Moles of } H_2}{\text{Total moles}} \]
Substituting the values:
\[ X_{H_2} = \frac{2.0 \, \text{mol}}{4.0 \, \text{mol}} = \frac{1}{2} = 0.5 \]

### Final Answer
The mole fraction of \( H_2 \) in the mixture is \( 0.5 \).

---