A methane `+H_(2)` mixture contains 10g methane and 5g Hydrogen.
If the pressure of the mixture is 30 atm. What is the partial
pressure of `H_(2)` in mixture :-

Options

A. 6 atm
B. 129 atm
C. 24 atm
D. 189 atm

Explanation

To find the partial pressure of hydrogen (H₂) in a mixture of methane (CH₄) and hydrogen, we can follow these steps:

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

- For hydrogen (H₂):
- Mass of H₂ = 5 g
- Molar mass of H₂ = 2 g/mol
\[ \text{Number of moles of H₂} = \frac{5 \text{ g}}{2 \text{ g/mol}} = 2.5 \text{ moles} \]

- For methane (CH₄):
- Mass of CH₄ = 10 g
- Molar mass of CH₄ = 16 g/mol
\[ \text{Number of moles of CH₄} = \frac{10 \text{ g}}{16 \text{ g/mol}} = 0.625 \text{ moles} \]

### Step 2: Calculate the total number of moles in the mixture
\[ \text{Total moles} = \text{moles of H₂} + \text{moles of CH₄} = 2.5 + 0.625 = 3.125 \text{ moles} \]

### Step 3: Calculate the mole fraction of hydrogen (H₂)
The mole fraction (X) of a gas is given by:
\[ X_{H₂} = \frac{\text{moles of H₂}}{\text{total moles}} \]
\[ X_{H₂} = \frac{2.5}{3.125} \approx 0.8 \]

### Step 4: Calculate the partial pressure of hydrogen
The partial pressure of a gas in a mixture can be calculated using Dalton's Law of Partial Pressures:
\[ P_{H₂} = X_{H₂} \times P_{\text{total}} \]
Where:
- \(P_{\text{total}} = 30 \text{ atm}\)

Substituting the values:
\[ P_{H₂} = 0.8 \times 30 \text{ atm} = 24 \text{ atm} \]

### Final Answer
The partial pressure of hydrogen (H₂) in the mixture is **24 atm**.

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