Equal weights of methane and hydrogen are mixed in an empty container at `25^@` C. The farction of total pressure exerted by hydrogen is

Options

A. `1//2 `
B. 8//9
C. 16//19
D. 1//9

Answer

To solve the problem of finding the fraction of total pressure exerted by hydrogen when equal weights of methane (CH₄) and hydrogen (H₂) are mixed in a container at 25°C, we can follow these steps:

### Step 1: Determine the molecular weights of methane and hydrogen
- The molecular weight of methane (CH₄) is 16 g/mol.
- The molecular weight of hydrogen (H₂) is 2 g/mol.

### Step 2: Assume equal weights of methane and hydrogen
- Let's assume we take 1 gram of each gas.
- Therefore, we have 1 g of CH₄ and 1 g of H₂.

### Step 3: Calculate the number of moles of each gas
- For methane (CH₄):
\[ \text{Number of moles of CH₄} = \frac{\text{Weight}}{\text{Molecular weight}} = \frac{1 \text{ g}}{16 \text{ g/mol}} = \frac{1}{16} \text{ mol} \]

- For hydrogen (H₂):
\[ \text{Number of moles of H₂} = \frac{\text{Weight}}{\text{Molecular weight}} = \frac{1 \text{ g}}{2 \text{ g/mol}} = \frac{1}{2} \text{ mol} \]

### Step 4: Calculate the total number of moles
- Total moles = moles of CH₄ + moles of H₂
\[ \text{Total moles} = \frac{1}{16} + \frac{1}{2} \]
To add these fractions, we need a common denominator:
\[ \frac{1}{2} = \frac{8}{16} \]
Therefore:
\[ \text{Total moles} = \frac{1}{16} + \frac{8}{16} = \frac{9}{16} \text{ mol} \]

### Step 5: Calculate the mole fraction of hydrogen
- The mole fraction of hydrogen (X_H₂) is given by:
\[ X_{H₂} = \frac{\text{moles of H₂}}{\text{total moles}} = \frac{\frac{1}{2}}{\frac{9}{16}} \]
Simplifying this:
\[ X_{H₂} = \frac{1/2}{9/16} = \frac{1}{2} \times \frac{16}{9} = \frac{8}{9} \]

### Step 6: Determine the fraction of total pressure exerted by hydrogen
- The fraction of total pressure exerted by hydrogen is equal to its mole fraction:
\[ \text{Fraction of total pressure by H₂} = X_{H₂} = \frac{8}{9} \]

### Final Answer
The fraction of total pressure exerted by hydrogen is \(\frac{8}{9}\).

---