If `16 g `of `CH_4` and 4 g of `H_2` are mixed and kept at 760 mm Hg pressure at `0^@C`, then volume occupied by the mixture would be

Options

A. 22.4L
B. 44.8 L
C. 67.2 L
D. 33.6 L

Explanation

To solve the problem of finding the volume occupied by a mixture of gases (16 g of CH₄ and 4 g of H₂) at a pressure of 760 mm Hg and a temperature of 0°C, we can follow these steps:

### Step 1: Calculate the number of moles of CH₄
- The molar mass of CH₄ (methane) is calculated as follows:
- Carbon (C) has an atomic mass of 12 g/mol.
- Hydrogen (H) has an atomic mass of 1 g/mol, and since there are 4 hydrogen atoms in CH₄, the total contribution from hydrogen is 4 g/mol.
- Therefore, the molar mass of CH₄ = 12 g/mol + 4 g/mol = 16 g/mol.

- Now, we can calculate the number of moles of CH₄:
\[ \text{Number of moles of CH₄} = \frac{\text{mass of CH₄}}{\text{molar mass of CH₄}} = \frac{16 \text{ g}}{16 \text{ g/mol}} = 1 \text{ mole} \]

### Step 2: Calculate the number of moles of H₂
- The molar mass of H₂ (hydrogen gas) is calculated as follows:
- Since H₂ consists of 2 hydrogen atoms, the molar mass of H₂ = 2 × 1 g/mol = 2 g/mol.

- Now, we can calculate the number of moles of H₂:
\[ \text{Number of moles of H₂} = \frac{\text{mass of H₂}}{\text{molar mass of H₂}} = \frac{4 \text{ g}}{2 \text{ g/mol}} = 2 \text{ moles} \]

### 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 CH₄ and H₂:
\[ \text{Total number of moles} = \text{Number of moles of CH₄} + \text{Number of moles of H₂} = 1 \text{ mole} + 2 \text{ moles} = 3 \text{ moles} \]

### Step 4: Use the ideal gas law to find the volume
- At standard temperature and pressure (STP), 1 mole of gas occupies 22.4 liters.
- Therefore, the volume occupied by 3 moles of gas can be calculated as follows:
\[ \text{Volume} = \text{Total number of moles} \times 22.4 \text{ L/mole} = 3 \text{ moles} \times 22.4 \text{ L/mole} = 67.2 \text{ L} \]

### Final Answer:
The volume occupied by the mixture is **67.2 liters**.

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