A gaseous mixture contains 56 g of `N_2` , 44 g `CO_2` and 16 g of `CH_4` The total pressure of the mixture is 720 mm Hg. The partial pressure of `CH_4` is

Options

A. 180mm
B. 360mm
C. 540 mm
D. 720mm

Answer

To find the partial pressure of CH₄ in the given gaseous mixture, we can follow these steps:

### Step 1: Calculate the number of moles of each gas

1. **For N₂:**
- Given mass = 56 g
- Molar mass of N₂ = 28 g/mol
- Number of moles (N₁) = Given mass / Molar mass = 56 g / 28 g/mol = 2 moles

2. **For CO₂:**
- Given mass = 44 g
- Molar mass of CO₂ = 44 g/mol
- Number of moles (N₂) = Given mass / Molar mass = 44 g / 44 g/mol = 1 mole

3. **For CH₄:**
- Given mass = 16 g
- Molar mass of CH₄ = 16 g/mol
- Number of moles (N₃) = Given mass / Molar mass = 16 g / 16 g/mol = 1 mole

### Step 2: Calculate the total number of moles in the mixture

Total number of moles = N₁ + N₂ + N₃ = 2 + 1 + 1 = 4 moles

### Step 3: Calculate the mole fraction of CH₄

Mole fraction of CH₄ = Number of moles of CH₄ / Total number of moles = 1 / 4 = 0.25

### Step 4: Calculate the partial pressure of CH₄

We use the formula for partial pressure:
\[ \text{Partial Pressure} = \text{Mole Fraction} \times \text{Total Pressure} \]

Given total pressure = 720 mm Hg,
\[ \text{Partial Pressure of CH₄} = 0.25 \times 720 \text{ mm Hg} = 180 \text{ mm Hg} \]

### Conclusion

The partial pressure of CH₄ in the mixture is **180 mm Hg**.

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