A gaseous mixture contains `40% O_(2), 40% N_(2), 10% CO_(2), 10% CH_(4)` by volume. Calculate the vapour density of the gaseous mixture.

Answer

To calculate the vapor density of the gaseous mixture containing 40% O₂, 40% N₂, 10% CO₂, and 10% CH₄ by volume, we can follow these steps:

### Step 1: Assume Total Volume
Assume the total volume of the gaseous mixture is 100 liters. This simplifies calculations since the percentages can be directly converted to volumes.

### Step 2: Calculate Individual Volumes
From the total volume, we can calculate the volume of each gas:
- Volume of O₂ = 40% of 100 L = 40 L
- Volume of N₂ = 40% of 100 L = 40 L
- Volume of CO₂ = 10% of 100 L = 10 L
- Volume of CH₄ = 10% of 100 L = 10 L

### Step 3: Calculate Mass of Each Gas
Next, we need to find the mass of each gas using the molar mass and the volume:
1. **Oxygen (O₂)**:
- Molar mass = 32 g/mol
- Mass of O₂ = (32 g/mol / 22.4 L/mol) × 40 L = 57.14 g

2. **Nitrogen (N₂)**:
- Molar mass = 28 g/mol
- Mass of N₂ = (28 g/mol / 22.4 L/mol) × 40 L = 50.00 g

3. **Carbon Dioxide (CO₂)**:
- Molar mass = 44 g/mol
- Mass of CO₂ = (44 g/mol / 22.4 L/mol) × 10 L = 19.64 g

4. **Methane (CH₄)**:
- Molar mass = 16 g/mol
- Mass of CH₄ = (16 g/mol / 22.4 L/mol) × 10 L = 7.14 g

### Step 4: Calculate Total Mass of the Mixture
Now, we sum the masses of all components:
- Total mass = Mass of O₂ + Mass of N₂ + Mass of CO₂ + Mass of CH₄
- Total mass = 57.14 g + 50.00 g + 19.64 g + 7.14 g = 133.92 g

### Step 5: Calculate Molar Mass of the Mixture
The molar mass of the mixture can be calculated using the total mass and the total volume:
- Molar mass = (Total mass / Total volume) × Molar volume
- Molar mass = (133.92 g / 100 L) × 22.4 L = 29.98 g/mol (approximately 30 g/mol)

### Step 6: Calculate Vapor Density
Finally, we can calculate the vapor density (VD) using the formula:
- Vapor density = Molar mass / 2
- Vapor density = 30 g/mol / 2 = 15 g/L

### Final Answer
The vapor density of the gaseous mixture is **15 g/L**.

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