8g of oxygen, 14 g of nitrogen and 22 g carbon dioxide are mixed in an encloser of volume 10 litre and temperature `27^(@)C`. Calculate the pressure exerted by the mixture , `R= 8.3 J "mole"^(-1)K^(-1)`, Molecular weight of oxygen , nitrogen and carbon 32 , 28 and 44 respectively.

Explanation

To calculate the pressure exerted by the mixture of gases, we will use the ideal gas law, which is given by the equation:

\[ PV = nRT \]

Where:
- \( P \) = Pressure (in Pascals)
- \( V \) = Volume (in cubic meters)
- \( n \) = Number of moles of gas
- \( R \) = Ideal gas constant (8.3 J/(mol·K))
- \( T \) = Temperature (in Kelvin)

### Step 1: Convert the given mass of each gas to moles.

1. **Oxygen (O₂)**:
- Molecular weight = 32 g/mol
- Mass = 8 g
- Moles of O₂ = \( \frac{8 \text{ g}}{32 \text{ g/mol}} = 0.25 \text{ mol} \)

2. **Nitrogen (N₂)**:
- Molecular weight = 28 g/mol
- Mass = 14 g
- Moles of N₂ = \( \frac{14 \text{ g}}{28 \text{ g/mol}} = 0.5 \text{ mol} \)

3. **Carbon Dioxide (CO₂)**:
- Molecular weight = 44 g/mol
- Mass = 22 g
- Moles of CO₂ = \( \frac{22 \text{ g}}{44 \text{ g/mol}} = 0.5 \text{ mol} \)

### Step 2: Calculate the total number of moles of the gas mixture.

Total moles \( n \) = Moles of O₂ + Moles of N₂ + Moles of CO₂

\[ n = 0.25 + 0.5 + 0.5 = 1.25 \text{ mol} \]

### Step 3: Convert the temperature from Celsius to Kelvin.

Temperature in Kelvin \( T \) = \( 27 + 273 = 300 \text{ K} \)

### Step 4: Convert the volume from liters to cubic meters.

Volume \( V \) = \( 10 \text{ L} = 10 \times 10^{-3} \text{ m}^3 = 0.01 \text{ m}^3 \)

### Step 5: Use the ideal gas law to calculate the pressure.

Substituting the values into the ideal gas law:

\[ P = \frac{nRT}{V} \]

\[ P = \frac{(1.25 \text{ mol}) \times (8.3 \text{ J/(mol·K)}) \times (300 \text{ K})}{0.01 \text{ m}^3} \]

Calculating the numerator:

\[ 1.25 \times 8.3 \times 300 = 3,112.5 \text{ J} \]

Now, substituting back to find \( P \):

\[ P = \frac{3,112.5 \text{ J}}{0.01 \text{ m}^3} = 311,250 \text{ Pa} \]

### Final Answer:

The pressure exerted by the mixture is \( 311,250 \text{ Pa} \) or \( 311.25 \text{ kPa} \).

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