2 moles of each of hydrogen, carbon dioxide and chlorine are mixed in a close vessel of volume 3 litres and temperature `0^(@)C`. Calculate the pressure exerted by the mixture. `(R=8.31" J "mol^(-1)K^(-1))`

Explanation

To calculate the pressure exerted by the mixture of gases, we can follow these steps:

### Step 1: Identify the number of moles of each gas
We have:
- Hydrogen (H₂): 2 moles
- Carbon Dioxide (CO₂): 2 moles
- Chlorine (Cl₂): 2 moles

### Step 2: Calculate the total number of moles
Total moles (n) = moles of H₂ + moles of CO₂ + moles of Cl₂
\[ n = 2 + 2 + 2 = 6 \text{ moles} \]

### Step 3: Convert the temperature from Celsius to Kelvin
The temperature given is \(0^\circ C\). To convert to Kelvin:
\[ T(K) = T(°C) + 273.15 = 0 + 273.15 = 273.15 \text{ K} \]

### Step 4: Use the Ideal Gas Law to find the pressure
The Ideal Gas Law is given by:
\[ PV = nRT \]
Where:
- \(P\) = pressure
- \(V\) = volume
- \(n\) = number of moles
- \(R\) = ideal gas constant (8.31 J/mol·K)
- \(T\) = temperature in Kelvin

Rearranging the equation to solve for pressure \(P\):
\[ P = \frac{nRT}{V} \]

### Step 5: Substitute the known values into the equation
Given:
- \(n = 6 \text{ moles}\)
- \(R = 8.31 \text{ J/mol·K}\)
- \(T = 273.15 \text{ K}\)
- \(V = 3 \text{ liters} = 3 \times 10^{-3} \text{ m}^3\) (converting liters to cubic meters)

Substituting these values into the equation:
\[ P = \frac{6 \times 8.31 \times 273.15}{3 \times 10^{-3}} \]

### Step 6: Calculate the pressure
Calculating the numerator:
\[ 6 \times 8.31 \times 273.15 = 136.78 \times 273.15 \approx 3737.57 \text{ J} \]
Now, substituting this back into the pressure equation:
\[ P = \frac{3737.57}{3 \times 10^{-3}} = \frac{3737.57}{0.003} \approx 1245850.00 \text{ Pa} \]

### Step 7: Convert pressure to a more convenient unit (if needed)
1 Pascal = 1 N/m², so:
\[ P \approx 1.25 \times 10^6 \text{ Pa} \text{ or } 1.25 \text{ MPa} \]

### Final Answer
The pressure exerted by the mixture is approximately \(1.25 \times 10^6 \text{ Pa}\) or \(1.25 \text{ MPa}\).

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