Calculate the temperature of 4.0 mol of a gas occupying d `dm^(3)` at 3.32 bar. (R=0.083 bar `dm^(3) K^(-1)mol^(-1))`.

Explanation

To calculate the temperature of the gas using the ideal gas equation, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Ideal Gas Equation**:
The ideal gas equation is given by:
\[ PV = nRT \]
where:
- \( P \) = pressure (in bar)
- \( V \) = volume (in dm³)
- \( n \) = number of moles (in mol)
- \( R \) = ideal gas constant (in bar dm³ K⁻¹ mol⁻¹)
- \( T \) = temperature (in K)

2. **Substitute the Known Values**:
From the problem, we have:
- \( P = 3.32 \, \text{bar} \)
- \( V = 5 \, \text{dm}^3 \)
- \( n = 4 \, \text{mol} \)
- \( R = 0.083 \, \text{bar dm}^3 \, \text{K}^{-1} \, \text{mol}^{-1} \)

Substituting these values into the ideal gas equation:
\[ 3.32 \times 5 = 4 \times 0.083 \times T \]

3. **Calculate the Left Side**:
Calculate \( 3.32 \times 5 \):
\[ 3.32 \times 5 = 16.6 \]

4. **Set Up the Equation**:
Now we have:
\[ 16.6 = 4 \times 0.083 \times T \]

5. **Calculate \( 4 \times 0.083 \)**:
Calculate \( 4 \times 0.083 \):
\[ 4 \times 0.083 = 0.332 \]

6. **Rearrange the Equation to Solve for \( T \)**:
Now we can rearrange the equation to solve for \( T \):
\[ T = \frac{16.6}{0.332} \]

7. **Perform the Division**:
Calculate \( \frac{16.6}{0.332} \):
\[ T \approx 50.0 \, \text{K} \]

### Final Answer:
The temperature of the gas is approximately \( 50.0 \, \text{K} \).