Calculate the volume occupied by 4 mole of an ideal gas at `2.5 xx 10^(5) Nm^(-2)` pressure and 300 K temperature

Explanation

To calculate the volume occupied by 4 moles of an ideal gas at a pressure of \(2.5 \times 10^{5} \, \text{Nm}^{-2}\) and a temperature of 300 K, we can use the ideal gas equation:

### Step-by-Step Solution:

1. **Identify the Ideal Gas Equation**:
The ideal gas equation is given by:
\[ PV = nRT \]
where:
- \(P\) = pressure (in Nm\(^{-2}\))
- \(V\) = volume (in m³)
- \(n\) = number of moles
- \(R\) = ideal gas constant
- \(T\) = temperature (in K)

2. **Rearrange the Equation to Solve for Volume**:
We want to find the volume \(V\), so we rearrange the equation:
\[ V = \frac{nRT}{P} \]

3. **Substitute the Known Values**:
- Number of moles \(n = 4\)
- Pressure \(P = 2.5 \times 10^{5} \, \text{Nm}^{-2}\)
- Temperature \(T = 300 \, \text{K}\)
- Ideal gas constant \(R = 8.314 \, \text{Nm}^{-2} \, \text{m}^{3} \, \text{K}^{-1} \, \text{mol}^{-1}\)

Now substitute these values into the equation:
\[ V = \frac{4 \times 8.314 \times 300}{2.5 \times 10^{5}} \]

4. **Calculate the Numerator**:
First, calculate the numerator:
\[ 4 \times 8.314 \times 300 = 9976.8 \]

5. **Calculate the Volume**:
Now, divide the numerator by the pressure:
\[ V = \frac{9976.8}{2.5 \times 10^{5}} = \frac{9976.8}{250000} \approx 0.03991 \, \text{m}^3 \]

6. **Convert to dm³**:
Since \(1 \, \text{m}^3 = 1000 \, \text{dm}^3\), we convert the volume:
\[ V \approx 0.03991 \times 1000 \approx 39.91 \, \text{dm}^3 \]

### Final Answer:
The volume occupied by 4 moles of the ideal gas is approximately \(39.91 \, \text{dm}^3\).