If the intermolecules forces vanish away, the volume occupied by the molecules contained in `4.5 kg` water at stantard temperature and pressure will be given by

Options

A. `5.6 m^(3)`
B. `4.5 m^(3)`
C. `11.2 L`
D. `11.2 m^(3)`

Explanation

To find the volume occupied by the molecules contained in 4.5 kg of water at standard temperature and pressure (STP) when intermolecular forces vanish, we can use the ideal gas equation:

### Step-by-Step Solution:

1. **Identify the Given Data:**
- Mass of water (m) = 4.5 kg = 4500 g
- Molar mass of water (H₂O) = 18 g/mol
- Standard pressure (P) = 1 atm = 10^5 Pa
- Standard temperature (T) = 0°C = 273 K
- Universal gas constant (R) = 8.314 J/(mol·K)

2. **Calculate the Number of Moles (n):**
\[ n = \frac{m}{\text{Molar mass}} = \frac{4500 \, \text{g}}{18 \, \text{g/mol}} = 250 \, \text{mol} \]

3. **Use the Ideal Gas Equation:**
The ideal gas equation is given by:
\[ PV = nRT \]
Rearranging for volume (V):
\[ V = \frac{nRT}{P} \]

4. **Substitute the Values:**
\[ V = \frac{250 \, \text{mol} \times 8.314 \, \text{J/(mol·K)} \times 273 \, \text{K}}{10^5 \, \text{Pa}} \]

5. **Calculate the Volume:**
\[ V = \frac{250 \times 8.314 \times 273}{10^5} \]
\[ V = \frac{57000.75}{10^5} \approx 0.5700 \, \text{m}^3 \]

6. **Convert to Cubic Meters:**
Since the question asks for the volume in cubic meters, we can express the final answer:
\[ V \approx 0.57 \, \text{m}^3 \]

### Final Answer:
The volume occupied by the molecules contained in 4.5 kg of water at standard temperature and pressure is approximately **0.57 m³**.