In which case is the number of molecules of water maximum?

Options

A. 18 mL of water
B. 0.18 g of water
C. 0.00224 L of water vapours at 1 atm and 273 K
D. `10^(-3)` mol of water

Answer

To determine in which case the number of molecules of water is maximum, we will analyze each option given in the question.

### Step-by-Step Solution:

1. **Understanding the Mole Concept**:
- One mole of any substance contains \(6.022 \times 10^{23}\) molecules (Avogadro's number).
- The mass of one mole of water (H₂O) is 18 grams.

2. **Analyzing Each Option**:
- **Option 1: 18 ml of water**
- Density of water = 1 g/ml.
- Therefore, 18 ml of water = 18 grams of water.
- Moles of water = \(\frac{18 \text{ grams}}{18 \text{ grams/mole}} = 1 \text{ mole}\).
- Number of molecules = \(1 \text{ mole} \times 6.022 \times 10^{23} = 6.022 \times 10^{23}\) molecules.

- **Option 2: 0.18 grams of water**
- Moles of water = \(\frac{0.18 \text{ grams}}{18 \text{ grams/mole}} = 0.01 \text{ moles}\).
- Number of molecules = \(0.01 \text{ moles} \times 6.022 \times 10^{23} = 6.022 \times 10^{21}\) molecules.

- **Option 3: 0.00224 liters of water vapor at 1 atm and 0°C (273 K)**
- Use the ideal gas law: \(PV = nRT\).
- Given: \(P = 1 \text{ atm}\), \(V = 0.00224 \text{ L}\), \(R = 0.0821 \text{ L atm K}^{-1} \text{ mol}^{-1}\), \(T = 273 \text{ K}\).
- Rearranging gives:
\[ n = \frac{PV}{RT} = \frac{(1 \text{ atm})(0.00224 \text{ L})}{(0.0821 \text{ L atm K}^{-1} \text{ mol}^{-1})(273 \text{ K})} \approx 0.0001 \text{ moles} \]
- Number of molecules = \(0.0001 \text{ moles} \times 6.022 \times 10^{23} = 6.022 \times 10^{19}\) molecules.

- **Option 4: \(10^{-3}\) moles of water**
- Number of molecules = \(10^{-3} \text{ moles} \times 6.022 \times 10^{23} = 6.022 \times 10^{20}\) molecules.

3. **Comparing the Results**:
- Option 1: \(6.022 \times 10^{23}\) molecules
- Option 2: \(6.022 \times 10^{21}\) molecules
- Option 3: \(6.022 \times 10^{19}\) molecules
- Option 4: \(6.022 \times 10^{20}\) molecules

### Conclusion:
The maximum number of molecules of water is found in **Option 1: 18 ml of water**, which contains \(6.022 \times 10^{23}\) molecules.