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

Options

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

Explanation

To determine which case has the maximum number of water molecules, we will analyze each option step by step.

### Step 1: Analyze Option A - 18 ml of Water
1. **Volume of Water**: 18 ml
2. **Density of Water**: 1 g/ml
3. **Mass of Water**:
\[ \text{Mass} = \text{Volume} \times \text{Density} = 18 \, \text{ml} \times 1 \, \text{g/ml} = 18 \, \text{g} \]
4. **Molecular Weight of Water (H₂O)**:
\[ \text{Molecular weight} = (2 \times 1) + 16 = 18 \, \text{g/mol} \]
5. **Number of Moles**:
\[ \text{Number of moles} = \frac{\text{Mass}}{\text{Molecular weight}} = \frac{18 \, \text{g}}{18 \, \text{g/mol}} = 1 \, \text{mol} \]
6. **Number of Molecules**:
\[ \text{Number of molecules} = 1 \, \text{mol} \times 6.022 \times 10^{23} \, \text{molecules/mol} = 6.022 \times 10^{23} \, \text{molecules} \]

### Step 2: Analyze Option B - 0.18 g of Water
1. **Mass of Water**: 0.18 g
2. **Number of Moles**:
\[ \text{Number of moles} = \frac{0.18 \, \text{g}}{18 \, \text{g/mol}} = 0.01 \, \text{mol} \]
3. **Number of Molecules**:
\[ \text{Number of molecules} = 0.01 \, \text{mol} \times 6.022 \times 10^{23} \, \text{molecules/mol} = 6.022 \times 10^{21} \, \text{molecules} \]

### Step 3: Analyze Option C - 0.00224 L of Water Vapor
1. **Volume of Gas**: 0.00224 L
2. **Moles of Gas at STP**:
\[ \text{Number of moles} = \frac{0.00224 \, \text{L}}{22.4 \, \text{L/mol}} = 10^{-4} \, \text{mol} \]
3. **Number of Molecules**:
\[ \text{Number of molecules} = 10^{-4} \, \text{mol} \times 6.022 \times 10^{23} \, \text{molecules/mol} = 6.022 \times 10^{19} \, \text{molecules} \]

### Step 4: Analyze Option D - 10^-3 moles of Water
1. **Number of Moles**: \(10^{-3} \, \text{mol}\)
2. **Number of Molecules**:
\[ \text{Number of molecules} = 10^{-3} \, \text{mol} \times 6.022 \times 10^{23} \, \text{molecules/mol} = 6.022 \times 10^{20} \, \text{molecules} \]

### Step 5: Compare the Number of Molecules from Each Option
- **Option A**: \(6.022 \times 10^{23}\) molecules
- **Option B**: \(6.022 \times 10^{21}\) molecules
- **Option C**: \(6.022 \times 10^{19}\) molecules
- **Option D**: \(6.022 \times 10^{20}\) molecules

### Conclusion
The maximum number of water molecules is in **Option A**, which has \(6.022 \times 10^{23}\) molecules.

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