The maximum number of molecules is present in

Options

A. 15 L of water at STP
B. 15 L of `H_(2)O` gas at STP
C. 15 g of ice
D. Same in all

Answer

To solve the question of which scenario has the maximum number of molecules, we will analyze three different cases: 15 liters of water, 15 liters of water vapor (H2O gas) at STP, and 15 grams of ice. We will calculate the number of molecules in each case step-by-step.

### Step 1: Calculate the number of molecules in 15 liters of water at STP

1. **Find the mass of water**:
- Density of water = 1 kg/L
- Volume = 15 L
- Mass = Density × Volume = 1 kg/L × 15 L = 15 kg

2. **Convert mass to grams**:
- Mass in grams = 15 kg × 1000 g/kg = 15000 g

3. **Calculate moles of water**:
- Molecular weight of H2O = 2(1) + 16 = 18 g/mol
- Moles of H2O = Mass / Molecular weight = 15000 g / 18 g/mol = 833.33 moles

4. **Convert moles to molecules**:
- Number of molecules = Moles × Avogadro's number
- Number of molecules = 833.33 moles × 6.022 × 10²³ molecules/mol = 5.01 × 10²³ molecules

### Step 2: Calculate the number of molecules in 15 liters of H2O gas at STP

1. **Use the molar volume of a gas**:
- At STP, 1 mole of gas occupies 22.4 L.
- Moles in 15 L = Volume / Molar volume = 15 L / 22.4 L/mol = 0.6696 moles

2. **Convert moles to molecules**:
- Number of molecules = Moles × Avogadro's number
- Number of molecules = 0.6696 moles × 6.022 × 10²³ molecules/mol = 4.02 × 10²³ molecules

### Step 3: Calculate the number of molecules in 15 grams of ice

1. **Calculate moles of ice**:
- Molecular weight of ice (H2O) = 18 g/mol
- Moles of ice = Mass / Molecular weight = 15 g / 18 g/mol = 0.8333 moles

2. **Convert moles to molecules**:
- Number of molecules = Moles × Avogadro's number
- Number of molecules = 0.8333 moles × 6.022 × 10²³ molecules/mol = 5.01 × 10²³ molecules

### Conclusion: Compare the number of molecules

- **15 liters of water**: 5.01 × 10²³ molecules
- **15 liters of H2O gas**: 4.02 × 10²³ molecules
- **15 grams of ice**: 5.01 × 10²³ molecules

The maximum number of molecules is present in **15 liters of water** and **15 grams of ice**, both having the same number of molecules (5.01 × 10²³).