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 determine which of the given options has the maximum number of molecules, we will calculate the number of molecules in each case: 15 liters of water, 14 liters of H2O gas at STP, and 15 grams of ice.

### Step-by-Step Solution:

1. **Calculate the number of molecules in 15 liters of water:**
- First, convert liters of water to grams. The density of water is approximately 1 g/mL, so:
\[ 15 \text{ liters} = 15,000 \text{ mL} = 15,000 \text{ g} \]
- Now, calculate the number of moles of water using the molecular weight of water (H2O), which is 18 g/mol:
\[ \text{Number of moles} = \frac{15,000 \text{ g}}{18 \text{ g/mol}} = 833.33 \text{ moles} \]
- To find the number of molecules, use Avogadro's number (\(N_A = 6.022 \times 10^{23} \text{ molecules/mol}\)):
\[ \text{Number of molecules} = 833.33 \text{ moles} \times 6.022 \times 10^{23} \text{ molecules/mol} \approx 5.02 \times 10^{26} \text{ molecules} \]

2. **Calculate the number of molecules in 14 liters of H2O gas at STP:**
- At STP, 1 mole of gas occupies 22.4 liters. Therefore, the number of moles in 14 liters of H2O gas is:
\[ \text{Number of moles} = \frac{14 \text{ liters}}{22.4 \text{ liters/mol}} \approx 0.625 \text{ moles} \]
- Now, calculate the number of molecules:
\[ \text{Number of molecules} = 0.625 \text{ moles} \times 6.022 \times 10^{23} \text{ molecules/mol} \approx 3.76 \times 10^{23} \text{ molecules} \]

3. **Calculate the number of molecules in 15 grams of ice:**
- The molecular weight of ice (H2O) is the same as that of water, which is 18 g/mol:
\[ \text{Number of moles} = \frac{15 \text{ g}}{18 \text{ g/mol}} \approx 0.833 \text{ moles} \]
- Now, calculate the number of molecules:
\[ \text{Number of molecules} = 0.833 \text{ moles} \times 6.022 \times 10^{23} \text{ molecules/mol} \approx 5.02 \times 10^{23} \text{ molecules} \]

4. **Compare the number of molecules:**
- 15 liters of water: \( \approx 5.02 \times 10^{26} \text{ molecules} \)
- 14 liters of H2O gas: \( \approx 3.76 \times 10^{23} \text{ molecules} \)
- 15 grams of ice: \( \approx 5.02 \times 10^{23} \text{ molecules} \)

### Conclusion:
The maximum number of molecules is present in **15 liters of water**.