The maximum number of molecules is present in

Options

A. `15L` of `H_(2)` gas at `STP`
B. `0.5g` of `H_(2)` gas
C. `10g` of `O_(2)` gas
D. `5 L` of `N_(2)` gas at `STP`

Explanation

To determine which option has the maximum number of molecules, we will calculate the number of molecules for each option provided. Here’s the step-by-step solution:

### Step 1: Calculate the number of molecules in 15 liters of hydrogen gas.

1. **Find the number of moles of hydrogen gas:**
\[ \text{Moles of } H_2 = \frac{\text{Volume}}{\text{Molar Volume}} = \frac{15 \, \text{L}}{22.4 \, \text{L/mol}} \approx 0.6696 \, \text{mol} \]

2. **Convert moles to molecules using Avogadro's number (6.022 x 10²³ molecules/mol):**
\[ \text{Number of molecules} = \text{Moles} \times \text{Avogadro's number} = 0.6696 \, \text{mol} \times 6.022 \times 10^{23} \, \text{molecules/mol} \approx 4.03 \times 10^{23} \, \text{molecules} \]

### Step 2: Calculate the number of molecules in 0.5 grams of hydrogen.

1. **Find the number of moles of hydrogen gas:**
\[ \text{Moles of } H_2 = \frac{\text{Weight}}{\text{Molecular Weight}} = \frac{0.5 \, \text{g}}{2 \, \text{g/mol}} = 0.25 \, \text{mol} \]

2. **Convert moles to molecules:**
\[ \text{Number of molecules} = 0.25 \, \text{mol} \times 6.022 \times 10^{23} \, \text{molecules/mol} \approx 1.51 \times 10^{23} \, \text{molecules} \]

### Step 3: Calculate the number of molecules in 10 grams of oxygen.

1. **Find the number of moles of oxygen gas:**
\[ \text{Moles of } O_2 = \frac{10 \, \text{g}}{32 \, \text{g/mol}} = 0.3125 \, \text{mol} \]

2. **Convert moles to molecules:**
\[ \text{Number of molecules} = 0.3125 \, \text{mol} \times 6.022 \times 10^{23} \, \text{molecules/mol} \approx 1.88 \times 10^{23} \, \text{molecules} \]

### Step 4: Calculate the number of molecules in 5 liters of nitrogen gas.

1. **Find the number of moles of nitrogen gas:**
\[ \text{Moles of } N_2 = \frac{5 \, \text{L}}{22.4 \, \text{L/mol}} \approx 0.2232 \, \text{mol} \]

2. **Convert moles to molecules:**
\[ \text{Number of molecules} = 0.2232 \, \text{mol} \times 6.022 \times 10^{23} \, \text{molecules/mol} \approx 1.34 \times 10^{23} \, \text{molecules} \]

### Conclusion: Compare the number of molecules from all options.

- 15 liters of hydrogen gas: \( 4.03 \times 10^{23} \) molecules
- 0.5 grams of hydrogen: \( 1.51 \times 10^{23} \) molecules
- 10 grams of oxygen: \( 1.88 \times 10^{23} \) molecules
- 5 liters of nitrogen: \( 1.34 \times 10^{23} \) molecules

The maximum number of molecules is found in **15 liters of hydrogen gas**, which has approximately \( 4.03 \times 10^{23} \) molecules.