The maximum number of molecules is present in :

Options

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

Explanation

To determine which option contains the maximum number of molecules, we will calculate the number of moles for each option and then convert that to the number of molecules using Avogadro's number (NA = 6.022 × 10²³).

### Step 1: Calculate the number of moles for each option

1. **15 liters of H₂ gas at STP**
- At STP, 1 mole of gas occupies 22.4 liters.
- Number of moles = Volume / Volume at STP = 15 L / 22.4 L = 0.67 moles.
- Number of molecules = 0.67 moles × NA = 0.67 × 6.022 × 10²³.

2. **5 liters of N₂ gas at STP**
- Number of moles = Volume / Volume at STP = 5 L / 22.4 L = 0.22 moles.
- Number of molecules = 0.22 moles × NA = 0.22 × 6.022 × 10²³.

3. **0.5 grams of H₂ gas**
- Molar mass of H₂ = 2 g/mol.
- Number of moles = Mass / Molar mass = 0.5 g / 2 g/mol = 0.25 moles.
- Number of molecules = 0.25 moles × NA = 0.25 × 6.022 × 10²³.

4. **10 grams of O₂ gas**
- Molar mass of O₂ = 32 g/mol.
- Number of moles = Mass / Molar mass = 10 g / 32 g/mol = 0.31 moles.
- Number of molecules = 0.31 moles × NA = 0.31 × 6.022 × 10²³.

### Step 2: Compare the number of molecules

Now we can summarize the number of moles calculated for each option:

- **15 liters of H₂ gas**: 0.67 moles
- **5 liters of N₂ gas**: 0.22 moles
- **0.5 grams of H₂ gas**: 0.25 moles
- **10 grams of O₂ gas**: 0.31 moles

### Step 3: Determine the maximum number of molecules

- The highest number of moles is from **15 liters of H₂ gas**, which corresponds to 0.67 moles.

Thus, the option with the maximum number of molecules is:

**15 liters of H₂ gas at STP.**

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