Which one of the following has maximum number of molecules ?

Options

A. 16 g of `O_(2)`
B. 16 g of `NO_(2)`
C. 4 g of `N_(2)`
D. 32 g of `N_(2)`

Explanation

To determine which substance has the maximum number of molecules, we need to calculate the number of moles for each given mass of the substances. The number of molecules can be found using the formula:

\[ \text{Number of molecules} = \text{Number of moles} \times \text{Avogadro's number} \]

However, since Avogadro's number is constant for all substances, we can directly compare the number of moles to find out which substance has the maximum number of molecules.

### Step-by-Step Solution:

1. **Calculate the number of moles for O2:**
- Given mass of O2 = 16 grams
- Molar mass of O2 = 32 grams/mole
- Number of moles of O2 = \(\frac{16 \text{ grams}}{32 \text{ grams/mole}} = 0.5 \text{ moles}\)

2. **Calculate the number of moles for NO2:**
- Given mass of NO2 = 16 grams
- Molar mass of NO2 = 14 (N) + 32 (O2) = 46 grams/mole
- Number of moles of NO2 = \(\frac{16 \text{ grams}}{46 \text{ grams/mole}} \approx 0.3478 \text{ moles}\)

3. **Calculate the number of moles for N2:**
- Given mass of N2 = 4 grams
- Molar mass of N2 = 28 grams/mole
- Number of moles of N2 = \(\frac{4 \text{ grams}}{28 \text{ grams/mole}} \approx 0.1429 \text{ moles}\)

4. **Calculate the number of moles for NO2 (second instance):**
- Given mass of NO2 = 32 grams
- Molar mass of NO2 = 46 grams/mole
- Number of moles of NO2 = \(\frac{32 \text{ grams}}{46 \text{ grams/mole}} \approx 0.6957 \text{ moles}\)

5. **Compare the number of moles:**
- O2: 0.5 moles
- NO2 (first instance): 0.3478 moles
- N2: 0.1429 moles
- NO2 (second instance): 0.6957 moles

6. **Conclusion:**
- The substance with the maximum number of moles is NO2 (32 grams), which has approximately 0.6957 moles. Therefore, it has the maximum number of molecules.

### Final Answer:
The substance with the maximum number of molecules is **32 grams of NO2**.