In which of the following pairs, `10 g` of each have an equal number of molecules?

Options

A. `N_(2)O` and `CO`
B. `N_(2)` and `C_(3)O_(2)`
C. `N_(2)` and `CO`
D. `N_(2)O` and `CO_(2)`

Explanation

To determine in which of the following pairs 10 g of each substance have an equal number of molecules, we need to calculate the number of moles for each substance in the pairs. The number of moles can be calculated using the formula:

\[ \text{Number of moles} = \frac{\text{Given mass (g)}}{\text{Molar mass (g/mol)}} \]

Since the given mass is the same (10 g) for all pairs, we will compare the molar masses of the substances in each pair. If the molar masses are the same, then the number of moles (and thus the number of molecules) will also be the same.

### Step-by-Step Solution:

1. **Identify the pairs of substances.** Let's denote them as:
- Pair 1: N₂ and CO
- Pair 2: N₂O and CO₂
- Pair 3: N₂ and C₃O₂

2. **Calculate the molar mass for each substance in the pairs.**

- **For N₂:**
\[ \text{Molar mass of N₂} = 14 \, \text{g/mol} \times 2 = 28 \, \text{g/mol} \]

- **For CO:**
\[ \text{Molar mass of CO} = 12 \, \text{g/mol (C)} + 16 \, \text{g/mol (O)} = 28 \, \text{g/mol} \]

- **For N₂O:**
\[ \text{Molar mass of N₂O} = 14 \, \text{g/mol} \times 2 + 16 \, \text{g/mol} = 28 + 16 = 44 \, \text{g/mol} \]

- **For CO₂:**
\[ \text{Molar mass of CO₂} = 12 \, \text{g/mol (C)} + 2 \times 16 \, \text{g/mol (O)} = 12 + 32 = 44 \, \text{g/mol} \]

- **For C₃O₂:**
\[ \text{Molar mass of C₃O₂} = 3 \times 12 \, \text{g/mol (C)} + 2 \times 16 \, \text{g/mol (O)} = 36 + 32 = 68 \, \text{g/mol} \]

3. **Compare the molar masses:**
- **Pair 1 (N₂ and CO):** Both have a molar mass of 28 g/mol.
- **Pair 2 (N₂O and CO₂):** Both have a molar mass of 44 g/mol.
- **Pair 3 (N₂ and C₃O₂):** N₂ has a molar mass of 28 g/mol, while C₃O₂ has a molar mass of 68 g/mol.

4. **Conclusion:**
- The pairs that have equal molar masses (and thus equal number of molecules for 10 g) are:
- Pair 1: N₂ and CO
- Pair 2: N₂O and CO₂

### Final Answer:
The correct pairs where 10 g of each have an equal number of molecules are:
- Pair 1: N₂ and CO
- Pair 2: N₂O and CO₂