The number of molecules in 11 g of `CO_(2)` is same as that in

Options

A. 8g of oxygen
B. 16 g of oxygen
C. 7g of CO
D. 3.5 g of CO

Explanation

To find the mass of another substance that contains the same number of molecules as 11 g of CO₂, we will follow these steps:

### Step 1: Calculate the number of moles of CO₂ in 11 g.
The formula for the number of moles is:
\[ \text{Number of moles} = \frac{\text{Given mass}}{\text{Molar mass}} \]

For CO₂:
- Given mass = 11 g
- Molar mass of CO₂ = 12 (C) + 16×2 (O) = 12 + 32 = 44 g/mol

So, the number of moles of CO₂ is:
\[ \text{Number of moles of CO₂} = \frac{11 \text{ g}}{44 \text{ g/mol}} = \frac{1}{4} \text{ mol} \]

### Step 2: Calculate the number of molecules in CO₂.
Using Avogadro's number (Na = \(6.022 \times 10^{23}\) molecules/mol):
\[ \text{Number of molecules} = \text{Number of moles} \times \text{Avogadro's number} \]
\[ \text{Number of molecules in 11 g of CO₂} = \frac{1}{4} \text{ mol} \times 6.022 \times 10^{23} \text{ molecules/mol} = \frac{6.022 \times 10^{23}}{4} \text{ molecules} \]

### Step 3: Find another substance with the same number of molecules.
We need to find a substance whose mass will yield the same number of molecules.

#### Option A: 8 g of O₂
- Molar mass of O₂ = 16 × 2 = 32 g/mol
- Number of moles of O₂ = \(\frac{8 \text{ g}}{32 \text{ g/mol}} = \frac{1}{4} \text{ mol}\)
- Number of molecules in 8 g of O₂ = \(\frac{1}{4} \text{ mol} \times 6.022 \times 10^{23} \text{ molecules/mol} = \frac{6.022 \times 10^{23}}{4} \text{ molecules}\)

This matches the number of molecules in 11 g of CO₂.

#### Option B: 16 g of O₂
- Number of moles of O₂ = \(\frac{16 \text{ g}}{32 \text{ g/mol}} = \frac{1}{2} \text{ mol}\)
- Number of molecules = \(\frac{1}{2} \text{ mol} \times 6.022 \times 10^{23} \text{ molecules/mol} = \frac{6.022 \times 10^{23}}{2} \text{ molecules}\)

This does not match.

#### Option C: 7 g of CO
- Molar mass of CO = 12 (C) + 16 (O) = 28 g/mol
- Number of moles of CO = \(\frac{7 \text{ g}}{28 \text{ g/mol}} = \frac{1}{4} \text{ mol}\)
- Number of molecules = \(\frac{1}{4} \text{ mol} \times 6.022 \times 10^{23} \text{ molecules/mol} = \frac{6.022 \times 10^{23}}{4} \text{ molecules}\)

This matches as well.

#### Option D: 3.5 g of CO
- Number of moles = \(\frac{3.5 \text{ g}}{28 \text{ g/mol}} = 0.125 \text{ mol}\)
- Number of molecules = \(0.125 \text{ mol} \times 6.022 \times 10^{23} \text{ molecules/mol}\)

This does not match.

### Conclusion:
The substances that have the same number of molecules as 11 g of CO₂ are 8 g of O₂ and 7 g of CO.