Which of the following molecules has highest number of particles?

Options

A. 8 g of `CH_(4)`
B. 4.4 g of `CO_(2)`
C. `34.2 g` of `C_(12)H_(22)O_(11)`
D. 2 g of `H_(2)`

Explanation

To determine which molecule has the highest number of particles, we will calculate the number of particles in each of the given samples. We will use the formula:

\[ \text{Number of moles} = \frac{\text{Given mass}}{\text{Molar mass}} \]

Then, we will use Avogadro's number (\(6.02 \times 10^{23}\)) to find the number of particles in each sample.

### Step-by-step Solution:

1. **Calculate the number of moles of CH₄ (Option A)**:
- Given mass = 8 g
- Molar mass of CH₄ = 12 (C) + 4 × 1 (H) = 16 g/mol
- Number of moles = \( \frac{8 \, \text{g}}{16 \, \text{g/mol}} = 0.5 \, \text{moles} \)
- Number of particles = \( 0.5 \times 6.02 \times 10^{23} = 3.01 \times 10^{23} \) particles

2. **Calculate the number of moles of CO₂ (Option B)**:
- Given mass = 4.4 g
- Molar mass of CO₂ = 12 (C) + 2 × 16 (O) = 44 g/mol
- Number of moles = \( \frac{4.4 \, \text{g}}{44 \, \text{g/mol}} = 0.1 \, \text{moles} \)
- Number of particles = \( 0.1 \times 6.02 \times 10^{23} = 6.02 \times 10^{22} \) particles

3. **Calculate the number of moles of C₁₂H₂₂O₁₁ (Option C)**:
- Given mass = 34.2 g
- Molar mass of C₁₂H₂₂O₁₁ = 12 × 12 (C) + 22 × 1 (H) + 16 × 11 (O) = 342 g/mol
- Number of moles = \( \frac{34.2 \, \text{g}}{342 \, \text{g/mol}} = 0.1 \, \text{moles} \)
- Number of particles = \( 0.1 \times 6.02 \times 10^{23} = 6.02 \times 10^{22} \) particles

4. **Calculate the number of moles of H₂O (Option D)**:
- Given mass = 2 g
- Molar mass of H₂O = 2 × 1 (H) + 16 (O) = 18 g/mol
- Number of moles = \( \frac{2 \, \text{g}}{18 \, \text{g/mol}} = \frac{1}{9} \, \text{moles} \approx 0.111 \, \text{moles} \)
- Number of particles = \( 0.111 \times 6.02 \times 10^{23} \approx 6.67 \times 10^{22} \) particles

### Summary of Results:
- CH₄: \( 3.01 \times 10^{23} \) particles
- CO₂: \( 6.02 \times 10^{22} \) particles
- C₁₂H₂₂O₁₁: \( 6.02 \times 10^{22} \) particles
- H₂O: \( 6.67 \times 10^{22} \) particles

### Conclusion:
The molecule with the highest number of particles is **CH₄** (Option A).

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