A compound contains `92.3%` of carbon and `7.7%` of hydrogen. The molecule of the compound is 39 times heavier than hydrogen molecule. The molecular formula of the compound is

Options

A. `C_(3)H_(3)`
B. `C_(2)H_(2)`
C. `C_(2)H_(4)`
D. `C_(6)H_(6)`

Explanation

To determine the molecular formula of the compound that contains 92.3% carbon and 7.7% hydrogen, and is 39 times heavier than a hydrogen molecule, we can follow these steps:

### Step 1: Calculate the moles of Carbon and Hydrogen
1. **Moles of Carbon**:
- Given percentage of Carbon = 92.3%
- Molar mass of Carbon (C) = 12 g/mol
- Moles of Carbon = (Percentage of Carbon / Molar mass of Carbon)
\[ \text{Moles of C} = \frac{92.3}{12} \approx 7.692 \text{ moles} \]

2. **Moles of Hydrogen**:
- Given percentage of Hydrogen = 7.7%
- Molar mass of Hydrogen (H) = 1 g/mol
- Moles of Hydrogen = (Percentage of Hydrogen / Molar mass of Hydrogen)
\[ \text{Moles of H} = \frac{7.7}{1} = 7.7 \text{ moles} \]

### Step 2: Determine the simplest mole ratio
- The ratio of moles of Carbon to Hydrogen is approximately:
\[ \text{Ratio} = \frac{7.692}{7.7} \approx 1:1 \]
- Thus, the empirical formula of the compound is \( \text{CH} \).

### Step 3: Calculate the molar mass of the empirical formula
- Molar mass of empirical formula \( \text{CH} \):
\[ \text{Molar mass of CH} = 12 \text{ (C)} + 1 \text{ (H)} = 13 \text{ g/mol} \]

### Step 4: Determine the molar mass of the compound
- The compound is 39 times heavier than the hydrogen molecule (H₂):
\[ \text{Molar mass of H}_2 = 2 \text{ g/mol} \]
\[ \text{Molar mass of the compound} = 39 \times 2 = 78 \text{ g/mol} \]

### Step 5: Find the molecular formula
- To find the molecular formula, we divide the molar mass of the compound by the molar mass of the empirical formula:
\[ n = \frac{\text{Molar mass of compound}}{\text{Molar mass of empirical formula}} = \frac{78}{13} = 6 \]
- Therefore, the molecular formula is obtained by multiplying the subscripts in the empirical formula by \( n \):
\[ \text{Molecular formula} = C_{1 \times 6}H_{1 \times 6} = C_6H_6 \]

### Final Answer:
The molecular formula of the compound is \( \text{C}_6\text{H}_6 \).

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