0.078 g of a hydrocarbon occupy 22.414 mL of volume at S.T.P. The empirical formula of the hydrocarbon is CH. The molecular formula of hydrocarbon is

Options

A. `C_2H_2`
B. `C_4H_4`
C. `C_6H_6`
D. `C_8H_8`

Answer

To determine the molecular formula of the hydrocarbon given its mass and volume at standard temperature and pressure (STP), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Given Data**:
- Mass of hydrocarbon = 0.078 g
- Volume of hydrocarbon at STP = 22.414 mL

2. **Convert Volume to Moles**:
At STP, 1 mole of any gas occupies 22.414 L (or 22,414 mL). Therefore, we can find the number of moles of the hydrocarbon using the formula:
\[ \text{Number of moles} = \frac{\text{Volume (mL)}}{22,414 \text{ mL/mol}} \]
Substituting the values:
\[ \text{Number of moles} = \frac{22.414 \text{ mL}}{22,414 \text{ mL/mol}} = 1 \text{ mole} \]

3. **Calculate the Molar Mass**:
The molar mass can be calculated using the mass of the hydrocarbon and the number of moles:
\[ \text{Molar mass} = \frac{\text{Mass}}{\text{Number of moles}} = \frac{0.078 \text{ g}}{1 \text{ mole}} = 0.078 \text{ g/mol} \]
However, since we are working with a gas, we need to convert this to a more standard form. Since 22.414 mL corresponds to 1 mole, we can consider the mass for 1 mole:
\[ \text{Molar mass} = 0.078 \text{ g} \times 1000 = 78 \text{ g/mol} \]

4. **Determine the Empirical Formula Mass**:
The empirical formula given is CH. The molar mass of CH is calculated as follows:
- Carbon (C) = 12 g/mol
- Hydrogen (H) = 1 g/mol
\[ \text{Empirical formula mass} = 12 + 1 = 13 \text{ g/mol} \]

5. **Calculate the Ratio (n)**:
To find the ratio of the molecular formula to the empirical formula, we use:
\[ n = \frac{\text{Molar mass}}{\text{Empirical formula mass}} = \frac{78 \text{ g/mol}}{13 \text{ g/mol}} = 6 \]

6. **Determine the Molecular Formula**:
The molecular formula is obtained by multiplying the subscripts in the empirical formula by n:
- Empirical formula = CH
- Molecular formula = C(1×6)H(1×6) = C6H6

### Final Answer:
The molecular formula of the hydrocarbon is **C6H6**.

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