A gaseous hydrocarbon gives upon combustion, 0.72 g of water and 3.08 g of `CO_(2)`. The empirical formula of the hydrocarbon is

Options

A. (a)`C_(2)H_(4)`
B. (b)`C_(3)H_(4)`
C. (c )`C_(6)H_(5)`
D. (d)`C_(7)H_(8)`

Explanation

To find the empirical formula of the gaseous hydrocarbon, we will follow these steps:

### Step 1: Calculate the number of moles of CO2 produced
The molecular mass of CO2 is calculated as follows:
- Carbon (C) = 12 g/mol
- Oxygen (O) = 16 g/mol
- Therefore, CO2 = 12 + (2 × 16) = 44 g/mol

Now, we can calculate the number of moles of CO2:
\[ \text{Number of moles of } CO2 = \frac{\text{mass of } CO2}{\text{molar mass of } CO2} = \frac{3.08 \text{ g}}{44 \text{ g/mol}} \approx 0.07 \text{ moles} \]

### Step 2: Calculate the number of moles of H2O produced
The molecular mass of H2O is calculated as follows:
- Hydrogen (H) = 1 g/mol
- Oxygen (O) = 16 g/mol
- Therefore, H2O = (2 × 1) + 16 = 18 g/mol

Now, we can calculate the number of moles of H2O:
\[ \text{Number of moles of } H2O = \frac{\text{mass of } H2O}{\text{molar mass of } H2O} = \frac{0.72 \text{ g}}{18 \text{ g/mol}} \approx 0.04 \text{ moles} \]

### Step 3: Determine the number of moles of carbon and hydrogen
From the combustion reaction:
- Each mole of CO2 contains 1 mole of carbon.
- Each mole of H2O contains 2 moles of hydrogen.

Thus, we can find the moles of carbon and hydrogen:
- Moles of Carbon = Moles of CO2 = 0.07 moles
- Moles of Hydrogen = 2 × Moles of H2O = 2 × 0.04 = 0.08 moles

### Step 4: Find the simplest mole ratio
Now, we need to find the simplest ratio of moles of carbon to moles of hydrogen:
\[ \text{Ratio of C to H} = \frac{\text{moles of C}}{\text{moles of H}} = \frac{0.07}{0.08} = \frac{7}{8} \]

### Step 5: Write the empirical formula
Based on the ratio of moles, the empirical formula of the hydrocarbon can be written as:
\[ \text{Empirical formula} = C_7H_8 \]

### Final Answer
The empirical formula of the hydrocarbon is **C7H8**.

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