4.4 gms of a hydrocarbon on complete combustion produced 13.2 gms of `CO_(2)` and 7.2 gms of `H_(2)O`.
What is the hydrocarbon?

Options

A. a. Propane
B. b. Propene
C. c. Butane
D. d. Butene

Answer

To determine the hydrocarbon from the given data, we will follow these steps:

### Step 1: Calculate the moles of CO2 produced
Given that 4.4 g of hydrocarbon produces 13.2 g of CO2, we first need to find the number of moles of CO2.

**Formula:**
\[ \text{Number of moles of } CO_2 = \frac{\text{mass of } CO_2}{\text{molar mass of } CO_2} \]

**Calculation:**
\[ \text{Molar mass of } CO_2 = 44 \, g/mol \]
\[ \text{Number of moles of } CO_2 = \frac{13.2 \, g}{44 \, g/mol} = 0.3 \, moles \]

### Step 2: Determine the moles of Carbon
Since each mole of CO2 contains one mole of Carbon, the number of moles of Carbon in the hydrocarbon is the same as the moles of CO2.

\[ \text{Moles of Carbon} = 0.3 \, moles \]

### Step 3: Calculate the moles of H2O produced
Next, we calculate the number of moles of H2O produced.

**Formula:**
\[ \text{Number of moles of } H_2O = \frac{\text{mass of } H_2O}{\text{molar mass of } H_2O} \]

**Calculation:**
\[ \text{Molar mass of } H_2O = 18 \, g/mol \]
\[ \text{Number of moles of } H_2O = \frac{7.2 \, g}{18 \, g/mol} = 0.4 \, moles \]

### Step 4: Determine the moles of Hydrogen
Each mole of H2O contains two moles of Hydrogen, so we calculate the total moles of Hydrogen.

\[ \text{Moles of Hydrogen} = 0.4 \times 2 = 0.8 \, moles \]

### Step 5: Determine the empirical formula
Now we have the moles of Carbon and Hydrogen:
- Moles of Carbon = 0.3
- Moles of Hydrogen = 0.8

To find the simplest ratio, we divide both by the smallest number of moles (0.3):

\[ \text{Ratio of Carbon} = \frac{0.3}{0.3} = 1 \]
\[ \text{Ratio of Hydrogen} = \frac{0.8}{0.3} \approx 2.67 \approx 2.67 \text{ (to get whole numbers, we can multiply by 3)} \]

Thus, we multiply both by 3:
- Carbon: \(1 \times 3 = 3\)
- Hydrogen: \(2.67 \times 3 \approx 8\)

The empirical formula is \(C_3H_8\).

### Step 6: Identify the hydrocarbon
The empirical formula \(C_3H_8\) corresponds to propane.

### Final Answer:
The hydrocarbon is **propane (C3H8)**.

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