1 litre of a hydrocarbon weight as much as one litre of `CO_(2)`. The molecular formula of hydrocarbon is :-

Options

A. `C_(3)H_(8)`
B. `C_(2)H_(6)`
C. `C_(2)H_(4)`
D. `C_(3)H_(6)`

Explanation

To find the molecular formula of a hydrocarbon that weighs the same as 1 litre of CO₂, we can follow these steps:

### Step 1: Understand the Given Information
We know that 1 litre of a hydrocarbon has the same mass as 1 litre of CO₂.

### Step 2: Use Molar Volume of Gases
At standard temperature and pressure (STP), 1 mole of any gas occupies 22.4 litres. Therefore, if 1 litre of CO₂ has the same mass as 1 litre of the hydrocarbon, we can extend this to 22.4 litres.

### Step 3: Calculate the Mass of 1 Litre of CO₂
The molar mass of CO₂ is calculated as follows:
- Carbon (C) = 12 g/mol
- Oxygen (O) = 16 g/mol
- Therefore, CO₂ = 12 + (16 × 2) = 44 g/mol

Since 1 mole of CO₂ occupies 22.4 litres, the mass of 1 litre of CO₂ is:
\[ \text{Mass of 1 litre of CO₂} = \frac{44 \text{ g}}{22.4 \text{ L}} = 1.964 \text{ g/L} \]

### Step 4: Set Up the Equation for Hydrocarbon
Since the mass of 1 litre of the hydrocarbon is equal to the mass of 1 litre of CO₂, we have:
\[ \text{Mass of 1 litre of hydrocarbon} = 1.964 \text{ g/L} \]

### Step 5: Determine the Molar Mass of the Hydrocarbon
Since 1 mole of the hydrocarbon also occupies 22.4 litres, the mass of 1 mole of the hydrocarbon must also equal 44 g (the same as CO₂).

### Step 6: Identify Possible Hydrocarbons
We need to find a hydrocarbon (CₓHᵧ) with a molar mass of 44 g/mol. The general formula for alkanes is CₙH₂ₙ₊₂.

### Step 7: Calculate Molar Mass for Common Hydrocarbons
1. For **C₃H₈ (Propane)**:
\[ \text{Molar mass} = (3 \times 12) + (8 \times 1) = 36 + 8 = 44 \text{ g/mol} \]

2. For **C₂H₆ (Ethane)**:
\[ \text{Molar mass} = (2 \times 12) + (6 \times 1) = 24 + 6 = 30 \text{ g/mol} \]

3. For **C₄H₁₀ (Butane)**:
\[ \text{Molar mass} = (4 \times 12) + (10 \times 1) = 48 + 10 = 58 \text{ g/mol} \]

4. For **C₃H₆ (Propene)**:
\[ \text{Molar mass} = (3 \times 12) + (6 \times 1) = 36 + 6 = 42 \text{ g/mol} \]

### Step 8: Conclusion
The only hydrocarbon with a molar mass of 44 g/mol is **C₃H₈ (Propane)**.

Thus, the molecular formula of the hydrocarbon is **C₃H₈**.

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