0.2 moles of a hydro carbon, cannot decolourise bromine water, on complete combustion it produces 26.4 gm of `CO_(2)`. The molecular weight of the hydro carbon is

Options

A. 44
B. 42
C. 40
D. 58

Explanation

To find the molecular weight of the hydrocarbon, we can follow these steps:

### Step 1: Determine the number of moles of CO2 produced
We know that 0.2 moles of the hydrocarbon produce 26.4 grams of CO2.

To find the number of moles of CO2, we use the formula:
\[ \text{Number of moles} = \frac{\text{Given weight}}{\text{Molecular weight}} \]
The molecular weight of CO2 is 44 g/mol. Thus, we can calculate the number of moles of CO2:
\[ \text{Number of moles of CO2} = \frac{26.4 \text{ g}}{44 \text{ g/mol}} = 0.6 \text{ moles} \]

### Step 2: Relate moles of hydrocarbon to moles of CO2
From the combustion reaction, we know that 1 mole of hydrocarbon produces 3 moles of CO2. Therefore, we can set up the following relationship:
\[ 0.2 \text{ moles of hydrocarbon} \rightarrow 0.6 \text{ moles of CO2} \]
To find the number of moles of CO2 produced per mole of hydrocarbon, we can calculate:
\[ \text{Moles of CO2 per mole of hydrocarbon} = \frac{0.6 \text{ moles}}{0.2 \text{ moles}} = 3 \]

### Step 3: Determine the number of carbon atoms in the hydrocarbon
Since 1 mole of hydrocarbon produces 3 moles of CO2, it indicates that there are 3 carbon atoms in the hydrocarbon. Therefore, we can conclude:
\[ n = 3 \quad (\text{where } n \text{ is the number of carbon atoms}) \]

### Step 4: Write the molecular formula of the hydrocarbon
The general formula for an alkane is given by:
\[ C_nH_{2n+2} \]
Substituting \( n = 3 \):
\[ \text{Molecular formula} = C_3H_{2(3)+2} = C_3H_8 \]

### Step 5: Calculate the molecular weight of the hydrocarbon
To find the molecular weight of C3H8, we calculate:
\[ \text{Molecular weight} = (3 \times 12 \text{ g/mol}) + (8 \times 1 \text{ g/mol}) = 36 \text{ g/mol} + 8 \text{ g/mol} = 44 \text{ g/mol} \]

### Conclusion
The molecular weight of the hydrocarbon is **44 g/mol**.

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