In the complete combustion of hydrocarbon `(C_(n)H_(2n+2))` the number of oxygen molecules required per mole of hydrocarbon is

Options

A. `(n)/(2)`
B. `((n+1))/(2)`
C. `((3n+1))/(2)`
D. `(n+(1)/(2))`

Answer

To solve the question regarding the number of oxygen molecules required for the complete combustion of a hydrocarbon represented by the formula \( C_nH_{2n+2} \), we can follow these steps:

### Step-by-Step Solution:

1. **Write the Combustion Reaction**:
The complete combustion of a hydrocarbon can be represented as:
\[ C_nH_{2n+2} + O_2 \rightarrow CO_2 + H_2O \]

2. **Determine the Products**:
During combustion, each carbon atom in the hydrocarbon produces one molecule of carbon dioxide (\( CO_2 \)), and the hydrogen atoms produce water (\( H_2O \)).

3. **Calculate the Number of \( CO_2 \) Produced**:
Since there are \( n \) carbon atoms in \( C_nH_{2n+2} \), the number of \( CO_2 \) molecules produced will be:
\[ n \, CO_2 \]

4. **Calculate the Number of \( H_2O \) Produced**:
The number of hydrogen atoms in \( C_nH_{2n+2} \) is \( 2n + 2 \). Each water molecule contains 2 hydrogen atoms, so the number of water molecules produced will be:
\[ \frac{2n + 2}{2} = n + 1 \, H_2O \]

5. **Count the Total Oxygen Atoms Required**:
Now, we need to calculate the total number of oxygen atoms required for the products:
- Each \( CO_2 \) molecule contains 2 oxygen atoms, so from \( n \) \( CO_2 \) molecules, the total oxygen atoms contributed is:
\[ 2n \, \text{(from } CO_2\text{)} \]
- Each \( H_2O \) molecule contains 1 oxygen atom, so from \( n + 1 \) \( H_2O \) molecules, the total oxygen atoms contributed is:
\[ n + 1 \, \text{(from } H_2O\text{)} \]

6. **Total Oxygen Atoms Needed**:
Adding these together gives the total number of oxygen atoms required:
\[ 2n + (n + 1) = 3n + 1 \]

7. **Calculate the Number of \( O_2 \) Molecules**:
Since each \( O_2 \) molecule contains 2 oxygen atoms, the number of \( O_2 \) molecules required is:
\[ \frac{3n + 1}{2} \]

### Final Answer:
Thus, the number of oxygen molecules required per mole of hydrocarbon \( C_nH_{2n+2} \) is:
\[ \frac{3n + 1}{2} \]