When a hydrocarbon A undergoes complete combustion it requires 11 equivalents of oxygen and produces 4 equivalents of water. What is the molecular formula of A ?

Options

A. `C_(11)H_(8)`
B. `C_(11)H_(4)`
C. `C_(5)H_(8)`
D. `C_(9)H_(8)`

Answer

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

### Step 1: Understand the combustion reaction
The general equation for the complete combustion of a hydrocarbon can be written as:
\[ C_xH_y + \left(x + \frac{y}{4}\right) O_2 \rightarrow x CO_2 + \frac{y}{2} H_2O \]
Here, \(x\) is the number of carbon atoms and \(y\) is the number of hydrogen atoms in the hydrocarbon.

### Step 2: Analyze the information given
From the problem, we know:
- The combustion of hydrocarbon A requires 11 equivalents of oxygen.
- It produces 4 equivalents of water.

### Step 3: Relate the water produced to the hydrogen atoms
The number of water molecules produced can be related to the number of hydrogen atoms:
\[ \frac{y}{2} = 4 \]
From this, we can solve for \(y\):
\[ y = 4 \times 2 = 8 \]

### Step 4: Relate the oxygen used to the carbon and hydrogen atoms
We know that the total oxygen required for the combustion is given by:
\[ x + \frac{y}{4} = 11 \]
Substituting the value of \(y\) we found:
\[ x + \frac{8}{4} = 11 \]
This simplifies to:
\[ x + 2 = 11 \]
Now, solving for \(x\):
\[ x = 11 - 2 = 9 \]

### Step 5: Write the molecular formula
Now that we have both \(x\) and \(y\):
- \(x = 9\)
- \(y = 8\)

The molecular formula of hydrocarbon A is:
\[ C_9H_8 \]

### Final Answer
The molecular formula of hydrocarbon A is \(C_9H_8\).

---