10 ml of hydrocarbon requries 55 ml of oxygen for complete combustion producing 40 ml of `CO_(2)`. The formula of the hydrocarbon is:

Options

A. `C_4H_10`
B. `C_4H_6`
C. `C_4H_7Cl`
D. `C_4H_8`

Answer

To determine the formula of the hydrocarbon, we will follow these steps:

### Step 1: Write the general formula for the combustion reaction
Assume the hydrocarbon has the formula \( C_xH_y \). The complete combustion of a hydrocarbon can be represented as:
\[ C_xH_y + O_2 \rightarrow CO_2 + H_2O \]

### Step 2: Balance the combustion reaction
From the combustion reaction:
- Each carbon atom produces one molecule of \( CO_2 \), so \( x \) moles of carbon will produce \( x \) moles of \( CO_2 \).
- Each two hydrogen atoms produce one molecule of \( H_2O \), so \( y \) moles of hydrogen will produce \( \frac{y}{2} \) moles of \( H_2O \).

Now, we can balance the oxygen:
- The total oxygen required will be \( x \) (from \( CO_2 \)) + \( \frac{y}{2} \) (from \( H_2O \)), which gives us:
\[ \text{Total O} = x + \frac{y}{4} \]

### Step 3: Set up the equations based on the given data
We know:
- 10 mL of hydrocarbon requires 55 mL of oxygen.
- The combustion produces 40 mL of \( CO_2 \).

From the information given:
1. The volume of \( CO_2 \) produced is \( 10x = 40 \) mL.
2. The volume of oxygen used is \( 10(x + \frac{y}{4}) = 55 \) mL.

### Step 4: Solve for \( x \)
From the first equation:
\[ 10x = 40 \implies x = \frac{40}{10} = 4 \]

### Step 5: Solve for \( y \)
Now substitute \( x \) into the second equation:
\[ 10(4 + \frac{y}{4}) = 55 \]
\[ 40 + \frac{10y}{4} = 55 \]
\[ \frac{10y}{4} = 55 - 40 \]
\[ \frac{10y}{4} = 15 \]
\[ 10y = 15 \times 4 \]
\[ 10y = 60 \implies y = \frac{60}{10} = 6 \]

### Step 6: Write the formula of the hydrocarbon
Now that we have \( x = 4 \) and \( y = 6 \), the formula of the hydrocarbon is:
\[ C_4H_6 \]

### Final Answer
The formula of the hydrocarbon is \( C_4H_6 \).

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