20 ml of a hydro carbon requires 100 ml of oxygen for complete combustion. In this reaction 60 ml of carbondioxide is produced. The formula of hydro carbon is

Options

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

Explanation

To determine the formula of the hydrocarbon based on the given data, we can follow these steps:

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

### Step 2: Identify the volumes given in the problem.
From the problem, we have:
- Volume of hydrocarbon (C_xH_y) = 20 ml
- Volume of oxygen (O_2) = 100 ml
- Volume of carbon dioxide (CO_2) produced = 60 ml

### Step 3: Use the stoichiometry of the reaction.
From the combustion reaction, we can deduce that:
- For every 1 volume of hydrocarbon, we need a certain amount of oxygen and produce a certain amount of carbon dioxide and water.

### Step 4: Relate the volumes of reactants and products.
According to the stoichiometry of the reaction:
- If 1 volume of hydrocarbon produces 1 volume of CO_2, then:
\[ \text{Volume of CO}_2 = \text{Volume of hydrocarbon} \times \frac{60 \text{ ml}}{20 \text{ ml}} = 3 \text{ volumes of hydrocarbon} \]
- Therefore, if 20 ml of hydrocarbon produces 60 ml of CO_2, it indicates that the hydrocarbon contains 3 carbon atoms.

### Step 5: Determine the number of hydrogen atoms.
We know that:
- The complete combustion of hydrocarbons also produces water (H_2O).
- The volume of oxygen used can be related to the number of hydrogen atoms in the hydrocarbon.
- The balanced equation shows that for every 1 mole of C_xH_y, \((x + \frac{y}{4})\) moles of O_2 are required.

### Step 6: Calculate the required oxygen.
From the stoichiometry, we know:
- 100 ml of O_2 is used for 20 ml of hydrocarbon.
- The ratio of oxygen to hydrocarbon is:
\[ \frac{100 \text{ ml}}{20 \text{ ml}} = 5 \]
- This means that for every 1 volume of hydrocarbon, 5 volumes of O_2 are required.

### Step 7: Set up the equation based on carbon and hydrogen.
From the combustion reaction:
- For 3 carbon atoms (C) in the hydrocarbon, we need 3 CO_2.
- For the hydrogen atoms, we can set up the equation based on the oxygen used:
\[ \text{Oxygen used} = \frac{3}{2} + \frac{y}{4} \]
- We know that 100 ml of O_2 is used, which corresponds to 5 volumes:
\[ 5 = \frac{3}{2} + \frac{y}{4} \]

### Step 8: Solve for y (the number of hydrogen atoms).
Rearranging the equation:
\[ 5 - \frac{3}{2} = \frac{y}{4} \]
\[ \frac{10}{2} - \frac{3}{2} = \frac{y}{4} \]
\[ \frac{7}{2} = \frac{y}{4} \]
Multiplying both sides by 4:
\[ y = 14 \]

### Step 9: Write the formula of the hydrocarbon.
Now we have:
- x (number of carbon atoms) = 3
- y (number of hydrogen atoms) = 14

Thus, the formula of the hydrocarbon is:
\[ C_3H_{14} \]

### Final Answer:
The formula of the hydrocarbon is \( C_3H_{14} \).