20 mL of a gaseous hydrocarbon was exploded with 120 mL of oxygen . A contraction of 60 mL was observed and a further contraction of 60 mL took place when KOH was added. What is the formula of the hydrocarbon?

Options

A. `C_(3)H_(6)`
B. `C_(3)H_(8)`
C. `C_(2)H_(6)`
D. `C_(4)H_(10)`

Answer

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

### Step 1: Understand the Reaction
The hydrocarbon (CxHy) reacts with oxygen (O2) to produce carbon dioxide (CO2) and water (H2O). The general combustion reaction can be represented as:
\[ C_xH_y + O_2 \rightarrow CO_2 + H_2O \]

### Step 2: Analyze the Volume Changes
- Initial volume of hydrocarbon = 20 mL
- Volume of oxygen used = 120 mL
- Contraction after combustion = 60 mL
- Further contraction after KOH addition = 60 mL

### Step 3: Calculate the Volume of Gases After Combustion
After the combustion of the hydrocarbon with oxygen, a contraction of 60 mL indicates that the volume of gaseous products (CO2 and H2O vapor) is less than the total volume of reactants.

The total volume of gases before the reaction:
\[ \text{Total initial volume} = \text{Volume of hydrocarbon} + \text{Volume of oxygen} = 20 \, \text{mL} + 120 \, \text{mL} = 140 \, \text{mL} \]

After the first contraction:
\[ \text{Volume after combustion} = 140 \, \text{mL} - 60 \, \text{mL} = 80 \, \text{mL} \]

### Step 4: Analyze the Effect of KOH
KOH absorbs CO2 from the gas mixture. The second contraction of 60 mL indicates that all the CO2 produced was absorbed by KOH.

Thus, the volume of CO2 produced is 60 mL.

### Step 5: Determine the Amount of Hydrocarbon
From the stoichiometry of the reaction:
1 mole of hydrocarbon produces 1 mole of CO2. Therefore, the volume of hydrocarbon that produced 60 mL of CO2 can be calculated using the ratio of volumes (at the same temperature and pressure).

Since 60 mL of CO2 was produced, the volume of hydrocarbon that reacted can be calculated as follows:
- The volume of hydrocarbon that produced 60 mL of CO2 is 20 mL (initial volume).
- The volume of oxygen consumed can be calculated using the stoichiometry of the reaction.

### Step 6: Calculate the Volume of Oxygen Consumed
From the reaction, we can assume that for every 1 mole of hydrocarbon, a certain amount of oxygen is required. Let's denote the hydrocarbon as CxHy:
- The combustion of hydrocarbons generally requires 1 mole of hydrocarbon to react with 1.5 moles of O2 for complete combustion.
- Therefore, if 60 mL of CO2 was produced, it would require 60 mL of O2.

### Step 7: Determine the Formula of the Hydrocarbon
From the stoichiometry:
- If 20 mL of hydrocarbon produces 60 mL of CO2, we can set up the equation:
\[ C_xH_y + 3O_2 \rightarrow 2CO_2 + 2H_2O \]

From the above, we can deduce:
- C: 2 moles (from 2 CO2)
- H: 4 moles (from 2 H2O)

Thus, the hydrocarbon can be represented as:
\[ C_2H_4 \]

### Final Answer
The formula of the hydrocarbon is \( C_2H_4 \) (ethene).