`10 mL` of a gaseous hydrocarbon is exploded with `100 mL` of oxygen. The residual gas on cooling is found to measure `95 mL` of which `20 mL` is absorbed by caustic soda and the remainder by alkaline pyrollgallol. The fomula of the hydrocarbon is

Options

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

Explanation

To solve the problem step by step, we will analyze the combustion of the hydrocarbon and the gases involved.

### Step 1: Write the general combustion reaction of a hydrocarbon.
The general reaction of a hydrocarbon (CxHy) with oxygen (O2) can be written as:
\[ \text{CxHy} + \left( \frac{x + y/4}{1} \right) \text{O2} \rightarrow x \text{CO2} + \frac{y}{2} \text{H2O} + \text{Heat} \]

### Step 2: Identify the volumes of gases involved.
From the question, we have:
- Volume of hydrocarbon (CxHy) = 10 mL
- Volume of oxygen (O2) = 100 mL
- Residual gas after the reaction = 95 mL
- Volume of CO2 absorbed by caustic soda = 20 mL

### Step 3: Calculate the volume of CO2 produced.
Since the volume of CO2 absorbed by caustic soda is 20 mL, we can conclude that:
\[ \text{Volume of CO2 produced} = 20 \text{ mL} \]

### Step 4: Relate the volume of CO2 to the hydrocarbon.
From the combustion reaction, we know that:
\[ \text{Volume of CO2} = 10x \]
Setting this equal to the volume we found:
\[ 10x = 20 \]
Thus, solving for x:
\[ x = 2 \]

### Step 5: Calculate the volume of residual oxygen.
The total volume of residual gas is 95 mL, which consists of CO2 and unreacted O2. Since we have 20 mL of CO2, the remaining volume must be O2:
\[ \text{Volume of O2 left} = 95 \text{ mL} - 20 \text{ mL} = 75 \text{ mL} \]

### Step 6: Relate the volume of remaining O2 to the initial O2.
The initial volume of O2 was 100 mL. The volume of O2 that reacted can be calculated as:
\[ \text{Volume of O2 reacted} = 100 \text{ mL} - 75 \text{ mL} = 25 \text{ mL} \]

### Step 7: Set up the equation for O2 consumption.
From the combustion reaction, the volume of O2 consumed can also be expressed as:
\[ \text{Volume of O2 reacted} = 10 \left( x + \frac{y}{4} \right) \]
Setting this equal to the volume we found:
\[ 10 \left( 2 + \frac{y}{4} \right) = 25 \]
Dividing both sides by 10 gives:
\[ 2 + \frac{y}{4} = 2.5 \]

### Step 8: Solve for y.
Rearranging the equation:
\[ \frac{y}{4} = 2.5 - 2 \]
\[ \frac{y}{4} = 0.5 \]
Multiplying both sides by 4:
\[ y = 2 \]

### Step 9: Write the formula of the hydrocarbon.
Now that we have both x and y:
- \( x = 2 \)
- \( y = 2 \)

Thus, the formula of the hydrocarbon is:
\[ \text{C}_2\text{H}_2 \]

### Final Answer:
The formula of the hydrocarbon is \( \text{C}_2\text{H}_2 \).

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