Twenty millilitres of a gaseous hydrocarbon required 400 ml of iar for complete cumbustion. The air contains `20%` by explosion and cooling was found to be 380 ml.
Q. Formula of the hydrocarbon is:

Options

A. `C_3H_8`
B. `C_3H_6`
C. `C_3H_4`
D. `C_2H_6`

Explanation

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

### Step 1: Understand the combustion reaction
The combustion of a hydrocarbon (CxHy) in the presence of oxygen (O2) produces carbon dioxide (CO2) and water (H2O). The general reaction can be written as:
\[ C_xH_y + \left( \frac{x + y/4}{1} \right) O_2 \rightarrow x CO_2 + \frac{y}{2} H_2O \]

### Step 2: Analyze the given data
We are given:
- Volume of hydrocarbon (V_h) = 20 ml
- Volume of air required for combustion (V_a) = 400 ml
- Air contains 20% O2
- Volume after cooling (V_c) = 380 ml

### Step 3: Calculate the volume of oxygen used
Since air contains 20% oxygen, the volume of oxygen in the air can be calculated as:
\[ V_{O2} = V_a \times \frac{20}{100} = 400 \times 0.2 = 80 \, ml \]

### Step 4: Calculate the volume of nitrogen
The remaining volume of air after subtracting the volume of oxygen gives us the volume of nitrogen (N2):
\[ V_{N2} = V_a - V_{O2} = 400 - 80 = 320 \, ml \]

### Step 5: Calculate the volume of carbon dioxide produced
The volume of carbon dioxide produced can be found by subtracting the volume of nitrogen from the total volume after combustion:
\[ V_{CO2} = V_c - V_{N2} = 380 - 320 = 60 \, ml \]

### Step 6: Relate the volumes to the hydrocarbon
From the combustion reaction, we know:
\[ V_{CO2} = 20x \]
Setting this equal to the calculated volume:
\[ 20x = 60 \]
Solving for x:
\[ x = \frac{60}{20} = 3 \]

### Step 7: Calculate the volume of oxygen in terms of y
From the combustion reaction, we also know:
\[ V_{O2} = 20 \times \left( \frac{x + y/4}{1} \right) \]
Substituting the value of V_{O2} and x:
\[ 80 = 20 \left( 3 + \frac{y}{4} \right) \]
Dividing both sides by 20:
\[ 4 = 3 + \frac{y}{4} \]

### Step 8: Solve for y
Rearranging gives:
\[ \frac{y}{4} = 4 - 3 \]
\[ \frac{y}{4} = 1 \]
Multiplying both sides by 4:
\[ y = 4 \]

### Step 9: Write the formula of the hydrocarbon
Now that we have both x and y, we can write the formula of the hydrocarbon:
\[ C_xH_y = C_3H_4 \]

### Final Answer
The formula of the hydrocarbon is \( C_3H_4 \).

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