A cylinder contains either ethylene or propylene 12 ml of gas required 54 ml of oxygen for complete combustion. The gas is

Options

A. Ethylene
B. Propylene
C. `1 : 1` mixture of two gases
D. `1 : 2 `mixture

Answer

To determine whether the gas in the cylinder is ethylene (C2H4) or propylene (C3H6), we need to analyze the stoichiometry of the combustion reactions for both gases and the amount of oxygen required for complete combustion.

### Step-by-Step Solution:

1. **Write the combustion reaction for ethylene (C2H4)**:
\[ \text{C}_2\text{H}_4 + 3\text{O}_2 \rightarrow 2\text{CO}_2 + 2\text{H}_2\text{O} \]
From the balanced equation, we see that 1 mole of ethylene reacts with 3 moles of oxygen.

2. **Calculate the volume of oxygen required for 12 ml of ethylene**:
- According to the stoichiometry, 1 ml of ethylene requires 3 ml of oxygen.
- Therefore, 12 ml of ethylene will require:
\[ 12 \text{ ml C}_2\text{H}_4 \times 3 \text{ ml O}_2/\text{ml C}_2\text{H}_4 = 36 \text{ ml O}_2 \]

3. **Compare with the given oxygen volume**:
- The problem states that 54 ml of oxygen is required for complete combustion.
- Since 36 ml of oxygen is required for 12 ml of ethylene, ethylene cannot be the gas in the cylinder because it does not satisfy the oxygen requirement.

4. **Write the combustion reaction for propylene (C3H6)**:
\[ \text{C}_3\text{H}_6 + \frac{9}{2}\text{O}_2 \rightarrow 3\text{CO}_2 + 3\text{H}_2\text{O} \]
This can also be written as:
\[ \text{C}_3\text{H}_6 + 4.5\text{O}_2 \rightarrow 3\text{CO}_2 + 3\text{H}_2\text{O} \]
From this equation, we see that 1 mole of propylene reacts with 4.5 moles of oxygen.

5. **Calculate the volume of oxygen required for 12 ml of propylene**:
- According to the stoichiometry, 1 ml of propylene requires 4.5 ml of oxygen.
- Therefore, 12 ml of propylene will require:
\[ 12 \text{ ml C}_3\text{H}_6 \times 4.5 \text{ ml O}_2/\text{ml C}_3\text{H}_6 = 54 \text{ ml O}_2 \]

6. **Conclusion**:
- Since 12 ml of propylene requires exactly 54 ml of oxygen for complete combustion, the gas in the cylinder must be propylene.

### Final Answer:
The gas present in the cylinder is **propylene (C3H6)**.

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