A gas mixture contains acetylene and carbondioxide. 20 litres of this mixture requires 20 litres of oxygen for complete combustion. If all gases are measured under similar conditions of temperature and pressure, the percentage of acetylene in the mixture is

Options

A. `50%`
B. `40%`
C. `60%`
D. `75%`

Explanation

To find the percentage of acetylene (C2H2) in a gas mixture that contains acetylene and carbon dioxide (CO2), we can follow these steps:

### Step 1: Understand the combustion reaction
The combustion of acetylene can be represented by the following balanced chemical equation:
\[ \text{C}_2\text{H}_2 + 2.5 \text{O}_2 \rightarrow 2 \text{CO}_2 + \text{H}_2\text{O} \]

From this equation, we see that 1 mole of acetylene reacts with 2.5 moles of oxygen.

### Step 2: Calculate the volume of oxygen required for combustion
Given that 20 liters of the gas mixture requires 20 liters of oxygen for complete combustion, we can conclude that all the oxygen is used for the combustion of acetylene since carbon dioxide does not participate in combustion.

### Step 3: Determine the volume of acetylene that reacts
Using the stoichiometry from the combustion reaction, we can calculate how much acetylene is consumed by 20 liters of oxygen.

From the equation:
- 2.5 liters of O2 are required for 1 liter of C2H2.

Using the unitary method:
- For 20 liters of O2, the volume of C2H2 consumed can be calculated as:
\[ \text{Volume of C2H2} = \left(\frac{1 \text{ liter C2H2}}{2.5 \text{ liters O2}}\right) \times 20 \text{ liters O2 = } \frac{20}{2.5} \text{ liters C2H2 = 8 liters C2H2} \]

### Step 4: Calculate the percentage of acetylene in the mixture
Now, we know that 8 liters of acetylene are present in the total 20 liters of the gas mixture. To find the percentage of acetylene in the mixture, we use the formula:
\[ \text{Percentage of C2H2} = \left(\frac{\text{Volume of C2H2}}{\text{Total volume of mixture}}\right) \times 100 \]
Substituting the values:
\[ \text{Percentage of C2H2} = \left(\frac{8 \text{ liters}}{20 \text{ liters}}\right) \times 100 = 40\% \]

### Conclusion
The percentage of acetylene in the mixture is **40%**.

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