12 Litres of `CO_(2)` gas is obtained on complete combustion of 5 litre gaseous mixture of ehtane and propane then what will be the percentage amount of ethane in mixture ?

Options

A. 0.6
B. 0.4
C. 0.5
D. 0.75

Answer

To solve the problem, we need to determine the percentage of ethane in a gaseous mixture of ethane and propane based on the volume of carbon dioxide produced during their combustion. Here’s a step-by-step breakdown:

### Step 1: Understand the combustion reactions
- The combustion of ethane (C₂H₆) can be represented as:
\[ \text{C}_2\text{H}_6 + \frac{7}{2} \text{O}_2 \rightarrow 2 \text{CO}_2 + 3 \text{H}_2\text{O} \]
From this reaction, we see that 1 liter of ethane produces 2 liters of carbon dioxide.

- The combustion of propane (C₃H₈) can be represented as:
\[ \text{C}_3\text{H}_8 + 5 \text{O}_2 \rightarrow 3 \text{CO}_2 + 4 \text{H}_2\text{O} \]
From this reaction, we see that 1 liter of propane produces 3 liters of carbon dioxide.

### Step 2: Define variables
Let:
- \( x \) = volume of ethane in liters
- \( 5 - x \) = volume of propane in liters (since the total volume of the mixture is 5 liters)

### Step 3: Calculate the total volume of CO₂ produced
From the combustion reactions:
- The volume of CO₂ produced from \( x \) liters of ethane:
\[ \text{CO}_2 \text{ from ethane} = 2x \text{ liters} \]
- The volume of CO₂ produced from \( 5 - x \) liters of propane:
\[ \text{CO}_2 \text{ from propane} = 3(5 - x) \text{ liters} \]

### Step 4: Set up the equation
According to the problem, the total volume of CO₂ produced is 12 liters:
\[ 2x + 3(5 - x) = 12 \]

### Step 5: Solve the equation
Expanding the equation:
\[ 2x + 15 - 3x = 12 \]
Combining like terms:
\[ -1x + 15 = 12 \]
Subtracting 15 from both sides:
\[ -1x = 12 - 15 \]
\[ -1x = -3 \]
Dividing by -1:
\[ x = 3 \]

### Step 6: Calculate the volume of propane
Now, substituting back to find the volume of propane:
\[ \text{Volume of propane} = 5 - x = 5 - 3 = 2 \text{ liters} \]

### Step 7: Calculate the percentage of ethane in the mixture
The percentage of ethane in the mixture is calculated as:
\[ \text{Percentage of ethane} = \left( \frac{x}{\text{Total volume}} \right) \times 100 = \left( \frac{3}{5} \right) \times 100 = 60\% \]

### Final Answer
The percentage amount of ethane in the mixture is **60%**.

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