6 litre of mixture of methane and propane on complete combustion gives 7 litre of `CO_(2)`. Find out the composition of the mixture ?

Options

A. `5.5 `lit, `0.5` lit.
B. `4.5` lit, `1.5 ` lit
C. `3.5` lit, `1.5 ` lit
D. None of these

Explanation

To find the composition of the mixture of methane (CH₄) and propane (C₃H₈) that produces 7 liters of carbon dioxide (CO₂) upon complete combustion, we can follow these steps:

### Step 1: Define Variables
Let:
- \( x \) = volume of methane (in liters)
- \( 6 - x \) = volume of propane (in liters)

### Step 2: Write the Combustion Reactions
1. The combustion of methane:
\[ \text{CH}_4 + 2\text{O}_2 \rightarrow \text{CO}_2 + 2\text{H}_2\text{O} \]
From this reaction, we see that 1 liter of methane produces 1 liter of CO₂.

2. The combustion of propane:
\[ \text{C}_3\text{H}_8 + 5\text{O}_2 \rightarrow 3\text{CO}_2 + 4\text{H}_2\text{O} \]
From this reaction, we see that 1 liter of propane produces 3 liters of CO₂.

### Step 3: Calculate CO₂ Production
From the combustion of the mixture:
- CO₂ produced from methane = \( x \) liters
- CO₂ produced from propane = \( 3(6 - x) \) liters

### Step 4: Set Up the Equation
The total volume of CO₂ produced from the combustion of the mixture is given as 7 liters:
\[ x + 3(6 - x) = 7 \]

### Step 5: Simplify the Equation
Expanding the equation:
\[ x + 18 - 3x = 7 \]
Combine like terms:
\[ -2x + 18 = 7 \]

### Step 6: Solve for \( x \)
Rearranging gives:
\[ -2x = 7 - 18 \]
\[ -2x = -11 \]
\[ x = \frac{11}{2} = 5.5 \text{ liters (volume of methane)} \]

### Step 7: Calculate Volume of Propane
Now, substitute \( x \) back to find the volume of propane:
\[ \text{Volume of propane} = 6 - x = 6 - \frac{11}{2} = \frac{12}{2} - \frac{11}{2} = \frac{1}{2} = 0.5 \text{ liters} \]

### Conclusion
The composition of the mixture is:
- Volume of methane = 5.5 liters
- Volume of propane = 0.5 liters