A gaseous mixture of propane and butane of volume 3 litre on complete combustion produces
11.0 litre `CO_(2)` under standard conditions of temperature and pressure.
The ration of volume of butane to propane is:

Options

A. `1:2`
B. `2:1`
C. `3:2`
D. `3:1`

Answer

To solve the problem, we need to determine the ratio of the volume of butane (C4H10) to the volume of propane (C3H8) in a gaseous mixture that produces a specific volume of CO2 upon complete combustion. Here’s a step-by-step solution:

### Step 1: Define the Variables
Let:
- \( V \) = volume of propane (C3H8) in liters
- \( 3 - V \) = volume of butane (C4H10) in liters

### Step 2: Write the Combustion Reactions
The complete combustion reactions for propane and butane are as follows:
- For propane (C3H8):
\[ C3H8 + 5O2 \rightarrow 3CO2 + 4H2O \]
This means that 1 liter of propane produces 3 liters of CO2.

- For butane (C4H10):
\[ C4H10 + 13/2 O2 \rightarrow 4CO2 + 5H2O \]
This means that 1 liter of butane produces 4 liters of CO2.

### Step 3: Calculate the Total Volume of CO2 Produced
From the combustion of propane:
- Volume of CO2 from propane = \( 3V \) liters

From the combustion of butane:
- Volume of CO2 from butane = \( 4(3 - V) \) liters

### Step 4: Set Up the Equation
According to the problem, the total volume of CO2 produced is 11 liters. Therefore, we can set up the following equation:
\[ 3V + 4(3 - V) = 11 \]

### Step 5: Simplify the Equation
Expanding the equation:
\[ 3V + 12 - 4V = 11 \]
Combining like terms:
\[ -1V + 12 = 11 \]

### Step 6: Solve for V
Rearranging the equation gives:
\[ -1V = 11 - 12 \]
\[ -1V = -1 \]
\[ V = 1 \text{ liter} \]

### Step 7: Determine the Volume of Butane
Now, substitute \( V \) back to find the volume of butane:
\[ \text{Volume of butane} = 3 - V = 3 - 1 = 2 \text{ liters} \]

### Step 8: Calculate the Ratio of Butane to Propane
Now, we can find the ratio of the volume of butane to the volume of propane:
\[ \text{Ratio of butane to propane} = \frac{\text{Volume of butane}}{\text{Volume of propane}} = \frac{2}{1} = 2 \]

### Final Answer
The ratio of the volume of butane to propane is \( 2:1 \).

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