40 ml of gaseous mixture of CO and ethyne is mixed with 100 ml of `O_2` and burnt. The volume of gases after combustion is 105 ml. The composition of the original mixture is

Options

A. 25 ml CO, 15 ml ethyne
B. 15 ml CO, 25 ml ethyne
C. 10 ml CO, 30 ml ethyne
D. 20 ml CO, 20 ml ethyne

Answer

To solve the problem step by step, we will analyze the combustion of carbon monoxide (CO) and ethyne (C2H2) in the presence of oxygen (O2) and determine their original volumes in the gaseous mixture.

### Step 1: Define Variables
Let:
- \( x \) = volume of CO in the mixture (in mL)
- \( 40 - x \) = volume of C2H2 in the mixture (in mL)

### Step 2: Write the Combustion Reactions
1. **Combustion of Ethyne (C2H2)**:
\[ 2 \text{C}_2\text{H}_2 + 5 \text{O}_2 \rightarrow 4 \text{CO}_2 + 2 \text{H}_2\text{O} \]
From this reaction, for every 2 mL of C2H2, 5 mL of O2 is consumed, producing 4 mL of CO2.

2. **Combustion of Carbon Monoxide (CO)**:
\[ 2 \text{CO} + \text{O}_2 \rightarrow 2 \text{CO}_2 \]
From this reaction, for every 1 mL of CO, 0.5 mL of O2 is consumed, producing 1 mL of CO2.

### Step 3: Calculate the Volume of Gases Produced
- The volume of CO2 produced from C2H2:
\[ \text{CO2 from C2H2} = 2 \times (40 - x) = 80 - 2x \text{ mL} \]
- The volume of CO2 produced from CO:
\[ \text{CO2 from CO} = x \text{ mL} \]

### Step 4: Total Volume of CO2 Produced
The total volume of CO2 produced after combustion is:
\[ \text{Total CO2} = (80 - 2x) + x = 80 - x \text{ mL} \]

### Step 5: Calculate the Volume of O2 Consumed
- Volume of O2 consumed from C2H2:
\[ \text{O2 from C2H2} = \frac{5}{2} \times (40 - x) = 100 - \frac{5}{2}x \text{ mL} \]
- Volume of O2 consumed from CO:
\[ \text{O2 from CO} = \frac{1}{2}x \text{ mL} \]

### Step 6: Total Volume of O2 Consumed
The total volume of O2 consumed is:
\[ \text{Total O2} = \left(100 - \frac{5}{2}x\right) + \left(\frac{1}{2}x\right) = 100 - 2x \text{ mL} \]

### Step 7: Set Up the Equation
The total volume of gases after combustion is given as 105 mL. The volume of gases after combustion includes the remaining O2 and the produced CO2:
\[ \text{Total Volume After Combustion} = \text{Total CO2} + \text{Remaining O2} \]
The remaining O2 is:
\[ \text{Remaining O2} = 100 - (100 - 2x) = 2x \text{ mL} \]
Thus, we have:
\[ (80 - x) + 2x = 105 \]

### Step 8: Solve the Equation
Simplifying the equation:
\[ 80 - x + 2x = 105 \]
\[ 80 + x = 105 \]
\[ x = 105 - 80 = 25 \text{ mL} \]

### Step 9: Find the Volume of C2H2
Using \( x = 25 \text{ mL} \):
\[ \text{Volume of C2H2} = 40 - x = 40 - 25 = 15 \text{ mL} \]

### Final Answer
The composition of the original mixture is:
- Volume of CO = 25 mL
- Volume of C2H2 = 15 mL