20 ml of a mixture of `C_(2)H_(2)` and CO was exploded with 30 ml of oxygen. The gases after the reaction had a volume of 34 ml. On treatment with KOH, 8 ml of oxygen gas remain unreacted. Which of the following options show a correct composition of the mixture? 

Options

A. `V_("ethyne")= 6ml` and `V_("co")= 14 ml`
B. `V_("ethyne")= 4ml` and `V_("co")= 16 ml`
C. `V_("ethyne")= 2ml` and `V_("co")= 18 ml`
D. `V_("ethyne")= 5ml` and `V_("co")= 15 ml`

Explanation

To solve the problem step by step, we will analyze the given information and apply the principles of stoichiometry and gas laws.

### Step 1: Understand the Reaction
The reaction between acetylene (C₂H₂) and carbon monoxide (CO) with oxygen (O₂) can be represented as:
\[ \text{C}_2\text{H}_2 + \text{CO} + \text{O}_2 \rightarrow \text{CO}_2 + \text{H}_2 \]

### Step 2: Analyze the Initial Conditions
We have a mixture of C₂H₂ and CO with a total volume of 20 ml. Let:
- Volume of C₂H₂ = \( x \) ml
- Volume of CO = \( 20 - x \) ml

### Step 3: Analyze the Reaction with Oxygen
The total volume of oxygen used is 30 ml. After the reaction, the total volume of gases left is 34 ml. The volume of gases after the reaction can be calculated as:
\[ \text{Volume of gases after reaction} = \text{Initial volume of gases} - \text{Volume of gases consumed} + \text{Volume of gases produced} \]

### Step 4: Calculate the Volume of Gases Consumed
The volume of gases consumed can be calculated as:
\[ \text{Volume of gases consumed} = \text{Initial volume of C}_2\text{H}_2 + \text{Initial volume of CO} + \text{Initial volume of O}_2 - \text{Volume of gases after reaction} \]
Substituting the values:
\[ = (x + (20 - x) + 30) - 34 = 16 + 30 - 34 = 12 \text{ ml} \]

### Step 5: Relate the Volume of Reactants to Products
From the reaction stoichiometry, we know:
- 1 ml of C₂H₂ reacts with 1 ml of O₂ to produce 1 ml of CO₂.
- 1 ml of CO reacts with 1 ml of O₂ to produce 1 ml of CO₂.

Thus, the total volume of O₂ consumed can be expressed as:
\[ \text{Volume of O}_2 = x + (20 - x) = 20 \text{ ml} \]

### Step 6: Set Up the Equation
From the previous steps, we can set up the equation:
\[ x + (20 - x) + \text{Volume of O}_2 = 12 \]
Given that the total volume of O₂ used is 30 ml, we can express:
\[ 30 - \text{Volume of O}_2 = 34 \]
This gives us:
\[ \text{Volume of O}_2 = 30 - 34 + 12 = 8 \text{ ml} \]

### Step 7: Solve for x
From the equation derived, we have:
\[ x + (20 - x) + 8 = 34 \]
This simplifies to:
\[ 20 + 8 = 34 \]
Thus, we can conclude:
\[ x = 6 \text{ ml} \]
So, the volume of C₂H₂ is 6 ml and the volume of CO is:
\[ 20 - x = 20 - 6 = 14 \text{ ml} \]

### Final Composition
- Volume of C₂H₂ = 6 ml
- Volume of CO = 14 ml

### Conclusion
The correct composition of the mixture is:
- C₂H₂: 6 ml
- CO: 14 ml