An organic compound is burnt with excess of `O_(2)` to produce `CO_(2)(g)` and `H_(2)O(l)`. Which results in `25%` volume contraction. Which of the following option`(s)` satisfy the given conditins.

Options

A. `10 ml C_(3)H_(8) + 110ml O_(2)`
B. `20ml C_(2)H_(6)O + 80mlO_(2)`
C. `10ml C_(3)H_(6)O_(2) + 50mlO_(2)`
D. `40 ml C_(2)H_(2)O_(4) + 60ml O_(2)`

Explanation

To solve the problem of determining which organic compounds result in a 25% volume contraction when burned with excess oxygen, we can follow these steps:

### Step 1: Understand the Reaction
When an organic compound (hydrocarbon) is burned in excess oxygen, it produces carbon dioxide (CO₂) and water (H₂O). The general reaction can be represented as:
\[ \text{C}_x\text{H}_y + O_2 \rightarrow CO_2 + H_2O \]

### Step 2: Identify Volume Contraction Formula
The percentage of volume contraction can be calculated using the formula:
\[ \text{Percentage Volume Contraction} = \frac{V_{\text{initial}} - V_{\text{final}}}{V_{\text{initial}}} \times 100 \]
Where:
- \( V_{\text{initial}} \) = total initial volume of reactants
- \( V_{\text{final}} \) = total final volume of products

### Step 3: Analyze Each Option
We will analyze each option provided in the question to see if it results in a 25% volume contraction.

#### Option A: 10 ml of Propane (C₃H₈) with 110 ml of O₂
1. **Initial Volume**: \( V_{\text{initial}} = 10 \, \text{ml (C₃H₈)} + 110 \, \text{ml (O₂)} = 120 \, \text{ml} \)
2. **Balanced Reaction**:
\[ C₃H₈ + 5O₂ \rightarrow 3CO₂ + 4H₂O \]
3. **Volume of Products**:
- Propane is limiting, so it will be fully consumed.
- \( 10 \, \text{ml of C₃H₈} \) produces \( 30 \, \text{ml of CO₂} \) and \( 40 \, \text{ml of H₂O} \).
- Remaining O₂: \( 110 - 50 = 60 \, \text{ml} \)
4. **Final Volume**: \( V_{\text{final}} = 30 \, \text{ml (CO₂)} + 40 \, \text{ml (H₂O)} + 60 \, \text{ml (O₂)} = 90 \, \text{ml} \)
5. **Calculate Volume Contraction**:
\[ \text{Percentage Volume Contraction} = \frac{120 - 90}{120} \times 100 = 25\% \]

#### Option B: 20 ml of C₂H₆ with 80 ml of O₂
1. **Initial Volume**: \( V_{\text{initial}} = 20 + 80 = 100 \, \text{ml} \)
2. **Balanced Reaction**:
\[ C₂H₆ + 3.5O₂ \rightarrow 2CO₂ + 3H₂O \]
3. **Volume of Products**:
- Propane is limiting, so it will be fully consumed.
- \( 20 \, \text{ml of C₂H₆} \) produces \( 40 \, \text{ml of CO₂} \) and \( 60 \, \text{ml of H₂O} \).
- Remaining O₂: \( 80 - 60 = 20 \, \text{ml} \)
4. **Final Volume**: \( V_{\text{final}} = 40 + 60 + 20 = 120 \, \text{ml} \)
5. **Calculate Volume Contraction**:
\[ \text{Percentage Volume Contraction} = \frac{100 - 120}{100} \times 100 = -20\% \]

#### Option C: 10 ml of C₃H₆ with 50 ml of O₂
1. **Initial Volume**: \( V_{\text{initial}} = 10 + 50 = 60 \, \text{ml} \)
2. **Balanced Reaction**:
\[ C₃H₆ + 7/2 O₂ \rightarrow 3CO₂ + 3H₂O \]
3. **Volume of Products**:
- Propane is limiting, so it will be fully consumed.
- \( 10 \, \text{ml of C₃H₆} \) produces \( 30 \, \text{ml of CO₂} \) and \( 30 \, \text{ml of H₂O} \).
- Remaining O₂: \( 50 - 35 = 15 \, \text{ml} \)
4. **Final Volume**: \( V_{\text{final}} = 30 + 30 + 15 = 75 \, \text{ml} \)
5. **Calculate Volume Contraction**:
\[ \text{Percentage Volume Contraction} = \frac{60 - 75}{60} \times 100 = -25\% \]

#### Option D: 40 ml of C₂H₄ with 60 ml of O₂
1. **Initial Volume**: \( V_{\text{initial}} = 40 + 60 = 100 \, \text{ml} \)
2. **Balanced Reaction**:
\[ C₂H₄ + 3O₂ \rightarrow 2CO₂ + 2H₂O \]
3. **Volume of Products**:
- Propane is limiting, so it will be fully consumed.
- \( 40 \, \text{ml of C₂H₄} \) produces \( 80 \, \text{ml of CO₂} \) and \( 40 \, \text{ml of H₂O} \).
- Remaining O₂: \( 60 - 60 = 0 \, \text{ml} \)
4. **Final Volume**: \( V_{\text{final}} = 80 + 40 + 0 = 120 \, \text{ml} \)
5. **Calculate Volume Contraction**:
\[ \text{Percentage Volume Contraction} = \frac{100 - 120}{100} \times 100 = -20\% \]

### Conclusion
From the analysis:
- **Option A** results in a 25% volume contraction.
- **Option C** also results in a 25% volume contraction.

### Final Answer
The options that satisfy the condition of a 25% volume contraction are **Option A and Option C**.