`Xg` of ethanal was subjected to combustion in a bomb calorimeter and the heat produced is `Y J`. Then

Options

A. `triangleE_(("combustion"))=-XJ`
B. `triangleE_(("combustion"))=-YJ`
C. `triangleE_(("combustion"))=(44Y)/(X)"J mol"^(-1)`
D. `triangleE_(("combustion"))=(44Y)/(X)"J mol"^(-1)`

Answer

To solve the problem of finding the internal energy change for the combustion of ethanol in a bomb calorimeter, we can follow these steps:

### Step-by-Step Solution:

1. **Write the Combustion Reaction**:
The balanced chemical equation for the combustion of ethanol (C₂H₅OH) is:
\[ \text{C}_2\text{H}_5\text{OH} + \frac{3}{2} \text{O}_2 \rightarrow 2 \text{CO}_2 + 3 \text{H}_2\text{O} \]

2. **Determine the Molecular Mass of Ethanol**:
The molecular mass of ethanol (C₂H₅OH) can be calculated as follows:
- Carbon (C): 12 g/mol × 2 = 24 g/mol
- Hydrogen (H): 1 g/mol × 6 = 6 g/mol
- Oxygen (O): 16 g/mol × 1 = 16 g/mol
- Total = 24 + 6 + 16 = 46 g/mol

3. **Calculate Heat Produced per Gram**:
Given that `Y` Joules of heat is produced from `X` grams of ethanol, the heat produced per gram of ethanol is:
\[ \text{Heat per gram} = \frac{Y}{X} \text{ J/g} \]

4. **Calculate Heat Produced for One Mole**:
Since 1 mole of ethanol weighs 46 grams, the heat produced for 44 grams (the molar mass) can be calculated as:
\[ \text{Heat for 44 g} = \frac{Y}{X} \times 44 \text{ J} \]

5. **Calculate Enthalpy of Combustion**:
The enthalpy change (ΔH) for the combustion reaction per mole of ethanol is:
\[ \Delta H = \frac{Y}{X} \times 44 \text{ J/mol} \]

6. **Relate Internal Energy Change and Enthalpy**:
In a bomb calorimeter, the change in volume (ΔV) is zero, which means:
\[ \Delta U = \Delta H - P \Delta V \]
Since \( P \Delta V = 0 \):
\[ \Delta U = \Delta H \]

7. **Final Expression for Internal Energy Change**:
Therefore, the internal energy change for the combustion reaction is:
\[ \Delta U = \frac{Y}{X} \times 44 \text{ J/mol} \]

### Conclusion:
The internal energy change for the combustion of ethanol in the bomb calorimeter is given by:
\[ \Delta U = \frac{Y \times 44}{X} \text{ J/mol} \]