The heat of atomization of a compound `XY_(3)` in gaseous state is E kJ `mol^(-1)` what is the X-Y bond energy of kJ `mol^(-1)` unit?

Options

A. `E`
B. `3E`
C. `(E)/(3)`
D. `(E)/(6)`

Explanation

To determine the X-Y bond energy from the given heat of atomization of the compound XY₃, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Heat of Atomization**:
The heat of atomization (ΔH) is the energy required to break all the bonds in one mole of a compound to form individual atoms in the gaseous state. For the compound XY₃, the heat of atomization is given as E kJ/mol.

2. **Breaking Down the Compound**:
The compound XY₃ consists of one atom of X and three atoms of Y. When we break down one mole of XY₃, it dissociates into one mole of X and three moles of Y:
\[ \text{XY}_3(g) \rightarrow \text{X}(g) + 3\text{Y}(g) \]

3. **Identifying the Bonds**:
In the compound XY₃, there are three X-Y bonds. Therefore, to completely dissociate one mole of XY₃ into its constituent atoms, we need to break three X-Y bonds.

4. **Relating Heat of Atomization to Bond Energy**:
The total energy required to break all three X-Y bonds is equal to the heat of atomization, which is E kJ/mol. Thus, we can express this relationship as:
\[ \text{Energy to break 3 X-Y bonds} = E \text{ kJ/mol} \]

5. **Calculating the Energy per Bond**:
To find the energy required to break one X-Y bond, we divide the total energy by the number of bonds:
\[ \text{Energy per X-Y bond} = \frac{E}{3} \text{ kJ/mol} \]

### Final Answer:
The X-Y bond energy is \(\frac{E}{3}\) kJ/mol.

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