To calculate the heat of reaction ([tex]\(\Delta H\)[/tex]) for the given reaction, we need to use the bond energies for the bonds involved in the reaction. The reaction is:
[tex]\[
2 \text{H-Cl} + \text{F-F} \rightarrow 2 \text{H-F} + \text{Cl-Cl}
\][/tex]
We will follow these steps to determine [tex]\(\Delta H\)[/tex]:
1. Identify the bonds broken and their energies:
- 2 bonds of H-Cl
- 1 bond of F-F
2. Identify the bonds formed and their energies:
- 2 bonds of H-F
- 1 bond of Cl-Cl
3. Sum the bond energies of the bonds broken (energy required to break these bonds).
4. Sum the bond energies of the bonds formed (energy released when these bonds are formed).
5. Calculate [tex]\(\Delta H\)[/tex] using the formula:
[tex]\[
\Delta H = \text{Total bond energies of bonds broken} - \text{Total bond energies of bonds formed}
\][/tex]
Given bond energies:
- Bond energy of H-Cl: 431 kJ/mol
- Bond energy of F-F: 158 kJ/mol
- Bond energy of H-F: 565 kJ/mol
- Bond energy of Cl-Cl: 243 kJ/mol
Step-by-Step Calculation:
### Bonds Broken:
- Breaking 2 H-Cl bonds:
[tex]\[
2 \times 431 \text{ kJ/mol} = 862 \text{ kJ/mol}
\][/tex]
- Breaking 1 F-F bond:
[tex]\[
1 \times 158 \text{ kJ/mol} = 158 \text{ kJ/mol}
\][/tex]
Total energy required to break the bonds:
[tex]\[
862 \text{ kJ/mol} + 158 \text{ kJ/mol} = 1020 \text{ kJ/mol}
\][/tex]
### Bonds Formed:
- Forming 2 H-F bonds:
[tex]\[
2 \times 565 \text{ kJ/mol} = 1130 \text{ kJ/mol}
\][/tex]
- Forming 1 Cl-Cl bond:
[tex]\[
1 \times 243 \text{ kJ/mol} = 243 \text{ kJ/mol}
\][/tex]
Total energy released when the bonds are formed:
[tex]\[
1130 \text{ kJ/mol} + 243 \text{ kJ/mol} = 1373 \text{ kJ/mol}
\][/tex]
### Calculate [tex]\(\Delta H\)[/tex]:
[tex]\[
\Delta H = \text{Total bond energies of bonds broken} - \text{Total bond energies of bonds formed}
\][/tex]
[tex]\[
\Delta H = 1020 \text{ kJ/mol} - 1373 \text{ kJ/mol}
\][/tex]
[tex]\[
\Delta H = -353 \text{ kJ/mol}
\][/tex]
Therefore, the heat of reaction ([tex]\(\Delta H\)[/tex]) is [tex]\(-353 \text{ kJ/mol}\)[/tex].
