To solve this question, we need to calculate the net energy change for the reaction between hydrogen and chlorine as shown:
[tex]\[
H - H + Cl - Cl \longrightarrow 2 H - Cl
\][/tex]
First, we need to break the bonds of [tex]\(H - H\)[/tex] and [tex]\(Cl - Cl\)[/tex]. These are the bond energies we must consider first:
- The bond energy for [tex]\(H - H\)[/tex] is [tex]\(436 \text{ kJ/mol}\)[/tex].
- The bond energy for [tex]\(Cl - Cl\)[/tex] is [tex]\(346 \text{ kJ/mol}\)[/tex].
The total energy required to break these bonds (energy input) is:
[tex]\[
436 + 346 \text{ kJ/mol} = 782 \text{ kJ/mol}
\][/tex]
Next, new bonds are formed to create [tex]\(2 \times H - Cl\)[/tex]:
- The bond energy for [tex]\(H - Cl\)[/tex] is [tex]\(432 \text{ kJ/mol}\)[/tex].
Since we form two [tex]\(H - Cl\)[/tex] bonds, the total energy released (energy output) is:
[tex]\[
2 \times 432 \text{ kJ/mol} = 864 \text{ kJ/mol}
\][/tex]
Finally, we calculate the net energy change for the reaction:
[tex]\[
\text{Net energy} = \text{Energy input} - \text{Energy output}
\][/tex]
[tex]\[
\text{Net energy} = 782 \text{ kJ/mol} - 864 \text{ kJ/mol} = -82 \text{ kJ/mol}
\][/tex]
The correct answer should reflect the energy changes we calculated. Out of the given options, the option that correctly represents our calculations is:
[tex]\[
436 + 346 - (2 \times 432) \text{ kJ/mol}
\][/tex]
Thus, the box with:
[tex]\[
\checkmark \quad 436 + 346 - (2 \times 432) \text{ kJ/mol}
\][/tex]
is the correct choice.
