Question

Use Hess's law to calculate ΔG°rxn using the following information.

ClO(g) + O3(g) → Cl(g) + 2 O2(g) ΔG°rxn = ?
2 O3(g)→ 3 O2(g) ΔG°rxn = +489.6 kJ
Cl(g) + O3(g) → ClO(g) + O2(g) ΔG°rxn = -34.5 kJ

Answer 1

To find the change in free energy (ΔG°rxn) for the reaction ClO(g) + O3(g) → Cl(g) + 2 O2(g) using Hess's law, we manipulate and sum the given reactions. After calculations, the ΔG°rxn is +558.6 kJ.

Step-by-step explanation:

To calculate the ΔG°rxn for the reaction ClO(g) + O3(g) → Cl(g) + 2 O2(g), we can employ Hess's law, which states that if a reaction is carried out in a series of steps, the ΔG° for the overall reaction will be the sum of the enthalpy changes for the individual steps.

The given reactions are:

1. 2 O3(g) → 3 O2(g) ΔG°rxn = +489.6 kJ
2. Cl(g) + O3(g) → ClO(g) + O2(g) ΔG°rxn = -34.5 kJ

We need to manipulate these reactions to sum up to the target reaction. By reversing the second reaction and multiplying it by 2, we align the reactions with the target reaction:

1. 2 O3(g) → 3 O2(g) ΔG°rxn = +489.6 kJ
2. 2 ClO(g) + 2 O2(g) → 2 Cl(g) + 2 O3(g) ΔG°rxn = +69.0 kJ

Add these equations:

4 O3(g) → 3 O2(g) + 2 ClO(g) + 2 O2(g) → 2 Cl(g) + 2 O3(g) + 3 O2(g)

Cancelling out the common species, the final equation looks like this:

ClO(g) + O3(g) → Cl(g) + 2 O2(g) ΔG°rxn = +489.6 kJ + 69.0 kJ
= +558.6 kJ