Exercise on ΔG°′ and K_eq

The citric acid cycle, which we will study at the end of the semester, has reactions with the following values for ΔG°′, going clockwise around the cycle.

1. What is ΔG°′ when reactions B and C are coupled?

2. Which three reactions are definitely reversible?

3. What is K_eqfor reaction E?

4. What is K_eqfor reaction D?

5. Since this is a cycle, reaction H is followed by reaction A (that is, the product of H is a reactant in A). What is ΔG?' for the coupled H-A reaction?

6. For reaction H alone (not coupled), what must the ([products]/[reactants]) ratio be when ΔG = 0?

7. Which reaction has the largest K_eq? Which has the smallest?

8. Choose a reaction with ΔG°′ > 0 and explain how this reaction can occur in the cell.

9. Try to answer this without doing the calculations. Which reaction is most favorable?
A has K_eq= 23; B has K_eq= 0.0023; C has K_eq= 0.23;

D has ΔG°′ = – 23 kJ/mol; E has ΔG°′ = + 2.3 J/mol; F has ΔG°′ = + 2.3 kJ/mol.

Answers to the Exercise

1. – 17.6 kJ/mol

2. E, F, and G (smallest values for ΔG°′)

3. – 2.9 kJ/mol = – (8.315 J/mol-K) (298 K) ln K_eq
– 2900 J/mol = – (2477.87 J/mol) ln K_eq
ln K_eq= 1.17
K_eq= 3.2

4. 7.4 x 10⁵

5. – 2.5 kJ/mol

6. 0 = 29.7 kJ/mol + R T ln ratio
      –  29,700 J/mol = 2477.87 J/mol (ln ratio)
      –  11.986 = ln ratio
        ratio = 6.2 x 10^–6

7. Largest is D (most favorable); smallest is H (least favorable)

8. H can occur when it is coupled with A, and it can also occur when [products]<<<[reactants].

9. D is most favorable, and B is least favorable.
Results of calculations:

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