For the reaction

glutamate - (aq) + oxaloacetate2 - (aq) α-ketoglutarate2 - (aq) + aspartate - (aq)

the equilibrium constant at standard temperature is Keq′ = 2.82. Suppose the concentrations of glutamate and oxaloacetate were 10 mM and the concentration of α-ketoglutarate was 25 mM when the system was at equilibrium. An additional 25 mM of α-ketoglutarate is added to the solution.

After the α-ketoglutarate is added, when the system has settled down and no net reaction is occurring, what is the value of ΔG' for this reaction?

We are asked to find the value of ΔG°rxn from the equilibrium concentrations of the reactants and products. We can use the following formula:

ΔG°rxn = - RTlnK

The value of R = 8.314 J/Kmol, T = 298.15 K and we are given the equilibrium constant Keq = 2.82.

The question provides equilibrium concentrations and then asks to find ΔG°rxn when more of a product is added to the reaction mixture. However, you are asked to find ΔG after the reaction has settled down and reached equilibrium once more. Therefore, we can simply use Keq = 2.82 still and solve for ΔG.

ΔG°rxn = - (8.314 J/Kmol) (298.15 K) (ln (2.82))

ΔG°rxn = - 2570 J/mol

ΔG°rxn = - 2.57 kJ/mol

Under equilibrium conditions at standard temperature and pressures, the value of ΔG°rxn = - 2.57 kJ/mol.