Question

Consider the malate dehydrogenase reaction from the citric acid cycle. Given the listed concentrations, calculate the free energy change for this reaction at energy change for this reaction at 37.0 ∘C37.0 ∘C (310 K). ΔG∘′ΔG∘′ for the reaction is +29.7 kJ/mol+29.7 kJ/mol . Assume that the reaction occurs at pH 7. [malate]=1.37 mM [malate]=1.37 mM [oxaloacetate]=0.130 mM [oxaloacetate]=0.130 mM [NAD+]=490 mM [NAD+]=490 mM [NADH]=2.0×102 mM

Answer 1

Answer: The Gibbs free energy of the reaction is 21.32 kJ/mol

Explanation:

The chemical equation follows:

$\text{Malate }+NAD^+\rightleftharpoons \text{Oxaloacetate }+NADH$

The equation used to Gibbs free energy of the reaction follows:

$\Delta G=\Delta G^o+RT\ln K_{eq}$

where,

$\Delta G$ = free energy of the reaction

$\Delta G^o$ = standard Gibbs free energy = 29.7 kJ/mol = 29700 J/mol  (Conversion factor: 1 kJ = 1000 J)

R = Gas constant = 8.314J/K mol

T = Temperature = $37^oC=[273+37]K=310K$

$K_{eq}$ = Ratio of concentration of products and reactants = $\frac{\text{[Oxaloacetate]}[NADH]}{\text{[Malate]}[NAD^+]}$

$\text{[Oxaloacetate]}=0.130mM$

$[NADH]=2.0\times 10^2mM$

$\text{[Malate]}=1.37mM$

$[NAD^+]=490mM$

Putting values in above expression, we get:

$\Delta G=29700J/mol+(8.314J/K.mol\times 310K\times \ln (\frac{0.130\times 2.0\times 10^2}{1.37\times 490}))\\\\\Delta G=21320.7J/mol=21.32kJ/mol$

Hence, the Gibbs free energy of the reaction is 21.32 kJ/mol