Respuesta :
Answer: The Gibbs free energy of the reaction is 22.491 kJ/mol.
Explanation:
The chemical equation for the conversion follows:
[tex]\text{Malate}+NAD^+\rightleftharpoons \text{Oxaloacetate}+NADH[/tex]
The expression for [tex]K_{eq}[/tex] of above equation is:
[tex]K_{eq}=\frac{\text{[Oxaloacetate]}\times [NaDH]}{\text{[Malate]}\times [NAD^+]}[/tex]
We are given:
[malate] = 1.35 mM
[oxaloacetate] = 0.210 mM
[NADH] = 150 mM
[tex][NAD^+]=380mM[/tex]
Putting values in above equation, we get:
[tex]K_{eq}=\frac{0.210\times 150}{1.35\times 380}=0.061[/tex]
Relation between standard Gibbs free energy and equilibrium constant follows:
[tex]\Delta G=\Delta G^o+RT\ln K_{eq}[/tex]
where,
[tex]\Delta G^o[/tex] = Standard Gibbs free energy = 29.7 kJ/mol = 29700 J/mol (Conversion factor: 1kJ = 1000J)
R = Gas constant = [tex]8.314J/K mol[/tex]
T = temperature = [tex]37^oC=[37+273]K=310K[/tex]
[tex]K_{eq}[/tex] = equilibrium constant of the reaction = 0.061
Putting values in above equation, we get:
[tex]\Delta G=29700J/mol+(8.3145J/Kmol)\times 310K\times \ln (0.061)\\\\\Delta G=22491.05J/mol=22.491kJ/mol[/tex]
Hence, the Gibbs free energy of the reaction is 22.491 kJ/mol.
