Question

The following reactions can be coupled to give alanine and oxaloacetate: glutamate + pyruvate ↔ ketoglutarate + alanine ∆Go ’rxn,303 = − 1004 J/mol glutamate + oxaloacetate ↔ ketoglutarate + aspartate ∆Go ’rxn,303 = − 4812 J/mol

(a) Write the form of the equilibrium constant for pyruvate + aspartate ↔ alanine + oxaloacetate and calculate the numerical value of the equilibrium constant at 30o C.

(b) In the cytoplasm of a certain cell, the components are at the following concentrations: pyruvate = 10-2 M, aspartate = 10-2 M, alanine = 10-4 M, and oxaloacetate = 10-5 M. Calculate the Gibbs free energy change for the reaction of part (a) under these conditions. What conclusion can you reach about the direction of this reaction under cytoplasmic conditions?

Answer 1

The following reactions can be coupled to produce alanine and oxalacetate.

glutamate + pyruvate ketoglutarate + alanine ΔG^o'₃₀₃ = -1.004 kJ mol^-1.........(1)

glutamate + oxalacetate ketoglutarate + aspartate ΔG^o'₃₀₃ = -4.812 kJ mol^{-1.....................}(2)

(a) The form of the equilibrium constant for pyruvate + aspartate ↔ alanine + oxaloacetate is given as follows

The steps are as follows:

Reverse equation (2) and write

  ketoglutarate + aspartate glutamate + oxalacetate ΔG^o'₃₀₃ = 4.812 kJ mol^-1.............(3)

Add equation (3) to (1) we get as follows

pyruvate + aspartate alanine + oxalacetate.....

ΔG^o'₃₀₃ = (-1.004) + (+4.812)

= 3.808 kJ mol^-1

ΔG^o'₃₀₃ = -RTlnK

3.808 x 10³ = -8.314 x 303 x lnK

lnK = (-3.808 x 10^³) /(8.314 x 303)

lnK = -1.5116

K = e^( -1.5116)

K = 0.2205

(b) The sign of G tells us in what direction the reaction will shift to reach equilibrium.

and the magnitude of G tells us how far the reaction is from equilibrium at that moment

G = G^o + RT ln Q

   G  = 3.808 x 10³ + 8.314 x 303 ln [products] / [reactants]

= 3.808 x 10³ + 8.314 x 303 ln [ 10-2 x 10-5 ] / [10-2 x 10-2]

= 3.808 x 10³ + 8.314 x 303 x ln (1.25)

= 954.354 J mol-1 = 0.954 kJ mol-1

Hence gibbs free energy change = G^o -  G =    3.808 kJ mol^-1 - 0.954 kJ mol-1 = 2.854  kJ mol-1

and as the change is gibbs free energy yields a positive result it means the direction of the reaction under cytoplasmic conditions is towards left side i.e towards the reactant side.