Question

Consider the following isomerization reactions of some simple sugars and values for their standard Gibbs free energy ΔG°:

glucose-1-phosphate ⟶ glucose-6-phosphate ΔG° = −7.28 kJ/mol

fructose-6-phosphate ⟶ glucose-6-phosphate ΔG° = −1.67 kJ/mol

3.1 Calculate ΔG° for the isomerization of glucose-1-phosphate to fructose-6-phosphate. [ANSWER = -5.61 kJ/mol]
3.2 Calculate the equilibrium constant K for the isomerization of glucose-1-phosphate to fructose-6-phosphate at 298K. [ANSWER = 9.62 ]
3.3. Suppose you dissolve fructose-6-phosphate in water to prepare a 0.1 M solution. What are the concentrations of fructose-6-phosphate and glucose-1-phosphate at equilibrium?

I JUST NEED PART 3.3

Answer 1

fructose -6-phosphate   ---> glucose -6-phosphate   , dG == - 1.67 KJ/mol = -1670 J/mol

we have relation dGo = -RT ln Keq

   - 1670 J/mol = - 8.314 J/molK x 298 K x ln Keq

Keq = exp ( 1670 /8.314 x 298)   = 1.96

At equilibrium fructose-1-6-phosphate concentration = 0.1-X ,   

Glucose-6-phosphate = X

we have Keq = [Glucose-6-phosphate] / [fructose-6-phosphate]

1.96    = ( X) / ( 0.1-X)

X = 0.066

hence at equilibrium glucose -6-phosphate concentration = 0.066 M

fructose -6-phopshate concentration = 0.1-0.066 = 0.034 M