Answer:
[tex]\Delta G^{\circ}=-15902 J/mol[/tex]
Explanation:
In this problem we only have information of the equilibrium, so we need to find a expression of the free energy in function of the constant of equilireium (Keq):
[tex]\Delta G^{\circ}=-R*T*ln(K_{eq})[/tex]
Being Keq:
[tex]K_{eq}=\frac{[fructose][Pi]}{[Fructose-1-P]}[/tex]
Initial conditions:
[tex][Fructose-1-P]=0.2M[/tex]
[tex][Fructose]=0M[/tex]
[tex][Pi]=0M[/tex]
Equilibrium conditions:
[tex][Fructose-1-P]=6.52*10^{-5}M[/tex]
[tex][Fructose]=0.2M-6.52*10^{-5}M[/tex]
[tex][Pi]=0.2M-6.52*10^{-5}M[/tex]
[tex]K_{eq}=\frac{(0.2M-6.52*10^{-5}M)*(0.2M-6.52*10^{-5}M)}{6.52*10^{-5}M}[/tex]
[tex]K_{eq}=613.1[/tex]
Free-energy for T=298K (standard):
[tex]\Delta G^{\circ}=-8.314\frac{J}{mol*K}*298K*ln(613.1)[/tex]
[tex]\Delta G^{\circ}=-15902 J/mol[/tex]