Fructose-1-P is hydrolyzed according to: Fructose-1-P + H2O → Fructose + Pi If a 0.2 M aqueous solution of Froctose-1-P is allowed to reach equilibrium, its final concentration is 6.52 × 10-5 M.

What is the standard free energy of Froctose-1-P hydrolysis?

Respuesta :

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]