Help with solving this problems

Question

The ratio of the two products to sucrose is 140,000 at 310K.

A) Calculate delta G^o for this reaction at 310K.

B) If the change in standard enthalpy for this reaction is -14.4 kJ/mol, what is the change in standard entropy at 310K?

C)If the concentrations of [Fructose] = 120 pM, [Glucose] = 130 uM and [Sucrose] = 15mM, will this reaction proceed towards reactants or towards products at 310K? also don’t forget to convert to molarity at the end

Answer 1

Let us assume you are referring to the following reaction:

sucrose + H₂O ==> glucose + fructose

C₁₂H₂₂O₅ + H₂O ==> C₆H₁₂O₆ + C₆H₁₂O₆

K = [glucose][fructose] / [sucrose] = 140,000 @310K

A) calculate ∆Gº@310K

∆Gº = -RT ln K

∆Gº = -8.314 J/Kmol x 310K ln 140,000

∆Gº = -2577 J/mol x 11.85

∆Gº = -30536 J/mol

∆Gº = -30.54 kJ/mol

B) ∆Hº = -14.4 kJ/mol, what is ∆Sº?

∆Gº = ∆Hº - TSº

-30.54 kJ/mol = -14.4 kJ/mol - (310K)(∆Sº)

-16.14 = -310∆Sº

∆Sº = 0.0521 kJ/molK

∆Sº = 52.1 J/molK

C) [Fructose] = 120 pM; [glucose] = 130 uM; [sucrose] = 15 mM. Will the reaction proceed toward reactants or products?

We want to compare Q to K to determine which way the reaction will proceed. First, we will convert all concentrations to molar.

[fructose] = 1.20x10^-10 M

[glucose] = 1.30x10^-4 M

[sucrose] = 1.5x10^-2 M

Q = (1.20x10^-10)(1.30x10^-4) / 1.5x10^-2

Q = 1.04x10^-12

Since Q is << K, the reaction will proceed toward the product side until equilibrium is reached.