Question

9- The hydrolysis of Sucrose (Sucrose+ HO change (AG) of- 6.3 Glucose + Fructose) has a standard free energy kcal/mol; what is the standard free energy change and the equilibrium constant for the synthesis of Sucrose from Glucose and Fructose?

Answer 1

ANSWER

A measure of free energy, the potential energy of a reaction, can be used to predict properties of chemical reactions. In the late 1800's, J. W. Gibbs showed that free energy (G) of a system can be defined as

G = H - TS

where H is the heat energy of the system, T is the temperature, and S is entropy. Heat energy (H) is a measure of the energy in a chemical bond: tightly bound molecules have higher heat energy. Entropy (S) is a measure of the disorder in a system. Molecules distributed randomly have high entropy (large S) while ordered molecules have low entropy (small S).

Every chemical reaction results in a change in free energy which we can measure as

DG = G_products - G_reactants = H_products - H_reactants - T(S_products - S_reactants) = DH - TDS

A chemical reaction will have a DH < 0 if the heat energy of the reactants is greater than the products. A reaction will have DS < 0 if the reaction results in increased order and DS > 0 if the reaction results in increased entropy.

The net direction of a chemical reaction will be from higher to lower energy. In other words, if the energy of the reactants is higher than the energy of the products, G_reactants > G_products, the reaction will occur spontaneously. In such a case, DG < 0, and the free energy of the system decreases with the reaction. In the opposite case, DG > 0, and energy is required for the reaction to occur.

In a mixture of reactants and products, the chemical reaction and its reverse occur until chemical equilibrium is achieved. If we begin with a large concentration of reactants, the free energy of reactants is much greater than products and the reaction proceeds. As the concentration of reactants decreases as products are formed, the difference in free energy decreases until the free energy of the products and reactants are equal. Therefore at chemical equilibrium, DG = 0.

Clearly, the free energy of a chemical reaction depends on the heat energy and entropy of the reactants and products. Free energy also depends on the concentration of reactants and products. This is because the movement of molecules from a more to less concentrated state can perform work. Reference books refer to DG^o' as the standard free energy of a reaction when temperature is 298 Kelvin, pressure is 1 atm, pH is 7.0, and initial concentrations of reactants and products are equal.

When the concentrations of reactants and products are variable, we can determine DG as

where R is the universal gas constant, T is temperature, and C_product, C_reactant are the initial concentrations of the products and reactants.

We can plot DG as a function of C_product/C_reactant to see how the free energy of the reaction changes as reactants are converted to product (C_product/C_reactant increases). As an example we will look at chemical reaction of photosynthesiswhich has a standard free energy DG^o' = +686 kcal/mol. The reverse reaction has DG^o' = -686 kcal/mol.

1000 AGo+686 kcal/mol 500 0.5 1.5 Cproducts / Creactants 500 AG-686 kcalmol Ш-1000 1500 2000 2500

When the concentration of the reactants is much greater than the products (C_product/C_reactant much less than 1), for both photosynthesis and the reverse reaction, DG is negative so the reaction progresses spontaneously. For the reverse reaction, as the concentration of product increases, the reaction approaches a chemical equilibrium where DG = 0. For photosynthesis, however, as the amount of product increases, DG quickly becomes positive even though less than half of the reactants have been converted to product (C_product/C_reactant < 0.5). In other words, for more product to be created, this reaction is not spontaneous, and energy is required for the chemical reaction to occur.

We can also use this equation for DG as a function of product and reactant concentrations to determine the equilibrium constant of a reaction. The equilibrium constant (K_eq) is C_product/C_reactant when chemical equilibrium is achieved (DG = 0). By setting DG = 0 and solving for K_eq we find

RT

We can plot K_eq as a function of DG^o', we can see how the equilibrium constant is affected by the standard free energy of a chemical reaction.

25 20 15 10 2000 1000 1000 2000 Standard Free Energy (AG)

For chemical reactions where the free energy of the reactants is much greater than the free energy of the products (DG^o' < 0), the reaction proceeds spontaneously and the net result is a large ratio of product to reactant (large K_eq). For reactions where DG^o' > 0, very little of the reactant may be converted to product without the input of additional energy into the system.