Thermodynamics:
Free Energy

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In this module:
Introduction
DG and Reactions
DG and Temperature
DGfº
Coupling Reactions
Free Energy in Industry
Free Energy in Living Things
Free Energy and Equilibrium

DG and Direction of Reactions

To see how DG values can be used to predict how reactions will go, consider the four cases you encountered in the Entropy Module:

1. DH < 0, DS > 0:

This is an exothermic reaction with an increase in entropy. Thus DSuniv > 0 and DG < 0. The Second Law of Thermodynamics says that such a reaction is product-favored, so a DG less than zero also means a product-favored reaction.

Example:     2CH4(g) + 3O2(g) 2CO2(g) + 2H2O(g)

2. DH > 0, DS < 0

This is an endothermic reaction with a decrease in entropy. Thus DSuniv < 0 and DG > 0. The Second Law of Thermodynamics says that such a reaction is reactant-favored, so a DG greater than zero also means a reaction is reactant-favored.

Example:     6CO2(g) + 6H2O(g) C6H12O6(s) + 6O2(g)

The minus sign in the definition of DG was given so that a negative values of DG corresponded to a product-favored process and a positive value to a reactant-favored process. Thus, a product-favored reaction will go on its own, without outside intervention, and can often be made to do useful work in the process. Thus, it is like an exothermic reaction with a negative value of DE or DH. A reaction with a negative DG is called exergonic to emphasize this. Conversely, a reaction with a positive value of DG is reactant-favored and requires the input of energy to go. Such a reaction is called endergonic .

3. DH > 0, DS > 0

This is an endothermic reaction with a positive entropy change. This sort of reaction is reactant-favored at low temperatures and product-favored at high temperatures. DG predicts the same thing, since at low temperatures the DH term of DH - TDS will dominate and DG will be greater than zero. Conversely, at high temperatures, the TDS term will dominate and DG will be less than zero.

Example:     CaCO3(s) CaO(s) + CO2(g)

4. DH < 0, DS < 0

This is an exothermic reaction with a negative entropy change. This sort of reaction is product-favored at low temperatures and reactant-favored at high temperatures. DG predicts the same thing, since at low temperatures the DH term of DH - TDS will dominate and DG will be less than zero. Conversely, at high temperatures, the TDS term will dominate and DG will be greater than zero.

Example:     N2(g) + 3H2(g) 2NH3(g)

Select positive or negative signs for DH and DS to see what sort of reaction results. Click on the mouse icon at left to clear the radio buttons and text.

Sign of DH Sign of DS Sign of DG Product-favored?
Positive
endothermic
exothermic
Positive
negative
(exergonic)
positive
(endergonic)
T-dependent
T-dependent
yes
no
yes at low T, no at high T
no at low T, yes at high T
Negative Negative

DG and Reactions