The Foundations of Chemistry

each other, the chemical reaction begins, heat is released or absorbed, and the concen-
trations of the substances in the mixture change. An additional change in entropy, which
depends on changes in the nature of the reactants and products, also begins to occur. The
evolution or absorption of heat energy, the changes in entropy, and the changes in concen-
trations all continue until equilibrium is established. Equilibrium may be reached with
large amounts of products formed, with virtually of all of the reactants remaining
unchanged, or at anyintermediate combination of concentrations.
The standard free energy change for a reaction is
G^0 rxn. This is the free energy change
that would accompany completeconversion of allreactants initially present at standard
conditions to allproducts at standard conditions—the standard reaction (Section 15-15).
The free energy change for any other concentrations or pressures is
Grxn(no superscript
zero). The two quantities are related by the equation

Grxn
G^0 rxnRTln Q

Ris the universal gas constant, Tis the absolute temperature, and Qis the reaction quotient
(Section 17-4). When a system is at equilibrium,
Grxn0 (Section 15-15) and QK
(Section 17-4). Recall that the reaction quotient may represent nonequilibrium concen-
trations (or partial pressures) of products and reactants. As reaction occurs, the free energy
of the mixture and the concentrations change until at equilibrium
Grxn0, and the
concentrations of reactants and products satisfy the equilibrium constant. At that point,
Qbecomes equal to K(Section 17-4). Then

0 
G^0 rxnRTln K (at equilibrium)

Rearranging gives

G^0 rxnRTln K

This equation shows the relationship between the standard free energy change and the
thermodynamic equilibrium constant.
For the following generalized reaction, the thermodynamic equilibrium constant is
defined in terms of the activities of the species involved.

aAbB 34 cCdD K

where aAis the activity of substance A, and so on. The mass action expression to which
it is related involves concentration terms for species in solution and partial pressures for
gases.

When the relationship 
G^0 rxnRTln Kis used with

1.all gaseous reactants and products, Krepresents KP;

2.all solution reactants and products, Krepresents Kc;

3.a mixture of solution and gaseous reactants, Krepresents the thermodynamic

equilibrium constant, and we do not make the distinction between KPand Kc.

(aC)c(aD)d



(aA)a(aB)b

Thermodynamic standard states are

(1) pure solids or pure liquids at 1 atm,

(2) solutions of one-molar

concentrations, and (3) gases at partial

pressures of 1 atm.

The energy units of R mustmatch

those of 
G^0. We usually use

R8.314 J/molTK

We will encounter equilibrium

calculations of solution and gaseous

species in Chapter 21,

“Electrochemistry.”

17-12 Relationship Between 
G^0 rxnand the Equilibrium Constant 739