The Foundations of Chemistry

Figure 17-4 displays the relationships between free energy and equilibrium. The left

end of each curve represents the total free energy of the reactants and the rightend of

each curve represents the total free energy of the products at standard state conditions.

The difference between them is 
G^0 rxn; like K,
G^0 rxndepends only on temperature and is

a constant for any given reaction.

From the preceding equation that relates 
G^0 rxnand K,we see that when 
G^0 rxnis nega-

tive, ln K mustbe positive, and Kis greater than 1. This tells us that products are favored

over reactants at equilibrium. This case is illustrated in Figure 17-4a. When 
G^0 rxnis posi-

tive, ln K mustbe negative, and Kis less than 1. This tells us that reactants are favored

over products at equilibrium (Figure 17-4b). In the rarecase of a chemical reaction for

which 
G^0 rxn0, then K1 and the numerator and the denominator must be equal in

the equilibrium constant expression, (i.e., [C]c[D]d...[A]a[B]b...). These relationships

are summarized as follows.

G^0 rxn K Product Formation

G^0 rxn    0 K 1 Products favored over reactants at equilibrium


G^0 rxn 0 K1 At equilibrium when [C]c[D]d... [A]a[B]b... (very rare)


G^0 rxn 

0 K 1 Reactants favored over products at equilibrium

The direction of approach to equilibrium and the actual free energy change (
Grxn)

are notconstants. They vary with the conditions and the initial concentrations. If the initial

concentrations correspond to Q K,equilibrium is approached from left to right on the

curves in Figure 17-4, and the forward reaction predominates. If Q K,equilibrium is

approached from right to left, and the reverse reaction predominates.

The magnitude of 
G^0 rxnindicates the extentto which a chemical reaction occurs under

standard state conditions, that is, how far the reaction goes toward the formation of prod-

ucts before equilibrium is reached. The more negative the 
G^0 rxnvalue, the larger is the

Figure 17-4 Variation in total free
energy for a reversible reaction
carried out at constant T.The
standardfree energy change,
G^0 ,
represents the free energy change
for the standard reaction—the
completeconversion of reactants
into products. In (a) this change is
negative, indicating that the
standard reaction is product-favored
(spontaneous); the collection of just
products would be more stable than
the collection of just reactants. The
mixture of reactants and products
corresponding to the minimum
of the curve is even more stable,
however, and represents the
equilibrium mixture. Because
G^0 is
negative, K 1, and the equilibrium
mixture contains more products than
reactants. At any point on the curve,
comparing Qand Kindicates the
direction in which the reaction must
proceed to approach equilibrium,
that is, which way is “downhill” in
free energy. The plot in (b) is for
positive
G^0 (the standard reaction
is reactant-favored). In this case
K 1, and the equilibrium mixture
contains more reactants than
products.

Increasing free energy,

G

Reaction coordinate

Reactants

only

(a)

Products

only

G^0     0

Q K

Q K

Q  K

Equilibrium

mixture

Increasing free energy,

G

Reaction coordinate

Reactants

only

Standard reaction is

spontaneous in reverse direction

(reactant-favored)


G^0 0, K 1

Standard reaction is

spontaneous in forward direction

(product-favored)


G^0 0, K 1

(b)

Products

only

G^0 

 0

Q K

Q K

Q  K

Equilibrium

mixture