The Foundations of Chemistry

6.Changes in the number of moles of gaseous substances.Processes that result in an increase

in the number of moles of gaseous substances have 
Ssys 0. Example 15-15 illus-

trates this. There are no gaseous reactants, but the products include five moles of

gas. Conversely, we would predict that the process 2H 2 (g)O 2 (g) n2H 2 O(g) has

a negative 
S^0 value; here, three moles of gas is consumed while only two moles

is produced, for a net decrease in the number of moles in the gas phase. You

should be able to calculate the value of 
S^0 for this reaction from the values in

Appendix K.

FREE ENERGY CHANGE, G,AND SPONTANEITY

Energy is the capacity to do work. If heat is released in a chemical reaction (
His nega-

tive), someof the heat may be converted into useful work. Some of it may be expended to

increase the order of the system (if 
Sis negative). If a system becomes more disordered

(
S 0), however, more useful energy becomes available than indicated by 
Halone.

J. Willard Gibbs (1839–1903), a prominent nineteenth-century American professor of

mathematics and physics, formulated the relationship between enthalpy and entropy in

terms of another state function that we now call the Gibbs free energy, G.It is defined

as

GHTS

The Gibbs free energy change, G,at constant temperature and pressure, is

G
HT
S (constant Tand P)

The amount by which the Gibbs free energy decreases is the maximum useful energy

obtainable in the form of work from a given process at constant temperature and pres-

sure. It is also the indicator of spontaneity of a reaction or physical changeat constant Tand

P.If there is a net decrease of useful energy, 
Gis negative and the process is sponta-

15-15

(a) The entropy of an organism
decreases (unfavorable) when new
cells are formed. The energy to
sustain animal life is provided by the
metabolism of food. This energy is
released when the chemical bonds in
the food are broken. Exhalation
of gases and excretion of waste
materials increase the entropy of the
surroundings enough so that the
entropy of the universe increases
and the overall process can occur.
(b) Stored chemical energy can later
be transformed by the organism to
the mechanical energy for muscle
contraction, to the electrical energy
for brain function, or to another
needed form.

628 CHAPTER 15: Chemical Thermodynamics

(a) (b)

Do you think that the reaction

2H 2 (g)O 2 (g)88n2H 2 O(
)

would have a higher or lower value of

S^0 than when the water is in the gas
phase? Confirm by calculation.

See the Saunders Interactive
General Chemistry CD-ROM,
Screen 20.7, Gibbs Free Energy.

This is often called simply the Gibbs
energy changeor the free energy change.