Page 179 - Physical chemistry understanding our chemical world

146 REACTION SPONTANEITY AND THE DIRECTION OF THERMODYNAMIC CHANGE

Justification Box 4.2

The total change in entropy is S (total) , which must be positive for a spontaneous
process. From Equation (4.8), we say

S (total) = S (system) + S (surroundings) > 0

We usually know a value for S (system) from tables. Almost universally, we do not know
avaluefor S (surroundings) .
The Clausius equality says that a microscopic process is at equilibrium if dS = dq/T
where q is the heat change and T is the thermody-
This sign change occur- namic temperature (in kelvin). Similarly, for a macro-
ring here follows since scopic process, S = q/T . In a chemical reaction,
energy is absorbed the heat energy emitted is, in fact, the enthalpy change
by the surroundings if of reaction H (system) , and the energy gained by the
energy has been emit- surroundings of the reaction vessel will therefore be
ted by the reaction, − H (system) . Accordingly, the value of S (surroundings)
and vice versa. is − H ÷ T .
Rewriting Equation (4.8) by substituting for
S (surroundings) gives

H
S (total) = S (system) − (4.22a)
T
The right-hand side must be positive if the process is spontaneous, so

H (system)
S (system) − > 0 (4.22b)
T
or
H (system)
0 > − S (system)
T
Multiplying throughout by T gives

(4.23)
0 > H (system) − T S (system)
So the compound variable H (system) − T S (system) must be negative if a process is
spontaneous.
This compound variable occurs so often in chemistry that we will give it a symbol
of its own: G, which we call the Gibbs function. Accordingly, a spontaneous process
in a system is characterized by saying,

(4.24)
0 > G (system)
In words, the Gibbs energy must be negative if a change occurs spontaneously.