Page 154 - Modern Analytical Chemistry

1400-CH06 9/9/99 7:40 AM Page 137

Chapter 6 Equilibrium Chemistry 137

the most important to chemistry is the study of the changes in energy occurring
during a chemical reaction.
Consider, for example, the general equilibrium reaction shown in equation 6.1,
involving the solutes A, B, C, and D, with stoichiometric coefficients a, b, c, and d.
aA+ bB t cC+ dD 6.1

By convention, species to the left of the arrows are called reactants, and those on the
right side of the arrows are called products. As Berthollet discovered, writing a reac-
tion in this fashion does not guarantee that the reaction of A and B to produce C and
D is favorable. Depending on initial conditions, the reaction may move to the left, to
the right, or be in a state of equilibrium. Understanding the factors that determine
the final position of a reaction is one of the goals of chemical thermodynamics.
Chemical systems spontaneously react in a fashion that lowers their overall free
energy. At a constant temperature and pressure, typical of many bench-top chemi-
cal reactions, the free energy of a chemical reaction is given by the Gibb’s free en- Gibb’s free energy
ergy function A thermodynamic function for systems
at constant temperature and pressure
∆G = ∆H – T ∆S 6.2 that indicates whether or not a reaction
is favorable (∆G < 0), unfavorable
where T is the temperature in kelvins, and ∆G, ∆H, and ∆S are the differences in the (∆G > 0), or at equilibrium (∆G = 0).
Gibb’s free energy, the enthalpy, and the entropy between the products and reactants.
Enthalpy is a measure of the net flow of energy, as heat, during a chemical re- enthalpy
action. Reactions in which heat is produced have a negative ∆H and are called A change in enthalpy indicates the heat
exothermic. Endothermic reactions absorb heat from their surroundings and have a absorbed or released during a chemical
positive ∆H. Entropy is a measure of randomness, or disorder. The entropy of an reaction at constant pressure.
individual species is always positive and tends to be larger for gases than for solids
and for more complex rather than simpler molecules. Reactions that result in a entropy
A measure of disorder.
large number of simple, gaseous products usually have a positive ∆S.
The sign of ∆G can be used to predict the direction in which a reaction moves
to reach its equilibrium position. A reaction is always thermodynamically favored
when enthalpy decreases and entropy increases. Substituting the inequalities ∆H <0
and ∆S > 0 into equation 6.2 shows that ∆G is negative when a reaction is thermo-
dynamically favored. When ∆G is positive, the reaction is unfavorable as written
(although the reverse reaction is favorable). Systems at equilibrium have a ∆G
of zero.
As a system moves from a nonequilibrium to an equilibrium position, ∆G must
change from its initial value to zero. At the same time, the species involved in the
reaction undergo a change in their concentrations. The Gibb’s free energy, there-
fore, must be a function of the concentrations of reactants and products.
As shown in equation 6.3, the Gibb’s free energy can be divided into two terms.
∆G = ∆G°+ RT ln Q 6.3
The first term, ∆G°, is the change in Gibb’s free energy under standard-state condi- standard state
tions; defined as a temperature of 298 K, all gases with partial pressures of 1 atm, all Condition in which solids and liquids are
solids and liquids pure, and all solutes present with 1 M concentrations. The second in pure form, gases have partial pressures
of 1 atm, solutes have concentrations of
term, which includes the reaction quotient, Q, accounts for nonstandard-state pres-
1 M, and the temperature is 298 K.
sures or concentrations. For reaction 6.1 the reaction quotient is
c
CD
[] [ ] d
Q = a b 6.4
B
A
[] [ ]
where the terms in brackets are the molar concentrations of the solutes. Note that
the reaction quotient is defined such that the concentrations of products are placed