Page 155 - Modern Analytical Chemistry

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138 Modern Analytical Chemistry

in the numerator, and the concentrations of reactants are placed in the denominator.
In addition, each concentration term is raised to a power equal to its stoichiometric
coefficient in the balanced chemical reaction. Partial pressures are substituted for
concentrations when the reactant or product is a gas. The concentrations of pure
solids and pure liquids do not change during a chemical reaction and are excluded
from the reaction quotient.
At equilibrium the Gibb’s free energy is zero, and equation 6.3 simplifies to
∆G°=–RT ln K
equilibrium constant where K is an equilibrium constant that defines the reaction’s equilibrium posi-
For a reaction at equilibrium, the tion. The equilibrium constant is just the numerical value obtained when substitut-
equilibrium constant determines the
ing the concentrations of reactants and products at equilibrium into equation 6.4;
relative concentrations of products and
thus,
reactants.
c d
D
[] [ ] eq
C eq
K= 6.5
a b
B
[] [ ] eq
A eq
where the subscript “eq” indicates a concentration at equilibrium. Although the
subscript “eq” is usually omitted, it is important to remember that the value of K is
determined by the concentrations of solutes at equilibrium.
As written, equation 6.5 is a limiting law that applies only to infinitely dilute
solutions, in which the chemical behavior of any species in the system is unaffected
by all other species. Corrections to equation 6.5 are possible and are discussed in
more detail at the end of the chapter.
6C Manipulating Equilibrium Constants
We will use two useful relationships when working with equilibrium constants.
First, if we reverse a reaction’s direction, the equilibrium constant for the new reac-
tion is simply the inverse of that for the original reaction. For example, the equilib-
rium constant for the reaction
A +2 t AB 2 1 K = [ AB 2 ]
B
AB]
[] [ 2
is the inverse of that for the reaction

AB]
AB 2 t A + 2 B K 2 = 1 = [] [ 2
1 K [ AB 2 ]
Second, if we add together two reactions to obtain a new reaction, the equilibrium
constant for the new reaction is the product of the equilibrium constants for the
original reactions.
A + t AC K 1 = [ AC]
C
AC]
[] [
AC + t AC 2 K 2 = [ AC ]
2
C
[
]
[ AC C]
2
2
A +2 C t AC 2 K 3 =K K 2 = [ AC] ´ [ AC ] = [ AC ]
1
[] [ [ AC C] [] [ 2
AC]
]
[
AC]