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E-4
As an example, consider solubility of the metal salt, MX2 in water: MX
2(s)
M
2+
(aq)
+ 2X
-
(aq)
(3)
The reaction quotient of this reaction is Q =
[M
2+
][X
-
]²
[MX2]
. The concentration of a solid is also known as
the density. Since the activity of a solid is assigned a value of 1 and does not change, it does not
appear in the reaction quotient expression. It too is incorporated into this expression. This simplifies
the reaction quotient for this reaction to Q = [M
2+
][X
-
]². The equilibrium constant for this type of
reaction is called the solubility product constant and for equation (3) is defined by following equation:
K = K
sp
= [M
2+
][X
-
]²
(4)
Part III. Interactive Equilibria
Interactive equilibria involve a series of reaction equilibria that have one or more species in common. Most
equilibria in natural systems are interactive. In a system of interactive equilibria, a change in the equilibrium
position of one reaction affects the equilibrium position of the other reactions. All of the reactions shift to come
to new equilibrium positions, so that the reaction quotient (Q) of each reaction is again equal to K for that
reaction. The stress created by the addition (or removal) of species is relieved by a shift in the position of
equilibrium. To see how this interaction works, let us consider how the oxalic acid (H2C2O
4
) equilibria might
interact with a solution containing acetic acid (CH3COOH) and acetate (CH3COO
-
). We have previously
discussed the acetic acid equilibrium:
CH3COOH
(aq)
+ H2O
(l)
CH3COO
-
(aq)
+ H3O
+
(aq)
(1)
Oxalic acid is a weak diprotic acid. The following two reactions describe the ionization of oxalic acid in water:
H2C2O
4
(aq)
+ H2O
(l)
HC2O
4
-
(aq)
+ H3O
+
(aq)
(5)
HC2O
4
-
(aq)
+ H2O
(l)
C2O
4
2-
(aq)
+ H3O
+
(aq)
(6)
The above equilibria can be combined to give:
H2C2O
4
(aq)
+ 2 H2O
(l)
©2O
4
2-
(aq)
+ 2 H3O
+
(aq)
(7)
The equilibrium constant, K', for the combined reactions is
K' =
[H3O
+
]²[C2O
4
2-
]
[H2C2O
4
]
Let us assume that both acetic acid and oxalic acid have been dissolved in the same aqueous solution, and that
the concentrations of all species have reached values such that both the K
a
of acetic acid and the K' of oxalic
acid are satisfied. Therefore, the system is at equilibrium.
