2.2 Ionization Constants: Ka, Kb, and Kw
Because acid/base solutions are systems at equilibrium, we can write equilibrium constant expressions for these systems. We'll return to the equilibrium constant, a concept we first addressed in the Equilibrium unit.
Ka and Kb
Here are several examples, including some that show water as a reactant. Pay attention to the physical states and whether or not a particular substance is included in the equilibrium expression. Also notice that we now identify the equilibrium constant as Ka for acids and Kb for bases.
| HCl(aq) → H+(aq) + Cl-(aq) |
| |
Ka |
= |
[H+] [Cl-]
[HCl] |
=1.3×106 |
|
|
| HCl(g) + H2O(l) → H3O+(aq) + Cl-(aq) |
| |
Ka |
= |
[H3O+] [Cl-]
[HCl]
|
=1.3×106 |
|
|
| HCHO2 (aq) ↔ H+(aq) + CHO2-(aq) |
| |
Ka |
= |
[H+] [CHO2-]
[HCHO2]
|
= 1.8 × 10-4 |
|
|
| Mg(OH)2 (aq) → Mg2+(aq) + 2 OH-(aq) |
| |
Kb |
= |
[Mg2+] [OH-]2
[Mg(OH)2] |
|
|
|
| NH3 (aq) + H2O(l) ↔ NH4+(aq) + OH-(aq) |
| |
Kb |
= |
[NH4+] [OH-]
[NH3]
|
= 1.8×10-5 |
|
|
Recall that the value of the equilibrium constant indicates which side of a reaction is favored. When Keq is greater than 1 the product side is favored; when Keq is less than 1 the reactants are favored.
So we now have a numerical way to indicate acid and base strength - Ka and Kb
A large value of Ka
means there are many
H+ ions in solution -
in other words, a strong acid
A large Kb indicates
many OH- ions -
a strong base |
The Table of Acid and Base Strengths gives Ka and Kb values for a number of acids and bases. Ka values for very strong acids are typically not given as there is little use in expressing them numerically. Be sure to print a copy of this table and keep it handy.
Kw
We usually do not think of water as producing ions, but that isn't the case. Water does ionize, although not very well.
We can write the ionization equation for water in two ways (both mean essentially the same thing). The equilibrium constant, Kw, can also be written for both equations as shown.
Notice that H2O does not appear in the Kw expression because it is a liquid, and you'll remember that liquids and solids are not included in equilibrium constant expressions.
| H2O(l) → H+(aq) + OH-(aq) |
| |
Kw |
= |
[H+] [OH-]
|
= |
1.0 × 10-14 |
|
|
| 2 H2O(l) → H3O+(aq) + OH-(aq) |
| |
Kw |
= |
[H3O+] [OH-]
|
= |
1.0 ×10-14 |
|
Values for Kw are given for 25°C.
Two more key items to note:
- In pure water, the balanced equation tells us that the concentrations of H+ and OH- will be equal to one another (this is what makes water neutral). Solving the equations shown in the table above, we find that [H+] = [OH-] = 1.0×10-7
- As long as temperature remains constant Kw is a constant - it's value will not change.
The value of Kw is very small, meaning that very few ions are present. Most water remains "intact" as H2O, and few ions form. Why, then, do we even mention it? For a very important reason that we will examine in the next section.
