Ka, Kw, Kb - The Acid, Water, and Base Dissociation Constant for AP Chemistry
Practice problems for these concepts can be found at:
- Equilibrium Multiple Choice Review Questions for AP Chemistry
- Equilibrium Free-Response Questions for AP Chemistry
Ka—The Acid Dissociation Constant
Strong acids completely dissociate (ionize) in water. Weak acids partially dissociate and establish an equilibrium system. But as shown in Figure 15.1 there is a large range of weak acids based upon their ability to donate protons. Consider the general weak acid, HA, and its reaction when placed in water:
An equilibrium constant expression can be written for this system:
The [H2O] is assumed to be a constant and is incorporated into the Ka value. It is not shown in the equilibrium constant expression.
Since this is the equilibrium constant associated with a weak acid dissociation, this particular Kc is most commonly called the acid dissociation constant, Ka. The Ka expression is then:
Many times the weak acid dissociation reaction will be shown in a shortened notation, omitting the water:
The greater the amount of dissociation is, the larger the value of Ka. Table 15.1 shows the Ka values of some common weak acids.
Here are a couple of tips: For every H+ formed, an A– is formed, so the numerator of the Ka expression can be expressed as [H+]2 (or [A–]2, although it is rarely done this way). Also, the [HA] is the equilibrium molar concentration of the undissociated weak acid, not its initial concentration. The exact expression would then be [HA] = Minitial – [H+], where Minitial is the initial concentration of the weak acid. This is true because for every H+ that is formed, an HA must have dissociated. However, many times if Ka is small, you can approximate the equilibrium concentration of the weak acid by its initial concentration, [HA] = Minitial.
If the initial molarity and Ka of the weak acid are known, the [H+] (or [A–]) can be calculated easily. And if the initial molarity and [H+] are known, Ka can be calculated.
For example, calculate the [H+] of a 0.300 M acetic acid solution.
For polyprotic acids, acids that can donate more than one proton, the Ka for the first dissociation is much larger than the Ka for the second dissociation. If there is a third Ka, it is much smaller still. For most practical purposes you can simply use the first Ka.
Kw—The Water Dissociation Constant
Before examining the equilibrium behavior of aqueous solutions of weak bases, let's look at the behavior of water itself. In the initial discussion of acid–base equilibrium above, we showed water acting both as an acid (proton donor when put with a base) and a base (proton acceptor when put with an acid). Water is amphoteric, it will act as either an acid or a base, depending on whether the other species is a base or acid. But in pure water the same amphoteric nature is noted. In pure water a very small amount of proton transfer is taking place:
This is commonly written as:
There is an equilibrium constant, called the water dissociation constant, Kw, which has the form:
Again, the concentration of water is a constant and is incorporated into Kw.
The numerical value of Kw of 1.0 × 10–14 is true for the product of the [H+] and [OH–] in pure water and for aqueous solutions of acids and bases.
In the discussion of weak acids, we indicated that the [H+] = [A–]. However, there are two sources of H+ in the system: the weak acid and water. The amount of H+ that is due to the water dissociation is very small and can be easily ignored.