5 Steps to a 5 AP Chemistry 2019

220 ❯ STEP 4. Review the Knowledge You Need to Score High

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 ampho-

teric nature is noted. In pure water, a very small amount of proton transfer is taking place:

H 22 O(l)++HO(l)H 3 O(+aq)OH(−aq)

This is commonly written as:

H 2 O(l)H(+aq)O+ H(−aq)

There is an equilibrium constant, called the water dissociation constant, Kw, which

has the form:

Kw==[H ][OH+ −−] 1.0 10×°^14 at 25 C

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.

pH

Because the concentration of the hydronium ion, H 3 O+, can vary tremendously in solu-

tions of acids and bases, a scale to easily represent the acidity of a solution was developed.

It is called the pH scale and is related to the [H 3 O+]:

pH = - log [H 3 O+] or -log [H+] using the shorthand notation

Remember that in pure water Kw = [H 3 O+][OH-] = 1.0 × 10 -^14. Since both the

hydronium ion and hydroxide ions are formed in equal amounts, the Kw expression can be

expressed as:

[H O] 3 +−^21 =×1.0 10 4

Solving for [H 3 O+] gives us [H 3 O+] = 1.0 × 10 -^7. If you then calculate the pH of pure

water:

pHl=−og[H 3 O]+ =−log[1.0×=10 ](−^7 −−7.00) 7.00=

The pH of pure water is 7.00. On the pH scale, this is called neutral. A solution whose

[H 3 O+] is greater than in pure water will have a pH less than 7.00 and is called acidic. A

solution whose [H 3 O+] is less than in pure water will have a pH greater than 7.00 and is

called basic. Figure 15.2, on the next page, shows the pH scale and the pH values of some

common substances.