5 Steps to a 5 AP Chemistry

For polyprotic acids, acids that can donate more than one proton, the Kafor the first
dissociation is much larger than the Kafor 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 Kwof 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 hydro-
nium ion and hydroxide ions are formed in equal amounts, the Kwexpression can be
expressed as:

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

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 shows the pH scale and the pH values of some common substances.

pH=−log[H O 3 +]log[.=− 10 10× −^7 ](.).=− −700 700=

[].HO 3 +2=×10 10−^14

Kw==×[][ ].HOH+ −−1 0 10^14 at C 25 o

H O(l) 2 H aq) + OH aq)+((−

HO(l)+HO(l)22 3HO aq)+OH aq)+((−

Equilibrium  219