Page 291 - Physical chemistry understanding our chemical world

258 ACIDS AND BASES

bases. It is possible to write an equilibrium constant K to describe the hydrolysis of
bases such as ammonia (see Equation (6.12)). We write the appropriate equilibrium
constant in just the same way as we wrote an expression for K to describe the acidic
behaviour of phenol:
+
[NH 4 ][OH ]
−
K = (6.32)
We sometimes call the [NH 3 ][H 2 O]
equilibrium constant
in Equation (6.33) a As with the expression in Equation (6.6), this equilibrium constant
basicity constant,and can be simplified by incorporating the water term into K, thereby
symbolize it as K b . yielding a new constant which we will call K b ,the basicity con-
stant:
[NH 4 ][OH ]
+
−
K b = (6.33)
[NH 3 ]
where K b in Equation (6.33) is quite different from the K in Equation (6.32). The
−5
value of K b for ammonia is 1.74 × 10 , which is quite small, causing us to say
ammonia is a weak base. The value of K b for sodium hydroxide is much larger at
0.6, so we say NaOH is a strong base.
But, curiously, this new equilibrium constant K b is redundant because we could
have calculated its value from known values of K a according to

K a × K b = K w (6.34)
where K w is the autoprotolysis constant of water from p. 236. Older textbooks some-
times cite values of K b , but we really do not need to employ two separate K constants.

+
SAQ 6.9 What is the value of K a for the ammonium ion, NH 4 ?Take K b
from the paragraphs immediately above, and K w = 10 −14 .

Justification Box 6.3

Consider a weak acid, HA, dissociating: HA → H 3 O + A . Its acidity constant K a is
+
−
given by
+
−
[A ][H 3 O ]
K a = (6.35)
[HA]
and then consider a weak base (the conjugate of the weak acid) forming a hydroxide
−
−
ion in solution, H 2 O + A → OH + HA. Its basicity constant is given by
−
[HA][OH ]
K b = (6.36)
−
[A ]