Since Ka x Kb = Kw, is the conjugate base of a weak acid a weak base or a strong base?
To determine whether the conjugate base of a weak acid is a weak base or a strong base, we need to consider the dissociation constant of the acid. The dissociation constant of an acid is a measure of its strength and is denoted by the symbol Ka.
If a weak acid (denoted by HA) undergoes partial dissociation in water to form its conjugate base (denoted by A-), the equilibrium constant expression for the dissociation reaction is:
HA ⇌ H+ + A-
The corresponding dissociation constant (Ka) can be expressed as:
Ka = [H+][A-]/[HA]
We know that the ion product constant of water, Kw, is equal to 1.0 x 10^-14 at 25°C. It can be expressed as:
Kw = [H+][OH-]
Now, if we multiply the equilibrium constant expression for the acidic dissociation (Ka) by the equilibrium constant expression for the basic dissociation (Kb) of the conjugate base, we get:
Ka x Kb = [H+][A-] x [OH-][HB]
Since [H+][OH-] is equal to Kw, we can substitute the value of Kw:
Ka x Kb = Kw x [A-][HB]
From this, we can see that Ka x Kb = Kw x [A-][HB], where [A-] represents the concentration of the conjugate base and [HB] represents the concentration of its conjugate acid.
Since Kw is a constant, we can conclude that the product of the dissociation constants of a conjugate acid-base pair is also constant. Therefore, if the conjugate acid is a weak acid (with a small Ka value), its conjugate base will be a weak base (with a small Kb value).
In conclusion, the conjugate base of a weak acid is a weak base.