Ionization of weak acids and bases

Weak acids and bases are miser kind of species, because even though they have H⁺ or OH^- ions, they don’t give them quickly and when they do give them, they only give a part of them. When weak acids/bases are dissolved in water they partly dissociate or ionize. To know how much H⁺ or OH^- ions they will release in water, we need to study their ionization reactions.

Let’s take an example of a weak acid HX and study its ionization in water:

HX_(aq) + H₂O_(l) ⇌ H₃O⁺_(aq)  + X^-_(aq)

If we have taken c mol/lit of HX initially at time t=0, when the concentration of H₃O⁺ and X^- were 0 and only a fraction of moles (α) underwent dissociation.

Suppose out of 1 mole of acid, α mole of acid undergoes dissociation.

Then from c moles of acid (c.α) will be dissociated.

At time t, (cα) moles of HX dissociate and produce (cα) moles of H₃O⁺ and (cα) moles of X^-. So at the time of equilibrium HX is left with (c-cα) moles/lit and H₃O⁺ and X^- each has (cα) moles/lit.

Dissociation Constant and Degree of Dissociation

Relation between Degree of Dissociation α and Dissociation Constant K_a:

Now we will calculate the equilibrium constant K_a  as it is the ionization reaction of an acid:

K_a = (cα) (cα)/ (c-cα)

K_a = cα² / (1- α)

K_a is the ionization or dissociation constant of acid HX and α is the degree of dissociation or the extent of ionization.

If we write equation of K_a in terms of molar concentration, we will get:

K_a = [H₃O⁺] [X^-]/ [HX]

Or

K_a = [H⁺] [X^-]/ [HX]

As you can see here that K_a is directly proportional to the H⁺ concentration, which means acids which have higher K_a value are stronger.

Similarly you can calculate the equilibrium constant K_b for a weak base. Let’s take an example of a weak base MOH and study its ionization in water:

MOH _(aq) ⇌ M⁺_(aq)  + OH^-_(aq)

If the initial concentration of MOH is c mole/lit and degree of dissociation is α, then at equilibrium MOH is left with (c-cα) moles/lit and M⁺ and OH^- each has (cα) moles/lit. So the K_b will be:

K_b = [M⁺] [OH^-]/ [MOH]

Or

K_b = cα² / (1- α)

K_b is directly proportional to the OH^- concentration, which means bases which have higher K_b value are stronger.

In the next post we will see if there is any relation between K_a and K_b.

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