In the last post we have seen that dissociation constant of acid Ka is directly proportional to the H+ concentration and dissociation constant of base Kb is directly proportional to the OH-concentration. As we know that H+ and OH- are related to each other too, so there must be some relation between Ka and Kb.
To find out their relation we have to study a reaction in which we can get both Ka and Kb, so that we can compare them with each other. And such a reaction can be provided by Brönsted acid base pair, so let’s take an example of Brönsted acid base pair:
NH3(aq) + H2O(l) ⇌ NH4+(aq) + OH- (aq)
In this reaction NH3 acts as base and it’s conjugate acid is NH4+. If we consider forward reaction, we can get the equation for Kb:
NH3(aq) + H2O(l) ⟶ NH4+(aq) + OH- (aq) ---------------(1)
Kb = [NH4+] [OH-]/ [NH3]
If we write a reaction for dissociation of acid NH4+, we can get the following equation for Ka:
NH4+(aq) + H2O(l) ⟶ H3O+(aq) + NH3(aq) ---------------(2)
Ka = [H3O+] [NH3]/ [NH4+]
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| Relation between pKa and pKb |
2H2O(l) ⟶ H3O+(aq) + OH- (aq)
This is the dissociation reaction of water we have studied before and we know that:
Kw = [H3O+][OH-]
Now you can see that if we multiply Ka and Kb we will get Kw
Ka × Kb = {[H3O+] [NH3]/ [NH4+]}{[NH4+] [OH-]/ [NH3]}
Ka × Kb = [H3O+] [NH3] [NH4+] [OH-]/[NH4+][NH3]
Ka × Kb = Kw
If we take (–log) of both sides, we will get:
pKa + pKb = pKw =14
A very important conclusion can be drawn from the above equation. If pKa of an acid is lower then its conjugate base must have higher pKb and vise versa, which means strong acid has a weak conjugate base.
We know that smaller the pKa, the stronger the acid. Very strong acids have pKa less than 1, moderately strong acids have pKain between 1 to 5 and weak acids have pKa in between 5 to 14.
What is the difference between pH and pKa?
Always remember that there is an important difference between pH and pKa, we use pH scale to measure the acidity and pKavalue indicates the strength of an acid. The pH is the characteristic of a solution, it means we can get solutions of different pH by dissolving the same acid in different quantities, like 1×10-2 M solution of HCl has pH 2 and 1×10-4 M solution of HCl has pH 4(HCl is a strong acid which dissociates completely i.e. its α is 1). On the other hand, pKa is the characteristic of the particular compound, for example, pKa of HCl is -7, HF is 3.5×10-4 and pKa of HCN is 4.9×10-10. It tells us how readily the compound gives up a proton H+. By pKa value you can also calculate the Kc
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| Relation Between equilibrium constant and pka |
NH3(aq) + H2O(l) ⇌ NH4+(aq) + OH- (aq)
Kc = [NH4+][OH-]/[NH3][H2O] -----------(3)
If we write equation for reactant acid H2O:
H2O(l) ⟶ H+(aq) + OH- (aq)
Ka (Reactant acid) = [H+][OH-]/[ H2O] -----------(4)
If we write equation for product acid NH4+
NH4+(aq) + H2O(l) ⟶ H+(aq) + NH3(aq)
Ka (Product acid) = [H+] [NH3]/ [NH4+] -----------(5)
When we compare equation 3, 4 and 5, we can infer that:
Kc = Ka (Reactant acid) / Ka (Product acid)
Now you are able to measure the strength of an acid, but what are the factors which make an acid strong or weak? Is it something which is hidden in its structure? In the next post we will try to reveal its secret.
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