5.1.3 (c) Acid Dissociation Constants

Syllabus

(i) the acid dissociation constant, K_a, for the extent of acid dissociation

(ii) the relationship between K_a and pK_a

What does this mean?

What is the point of Dissociation Constants?

At least in theory Strong Acids are 100% dissociated in water - that is every acid molecule breaks up on dissolving, producing all the H⁺ ions that it possibly can immediately.

Weak Acids are only partly dissociated in water - that is most acid molecules dissolve without breaking up at all, producing no H⁺ ions. And only the small % of molecules that do dissociate produce any H⁺ ions at all.

But there is a range of Strength - acids that are 1% dissociated are clearly weaker than those that are 5% dissociated because they produce a lower concentration of H⁺ ions.

Rather than measure this by % we use an Acid Dissociation Constant (K_a) rather like K_c.

Sometimes we use the pK_a - of which more later - which is a simpler number, and therefore easier to use.

As you can see, the smaller the K_a the weaker the acid, but the higher the pK_a the weaker the acid.

What is the Dissociation Constant, K_a?

Imagine a weak, monobasic acid, HA.

It can dissociate to make an H⁺ ion and an A^- ion.

But because it is weak it doesn't fully do this.

The few dissociated ions sometimes recombine to reform HA, and some HA will occasionally dissociate to make more H⁺ ions and A^- ions.

It is in equilibrium.

The Equilibrium Constant, Kc = [H₃O⁺][A^-]/[HA][H₂O]

But the concentration of water is so high that this number would be almost meaninglessly small.

So H_a simply drops the H₂O term.

And we generally write [H₃O⁺] as [H⁺].

An acid that is particularly bad at dissociating (very weak) will produce incredibly small H⁺ and A^- concentrations and leave very high HA concentrations.

This will clearly make K_a a small number since it is a small numerator divided by a large denominator.

Conversely, an acid that is quite good at dissociating (not very weak) will produce higher H⁺ and A^- concentrations and leave lower HA concentrations.

This will clearly make K_a a larger number since it is a larger numerator divided by a smaller denominator.

What is pK_a?

You will become familiar with the idea the p is mathematical shorthand for -Log₁₀

Mostly, you will use the relationship: pH = -log₁₀[H⁺]

But some other exam boards (not OCR) also use pOH = -log₁₀[OH^-]

So, it will hardly come as a shock that pK_a = -log₁₀[K_a]

The only reason anyone ever uses pKa is that the numbers are much simpler.

Generally, you can't avoid learning about K_a anyway so if you don't like pK_a's you can always convert them back to K_a's providing you know how to reverse the formula pK_a = -log₁₀[K_a].

And you'll have to be able to covert pH to [H+] (as well as the reverse) - so it's really nothing to worry about.