# The Relationship Between Dilution and Dissociation

## #H: Some Definitions

Be advised the equilibrium constant, $K$ The equilibrium constant relates reactant and product concentrations, representing the position of equilibrium for a reaction. , of a weak acid:

where $\mathrm H^+$ is the hydrogen ion, $\mathrm A^-$ is the conjugate base, and $\mathrm H\mathrm A$ is the weak acid. If $x$ is the concentration of the hydronium, then because $\mathrm H\mathrm A$ is monoprotic,

and because $\mathrm H\mathrm A$ is a weak acid,

Where $[\mathrm H\mathrm A]_0$ is the initial acid concentration.

Exciting stuff, I know! But this is where the fun starts. Firstly, note two things:

1. The equilibrium constant is roughly the square of the hydronium concentration, divided by initial acid concentration.
2. The reaction of the weak acid can be said to have some active describer ∂ representing the percent of the acid dissociated at equilibrium.

Okay. So consider the following:

## #He: What will happen to ∂ if we dilute the solution?

Hastily, most will say ,

Well, that’s obvious, clearly the percent dissociation must decrease!

Why?

If it’s diluted, the solution is less concentrated with hydronium ions, so a lesser percentage of the acid dissociates.

In a haste, this makes sense - a sort-of ‘duh’ derivation. Unfortunately, it’s a fallacy.

## #Li: Percent dissociation is inversely proportional to the concentration.

With some thought, we can understand why this is - first intuitively, then mathematically. When we dilute an acid, we are essentially adding more area upon which the acid can react, thus leading to a higher rate of dissociation. To prove this:

Let’s say we dilute our solution by a factor of ten. The reaction quotient $Q$ The reaction quotient describes the direction a reaction will proceed to establish equilibrium. can then be described as

Because the reaction quotient is an order of magnitude less than the equilibrium constant, the reaction will shift to the right The acid will dissociate further, increasing the numerator of the reaction quotient. in order to reach equilibrium.

QED - diluting a weak acid shifts the concentration of a reaction’s products to the left, leading the acid to dissociate more in order to reestablish equilibrium, thus increasing the percent dissociation.

Phew!