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# Weak Acids and Bases

Our generic reactions for a weak acid (HA) and a weak base (B) in water are the following:

HA(aq) + H2O(ℓ) ⇌ H3O+(aq) + A(aq)

B(aq) + H2O(ℓ) ⇌ BH+(aq) + OH(aq)

Notice that these are both ionizations. The fact that they are playing the role of a weak acid and a weak base also means that the forward reaction only proceeds by 1%. This means that 99% the original HA and B put into water stays as a soluble neutral molecule (no ionizing). This is why when you mix a weak acid or weak base at the same concentration as a strong acid or base, you will get a pH that is nearer 7 for both. Remember, the nearer to pH 7 you are, the more neutral the water is and that means the substance you put into solution is weaker than the one with the pH further from 7.

Compare below the same concentrations of three acids and the resulting pH and percent ionizations of the solutions. The first is a hydrochloric acid (HCl) - a strong acid. The second is acetic acid (CH3COOH) - a weak acid. And the third is hydrocyanic acid (HCN) - an even weaker acid.

#### We Chemists Prefer K's over %'s

Notice that underneath the percent ionizations in the figure are the $$K_{\rm a}$$ values. If you lookup a weak acid and are hoping to find its percent ionization, you will be disappointed. The problem with percent ionization is that it changes with concentration. All weak acids will ionize a bit more the more dilute the solution is. The limit of this rule is that at infinite dilution, all weak electrolytes (weak acids and bases) will ionize 100%, just like a strong electrolyte. The problem is the pH will be 7 at that point because it is infinitely dilute. We could list percent ionization WITH a matching popular concentration - like 0.10 M... but that is pretty limiting. This is why we use equilibrium constants (K) as our reference. K's do NOT change with concentration - they are true to their name - a constant.

Remember that equilibrium constants show a mathematical ratio based on the product concentrations over the reactant concentrations (see section 6.4). And, to make it even more obvious that you are dealing with a weak acid, the equilibrium constant will be Ka. And, if you have a weak base, the equilibrium constant will be Kb. So here are the two equilibrium constant expressions for both of those reactions at the top of the page.

$K_{\rm a} ={[\rm H_3O^+][\rm A^-]\over [\rm HA]}$

$K_{\rm b} ={[\rm BH^+][\rm OH^-]\over [\rm B]}$

The Table below is for a 0.10 M HA (weak acid) solution showing a series of Ka values and the matching percent ionization and pH.

KaionizationpH
1.1 × 10-310%2.00
1.0 × 10-51%3.00
1.0 × 10-70.1%4.00
1.0 × 10-90.01%5.00
1.0 × 10-110.001%6.00