Acidity of carboxylic acids

Strength of an acid

A carboxylic acid gives up its proton to water.

$\text{RCOOH} + \text{H}_{2}\text{O} \rightleftharpoons \text{RCOO}^{-} + \text{H}_{3}\text{O}^{+}$

The acid constant is $K_a = \dfrac{[\text{RCOO}^-][\text{H}_3\text{O}^+]}{[\text{RCOOH}]}$, and $\text{p}K_a = -\log K_a$. A smaller pKa means a stronger acid. A difference of one unit is a factor of ten in $K_a$.

Carboxylic acids are weak. A solution of $0.10\ \text{mol/L}$ ethanoic acid is only about $1.3\ \%$ ionised.

Why they are so much stronger than alcohols and phenols

The strength of an acid depends on how stable its conjugate base is. Compare three bases.

• An alkoxide ion, RO$^-$: the charge is on one oxygen and cannot spread.
• A phenoxide ion: the charge spreads into the ring. It is more stable. Phenol has a pKa near $10$.
• A carboxylate ion, RCOO$^-$: the charge spreads over two oxygen atoms, equally. Resonance puts a half charge on each. This is the most stable of the three.

So the pKa of ethanol is about $15.9$, phenol is about $10$, and ethanoic acid is $4.76$. The carboxylate ion has two equal C-O bonds. The acid has one C=O and one C-O of different lengths.

Carbonic acid and the test with hydrogencarbonate

Carbonic acid has a first pKa near $6.4$ (the value for dissolved carbon dioxide). A carboxylic acid is stronger, so it releases carbon dioxide from sodium hydrogencarbonate, with effervescence. Phenol is weaker, so it does not.

$\text{RCOOH} + \text{NaHCO}_{3} \longrightarrow \text{RCOONa} + \text{H}_{2}\text{O} + \text{CO}_{2}$

Carboxylic acids are also sparingly or fully soluble in water as their sodium salts. So an acid that does not dissolve in water will dissolve in aqueous sodium hydroxide or sodium hydrogencarbonate.

What a substituent does

The picture gives a ladder of pKa values. Read it from the top.

Electron-withdrawing groups make the acid stronger. A chlorine atom pulls electrons through the sigma bonds (the $-I$ effect). It lowers the negative charge on the carboxylate and stabilises it. So:

• Each extra chlorine strengthens the acid. $\text{CCl}_3\text{COOH}$ ($0.65$) is stronger than $\text{CHCl}_2\text{COOH}$ ($1.29$), which is stronger than $\text{ClCH}_2\text{COOH}$ ($2.86$).
• Fluorine is the strongest withdrawing halogen: the order is F, Cl, Br, I.
• The effect falls with distance. 2-Chlorobutanoic acid has a pKa of about $2.8$, 3-chlorobutanoic acid about $4.1$ and 4-chlorobutanoic acid about $4.5$. Butanoic acid itself is $4.82$.

Electron-releasing groups make the acid weaker. An alkyl group pushes electrons ($+I$). Methanoic acid ($3.75$) is stronger than ethanoic acid ($4.76$). Propanoic acid ($4.87$) is slightly weaker still.

In benzoic acids a group on the ring acts through the ring. A nitro group, which withdraws electrons, strengthens the acid. A methoxy group, which donates electrons by resonance, weakens it. Benzoic acid ($4.20$) is stronger than ethanoic acid ($4.76$), because the $sp^2$ carbon of the ring pulls electrons a little more than an alkyl group.

The ortho effect. Almost any group in the ortho position strengthens benzoic acid, whatever its electronic nature. The group twists the carboxyl group out of the plane of the ring, and this favours ionisation.

Dicarboxylic acids. The first ionisation is easier than the second. After one proton has gone, a second negative charge is harder to make.

At $\text{p}K_a = 4.76$ and $c = 0.10\ \text{mol/L}$, the pH is $2.88$. Move the pKa down to $1.29$. The acid is now half ionised, and the pH is not $\tfrac{1}{2}(\text{p}K_a - \log c)$ any more. Only the exact equation works.

Practise with new numbers

Try it in Python

The program solves the quadratic exactly for six acids at $0.10\ \text{mol/L}$. It prints $K_a$, the pH and the percentage ionised.

Common mistakes

• Using the approximation for a strong acid. The approximation needs a small percentage ionised. Trichloroethanoic acid is not.
• Saying that a bigger pKa means a stronger acid. It means a weaker acid.
• Ranking by the number of carbons. Look for withdrawing and releasing groups first.
• Forgetting the distance. A chlorine far from the carboxyl group does little.
• Expecting phenol to react with sodium hydrogencarbonate. It is too weak.

Remember these

• Carboxylate ion: charge shared by two oxygens. This makes carboxylic acids much stronger than alcohols and phenols.
• Electron-withdrawing groups strengthen the acid and the effect falls with distance. Alkyl groups weaken it.
• A smaller pKa means a stronger acid. $K_a = 10^{-\text{p}K_a}$.
• Carboxylic acids give carbon dioxide with NaHCO$_3$. Phenols do not.

Check yourself

Try each one on your own first. If you are stuck, open a hint. Then check with Show the answer.

1. Which is the stronger acid, methanoic or ethanoic?

2. Arrange in order of increasing acidity: ethanoic acid, chloroethanoic acid, trichloroethanoic acid.

3. How does one tell ethanoic acid from phenol with sodium hydrogencarbonate?

4. Why is 2-chlorobutanoic acid stronger than 4-chlorobutanoic acid?

References

• OpenStax, Chemistry 2e, Chapter 20, section 20.3 Aldehydes, Ketones, Carboxylic Acids, and Esters; Chapter 14 on acid-base equilibria.
• NCERT, Chemistry Part II for Class XII, Chapter 8, the section on the acidity of carboxylic acids and the effect of substituents.