Conjugate acids/bases — Acids & Bases

Acids and bases come in pairs, and the pairing is not a bookkeeping convenience — it is the reason the pKa table is useful in both directions. Every time you look up an acid, you have also looked up a base, and the two carry exactly the same information.

What "conjugate" means

A conjugate acid–base pair is two species that differ by exactly one proton. Remove a proton from an acid and what remains is its conjugate base. Add a proton to a base and what you get is its conjugate acid.

HCl and Cl⁻ are a conjugate pair. NH₃ and NH₄⁺ are a conjugate pair. So are CH₃COOH and CH₃COO⁻, and H₂O and HO⁻, and H₃O⁺ and H₂O. "Exactly one proton" is the whole definition: same atoms otherwise, differing by one H and one unit of charge.

Water appears in that list twice, as both a conjugate acid and a conjugate base, because it can lose a proton to become HO⁻ or gain one to become H₃O⁺. A species that can act as either is amphoteric, and several of the most important molecules in this course qualify: water, alcohols, amines, and — importantly for Module 12 — amino acids.

Worked example — labelling all four species

CH₃COOH + NH₃ ⇌ CH₃COO⁻ + NH₄⁺

Acetic acid loses a proton, so it is the acid, and acetate is its conjugate base. Ammonia gains a proton, so it is the base, and ammonium is its conjugate acid.

Every proton transfer has all four roles filled. The acid and its conjugate base are on opposite sides of the arrow, as are the base and its conjugate acid — that diagonal relationship is worth noticing, because it is what trips people up when labelling.

One reaction, four roles, filled simultaneously. Read the pairings vertically: acetic acid loses a proton to become acetate, ammonia gains one to become ammonium. Read them diagonally, as the dashed lines invite you to, and you get the classic mislabelling — acetate and ammonia are not a conjugate pair; they are simply the two species that happen to end up on opposite sides. A conjugate pair always differs by exactly one proton, nothing else.

Which way does it go? Left acid: acetic acid, pKa 4.76. Right acid: ammonium, pKa 9.2. The right has the higher pKa and therefore the weaker acid, so the equilibrium lies to the right by about 10⁴.

The inverse relationship

The stronger an acid is, the weaker its conjugate base — and the reverse. This is not a coincidence or a separate fact to memorize; it follows from what "strong acid" means. An acid is strong precisely because it gives up its proton readily, which means whatever is left behind must be comfortable holding the resulting electron pair without wanting the proton back. Comfortable holding it is exactly what "weak base" means.

Run the comparison in both directions. HCl has a pKa of −7, making it a very strong acid; chloride is correspondingly an extremely weak, stable, unreactive base — you can have sodium chloride in your food. Water has a pKa of 15.7, making it a weak acid; hydroxide is correspondingly a strong and reactive base. Ammonia has a pKa of 38, making it a vanishingly weak acid; amide ion (⁻NH₂) is correspondingly one of the strongest bases you will use.

This is the same idea as leaving-group ability from Module 2, seen from the other side. A good leaving group is a weak base, which is the conjugate base of a strong acid. "Conjugate base of a strong acid," "weak base," "stable anion" and "good leaving group" are four names for one property, and moving between them fluently is most of what makes Module 6 tractable.

One table, read in both directions. The stronger the acid, the more stable — and therefore the less basic — the anion it leaves behind. That is why chloride, the conjugate base of a ferociously strong acid, does essentially nothing as a base, while amide ion, left behind by the feeblest acid here, will deprotonate almost anything. It is also why "weak base", "stable anion" and "good leaving group" turn out to be three names for the same property in Module 6.Strong acid ↔ weak conjugate base. The pKa column is doing double duty: read it left to right for acid strength, right to left for base strength.

Reading a pKa table in both directions

A pKa table carries two rankings at once. Read down the acid column and acids get weaker. Read down the corresponding conjugate base column and bases get stronger. One table, two answers, depending on which question you are asking.

This explains something that otherwise looks strange about the reagents used in organic synthesis. The strongest bases in common use — LDA, NaNH₂, NaH, butyllithium — are all the conjugate bases of extraordinarily weak acids: an amine at pKa 38, hydrogen gas at 36, an alkane at 50. A base is strong because its conjugate acid is a terrible acid. If you want a ferociously strong base, you look for the weakest acid you can find and take its proton off.

Worked example — reading backwards to choose a reagent

You need to deprotonate a ketone's alpha hydrogen (pKa ≈ 20) completely, not partially.

Reading the table backwards: any base whose conjugate acid has a pKa well above 20 will do it. Hydroxide's conjugate acid is water at 15.7 — below 20, so hydroxide gives only a tiny equilibrium concentration of enolate. LDA's conjugate acid is diisopropylamine at about 36 — sixteen units above, so deprotonation is complete.

Both reagents are used deliberately in Module 11: hydroxide when you want a small equilibrium amount of enolate coexisting with unreacted ketone (for an aldol), LDA when you want quantitative, irreversible deprotonation.

"Conjugate" describes a relationship, not a property. Chloride is not "a conjugate base" in the abstract — it is the conjugate base of HCl. Every base is the conjugate base of something. Asking "is this a conjugate base?" is like asking "is this a sibling?"; the answer requires naming the other party.

Conjugate pairs differ by one proton, not by any other change. HSO₄⁻ is the conjugate base of H₂SO₄, and SO₄²⁻ is the conjugate base of HSO₄⁻ — but SO₄²⁻ is not the conjugate base of H₂SO₄, because they differ by two. Multi-proton acids have multiple pKa values, one per step, and each step is its own conjugate pair.

What carries forward

The conjugate relationship is what lets you use one table for everything: acid strength, base strength, leaving-group ability and anion stability are a single ranking read from different directions. That unification is what makes the next section — the four structural factors that set where a species sits on that ranking — worth studying once rather than four times.