Cysteine — pK a Assignment and Ionisation States: 04-BS-12, May 2016, Q2

Question 2: Cysteine — pK_a Assignment and Ionisation States

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(a) Assignment. Cysteine, HSCH₂CH(NH₃⁺)CO₂H, carries three ionisable groups, and each class of group has a well-separated characteristic acidity range: an α-carboxylic acid (pK_a typically 1.7–2.3, strongly acidified by the adjacent, inductively-withdrawing ammonium), a thiol (pK_a typically 8–10, thiols being noticeably more acidic than alcohols because sulfur's larger, more polarisable orbitals stabilise the thiolate's negative charge better than oxygen does), and an α-ammonium (pK_a typically 9–11, an ordinary primary ammonium). These three windows do not overlap, so the assignment is unambiguous:

pK_a	Group	Reasoning
1.8	α-CO₂H	most acidic class by a wide margin; the adjacent NH₃⁺ withdraws further, lowering it from a "normal" acid's ~4.8
8.3	–SH (thiol)	thiols are intrinsically more acidic than the ammonium window
10.8	α-NH₃⁺	ordinary primary ammonium, least acidic of the three

(b) Ionisation state at each pH. Moving up in pH, each group loses its proton in turn, in order of increasing pK_a, once the pH passes that group's pK_a:

pH 1 (below all three pK_a's) — fully protonated cation, net charge +1. CO₂H, SH and NH₃⁺ all remain protonated.
pH 1: fully protonated cation (+1)
pH 5 (between pK_a1=1.8 and pK_a2=8.3) — the zwitterion, net charge 0. The carboxylic acid has lost its proton (CO₂⁻); the thiol and ammonium are still protonated. This is the dominant, overall-neutral form found near physiological pH.
pH 5: zwitterion (0) — dominant physiological form
pH 9 (between pK_a2=8.3 and pK_a3=10.8) — net charge −1. The thiol has now also lost its proton (thiolate, S⁻); the ammonium is still protonated.
pH 9: thiolate anion (−1)
pH 12 (above all three pK_a's) — net charge −2. The ammonium has finally lost its proton too (free amine, NH₂), leaving carboxylate and thiolate both deprotonated.
pH 12: dianion (−2), free amine

Concept & Theory

Topic. Stepwise acid–base ionisation of a polyprotic amino acid.

Key relations. Henderson–Hasselbalch: a group is predominantly deprotonated once pH exceeds its pK_a by ≳1–2 units, and predominantly protonated when pH is below it by the same margin; each ionisable group's state can be read off independently once the groups are ordered by pK_a.

Why this works. Because the three pK_a's are well separated (1.8, 8.3, 10.8), at any pH tested here only one group is near its transition — the other two are unambiguously fully protonated or fully deprotonated, so the structure at each pH follows directly from counting how many of the three pK_a's have been passed.

Common pitfall. Assuming the free-base amine (NH₂, not NH₃⁺) is present at neutral/physiological pH — it is not; the ammonium (pK_a 10.8) stays protonated all the way up to pH 9, which is why the pH 5 zwitterion (not a fully neutral, uncharged-everywhere species) is the physiologically relevant form.

Source. McMurry, Organic Chemistry, 9th ed., Ch.26 (amino acid ionisation, isoelectric behaviour).

Question 2 of 13: Cysteine — pK a Assignment and Ionisation States

Question 2: Cysteine — pKa Assignment and Ionisation States

Question 2: Cysteine — pK_a Assignment and Ionisation States