Lactic Acid, Tartaric Acid and Counting Stereoisomers

Lactic acid has one chiral centre, tartaric acid two similar ones. Their forms lead to formulas for the number of optical isomers of any molecule.

Builds on: Part 8 · Optical Activity, Symmetry and Chirality.

Lactic acid

One chiral centre

Two enantiomers: (+) from meat extract, (−) from fermentation, and the racemic (±) acid in sour milk. The Fischer projection with OH on the right is D-lactic acid; capital D is the arrangement, not the sign.

Lactic acid enantiomers. — The two enantiomers in Fischer projection.

Tartaric acid

d, l and meso

Two similar centres give (+) (natural, m.p. 443 K), (−), and meso-tartaric acid (plane of symmetry, internal compensation, m.p. 416 K). Racemic acid (478 K) is a d + l mixture: 3 stereoisomers, not 4.

Counting

Optical isomers for n centres

Unsymmetrical: a = 2ⁿ, m = 0. Symmetrical, n even: a = 2ⁿ⁻¹, m = 2^(n/2−1). Symmetrical, n odd: a = 2ⁿ⁻¹ − 2^((n−1)/2), m = 2^((n−1)/2). Total = a + m; racemic forms r = a/2.

Formulas for optical isomers. — a = active forms, m = meso forms.

Table of stereoisomer counts. — Totals are tinted.

Worked examples

Plug in n

Lactic 2 · tartaric 3 · CH₃(CHOH)₂COOH 4 · pentitol 4 · glucose 16 · sorbitol 10 · the symmetrical n = 5 acid 16 (a = 12, m = 4).

Summary

Key formulas

a = 2^{n}, m = 0

Number of optical isomers

a = 2^{n - 1}, m = 2^{n /2 - 1}

Number of optical isomers

a = 2^{n - 1} - 2^{(n - 1) /2}, m = 2^{(n - 1) /2}

Number of optical isomers

total = a + m

Number of optical isomers

r = \frac{a}{2}

Number of optical isomers

JEE-style question

Your turn

How many stereoisomers does HOOC–(CHOH)₃–COOH have?

(a)8

(b)4

(c)6

(d)2

Show the answer and the traps

Symmetrical, n = 3: a = 2² − 2¹ = 2 active forms, and m = 2¹ = 2 meso forms. Total 4: option (b).

8 is 2³, used on a symmetrical molecule. 6 is the polyene formula from Part 7. 2 counts only the active forms.

Watch out

Common mistakes

Applying 2ⁿ to a symmetrical molecule.Identical halves give meso forms; the total is fewer than 2ⁿ.

Confusing meso with racemic.Meso: one compound, internal compensation. Racemic: a mixture, external compensation.

Practice

Try these

1. How many stereoisomers does CH₃CHBrCHBrCH₃ have?

Symmetrical, n = 2: a = 2, m = 1 → 3.

2. How many stereoisomers does CH₃CHClCHBrCH₃ have?

Unsymmetrical, n = 2: 2² = 4.

3. How many racemic forms does open-chain glucose have?

a = 16, so r = 8.

4. How many stereoisomers does HOOC–(CHOH)₄–COOH have?

Symmetrical, n = 4: a = 8, m = 2 → 10.