A Fischer projection of 2,3,4-trihydroxypentanedioic acid (trihydroxyglutaric acid) has the vertical chain, top to bottom: $COOH$ , C2, C3, C4, $COOH$ . The $OH$ groups are on the right of C2, the left of C3 and the right of C4 (the other group on each centre is $H$ ). Using the rule that $R$ ranks above $S$ for the two ligand branches at C3, which description is correct?

A $(2 R, 3 R, 4 S)$ , chiral
B $(2 R, 3 S, 4 S)$ , chiral
C $(2 R, 3 s, 4 S)$ , meso (achiral)
D $(2 R, 3 r, 4 S)$ , meso (achiral)

Answer: C

C2 and C4 have the same constitution but mirror-image arrangements (OH both on the right), so one is

R

and the other

S

(2 R, 4 S)

, and the compound has an internal mirror plane, so it is meso. C3 carries two constitutionally identical branches of opposite chirality, so it is pseudo-asymmetric and takes a lower-case descriptor. Priorities at C3:

OH > C2 (R) > C4 (S) > H

OH

(left)

\to

C2 (top)

\to

C4 (bottom) is clockwise;

H

is horizontal, so reverse:

s

. Result:

(2 R, 3 s, 4 S)

, meso.

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Answer: C

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