= Solution
\b[A and C are <chiral>; B is <achiral>.] In A, a <quaternary ammonium stereocenter> occurs because <nitrogen> has four different <substituents>: phenyl, methyl, ethyl, and the sulfinylethyl chain. It has no <nitrogen> <lone pair> available for ordinary <pyramidal inversion> of an <amine>. The <sulfoxide> <sulfur> is also stereogenic: its pyramidal arrangement distinguishes <oxygen>, methyl, the <nitrogen>-containing chain, and the lone-pair direction. There are two independent <stereocenters> and no internal symmetry, giving four configurations in two pairs of <enantiomers>. This is <chirality (chemistry)> of the <cation>; a <bromide> <counterion> does not remove it.
B can adopt a trans-1,4-dimethylcyclohexane chair with both methyl groups equatorial. An <inversion centre> at the chair centre exchanges its opposite <carbon> atoms and methyl groups. Its mirror image is therefore superposable: trans <substituents> in a flat ring drawing do not by themselves prove <chirality (chemistry)>. <ring inversion> gives the less favourable diaxial conformer without changing the <trans configuration>.
In C, tetrahedral <phosphorus> has four different <substituent> directions: oxo, methoxy, ethoxy, and phenoxy. \b[C has a <phosphorus stereocenter>.] Delocalization in the P–O bonds does not make these four ligand environments identical. A tetrahedral drawing and its mirror cannot be superposed without exchanging two ligands.
\Image[/past-exam-of-the-chemistry-b-course-of-the-university-of-cambridge/2023/paper-1-stereochemical-models.png]
{title=Original three-dimensional models of the two stereocenters in A, the inversion symmetry of trans-1,4-dimethylcyclohexane, and tetrahedral phosphorus in C}
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