Question

The correct statement about the following quaternary ammonium ion is:

• A. It has only \(C_2\)-symmetry, hence chiral
• B. It has \(S_4\)-symmetry, hence achiral
• C. It has no symmetry, hence chiral
• D. It has a centre of symmetry, hence achiral

Hint:

Do not just count stereocenters, check for an improper symmetry element (\(\sigma\), \(i\), or \(S_n\)); an \(S_4\) axis alone, without a separate mirror plane or inversion center, is enough to make a molecule with several stereocenters achiral.

Answer 1

The Correct Option is B

The trick in this question is not to stop at "how many stereocenters does it have," but to ask whether the whole molecule can be superimposed on its own mirror image. That is a question about symmetry elements, not about counting stereocenters.

1. It has only $C_2$-symmetry, hence chiral: a $C_2$ axis, a plain rotation axis, is indeed present here, running through $\mathrm{N}$ and the midpoint of the far $C{-}C$ bond. But a proper rotation axis by itself never makes a molecule chiral or achiral, chirality depends only on whether an improper element ($\sigma$, $i$, or $S_n$) exists. This option misses the improper axis that is actually present, so it wrongly calls the ion chiral.
2. It has $S_4$-symmetry, hence achiral: the four ring stereocenters are arranged as two methyls "up", next to $\mathrm{N}$, and two methyls "down", further from $\mathrm{N}$. A $90^{\circ}$ rotation about the axis through $\mathrm{N}$, combined with a reflection, swaps the up-pair with the down-pair and reproduces the exact same structure. That rotation-plus-reflection is an $S_4$ operation, and any molecule with an $S_n$ axis is achiral by definition.
3. It has no symmetry, hence chiral: this ignores the very regular "up, down, down, up" pattern the wedges and hashes show. The methyls are not placed randomly, so "no symmetry" is not correct.
4. It has a centre of symmetry, hence achiral: a true inversion center $i$ would require every atom to have a matching atom directly opposite through one central point, which the puckered five-membered ring does not provide. The achirality here comes from $S_4$, not from $i$.

Only the $S_4$ description fits both the observed wedge and hash pattern and the correct rule for chirality, the presence of any improper symmetry element makes a molecule achiral.

Let's summarize:

• Four stereocenters do not automatically make a molecule chiral, symmetry is what decides it.
• Any $S_n$ axis, not just a mirror plane or inversion center, is enough to make a molecule achiral.
• The "up-up, down-down" methyl pattern here generates an $S_4$ axis through $\mathrm{N}$.

The correct statement is that the ion has $S_4$ symmetry and is achiral, option (B).