Introduction

In substituted cyclohexanes such as methoxycyclohexane, conformational equilibrium depends on whether the substituent occupies an axial or equatorial position in the chair form. Because steric and electronic effects strongly favor equatorial substituents, the more stable chair conformer dominates the equilibrium mixture and shifts the equilibrium “to the right” toward that conformer.​

Concept: axial vs equatorial and equilibrium position

In a cyclohexane chair, each carbon bears one axial and one equatorial bond, and a substituent can flip between these positions via ring flip, giving two conformers in equilibrium. For most substituents, including methoxy, the equatorial conformer is lower in energy because it suffers fewer 1,3‑diaxial (gauche‑like) interactions than the axial conformer.​

When the equatorial conformer is more stable, the equilibrium constant $K$ for “axial ⇌ equatorial” is greater than 1, which means the equilibrium lies to the right, towards the equatorial product side. Experimental data for methoxycyclohexane show a clear preference for the equatorial methoxy conformer (equatorial population higher than axial), confirming that its equilibrium lies appreciably to the equatorial side.​

Detailed option‑wise explanation

Option A: equal populations in (a) and (b)

Option A states that both equilibria (a) and (b) have equal populations of their isomers, which would mean each equilibrium has $K\approx 1$ and roughly a 50:50 mixture of the two chair conformers. However, methoxy and related substituents do not give equal axial and equatorial populations; the equatorial conformer is significantly more stable and thus more populated, so this statement is incorrect for both (a) and (b).​

Option B: much greater amounts of left‑hand isomer

Option B claims that in both equilibria the isomer on the left dominates, which would imply that in each case the left structure is the equatorial and more stable conformer. In the given problem, equilibrium (a) is arranged such that the more stable conformer (equatorial methoxy) is on the right, while in (b) steric or electronic factors make the right‑hand structure less strongly favored, so both cannot simultaneously have “much greater” left‑hand populations; therefore option B is also incorrect.​

Option C: equilibrium (a) lies more to the right than (b) – correct

Saying “equilibrium (a) lies more to the right than equilibrium (b)” means that the equilibrium constant for (a) is larger, so the product side (right‑hand isomer) is more heavily populated in (a) than in (b). In equilibrium (a), the right‑hand conformer has the methoxy group in a strongly preferred, less hindered equatorial position with minimal 1,3‑diaxial interactions, giving a large $K$ value and hence a strong right‑hand shift; in equilibrium (b), additional electronic or steric factors reduce this preference, so its $K$ is smaller and the shift to the right is less pronounced, making option C correct.​

Option D: equilibrium (b) lies more to the right

Option D reverses the actual situation by claiming that equilibrium (b) is more product‑favored than (a). Because methoxycyclohexane and similar systems show a well‑established equatorial preference that is strongest when no extra destabilizing interactions are present—as in (a)—equilibrium (b) cannot surpass (a) in right‑hand preference; thus option D is incorrect.​

Key takeaways for exam preparation

• In substituted cyclohexanes, always identify which conformer places bulky or heteroatom‑containing substituents equatorial; that conformer is typically more stable and more populated.​

• When a question states “equilibrium lies to the right,” interpret it as a larger equilibrium constant and a higher fraction of the right‑hand conformer or product in the equilibrium mixture.​