See image — Isomerism and Stereochemistry Chemistry Question

💡 Solution & Explanation

Concept: In cyclohexane ring-flip equilibrium, the equilibrium constant Keq = [equatorial] / [axial] reflects the conformational preference of the substituent R for the equatorial position. This preference is quantified by the A-value (conformational energy difference, ΔG°). A larger, bulkier substituent has a greater preference for the equatorial position, giving a larger Keq. The relationship is Keq = exp(ΔG°/RT), where ΔG° is the A-value. Step 1: Identify A-values for each substituent: - R = H: There is no preference (both positions are identical for H), so Keq = 1. A-value ≈ 0 kcal/mol. - R = CH3 (methyl): A-value ≈ 1.74 kcal/mol, giving Keq ≈ 18 at room temperature. - R = Et (ethyl): A-value ≈ 1.79 kcal/mol, giving Keq ≈ 23 (slightly larger than methyl due to modest additional bulk, but ethyl's effective A-value leads to Keq ~23). - R = iPr (isopropyl, -CH(CH3)2): A-value ≈ 2.21 kcal/mol, giving Keq ≈ 38 at room temperature. Step 2: Match by size of Keq: - (a) R = H → Keq = 1 → matches (s) - (b) R = CH3 → Keq = 18 → matches (r) - (c) R = Et → Keq = 23 → matches (q) - (d) R = iPr → Keq = 38 → matches (p) Step 3: Why other options fail: - H cannot have Keq > 1 because axial and equatorial H are identical; there is no steric preference. - Isopropyl is bulkier than ethyl which is bulkier than methyl, so the Keq order must increase as: H < CH3 < Et < iPr, corresponding to 1 < 18 < 23 < 38. Therefore, the correct answer is a-s; b-r; c-q; d-p.