Question bank — Cycloalkanes — Baeyer's strain theory; cyclohexane chair - boat, axial vs equatorial

False — the formula only applies to a FLAT ring, and cyclohexane is NOT flat. It puckers into a chair so every angle is ≈ $111°$, giving essentially zero angle strain; the flat number is irrelevant.

False — $d<0$ in the flat model means the angle is forced too wide, which Baeyer counted as strain. It signals nothing good; it just flags that the flat assumption has broken down and the ring will pucker instead.

True — that is precisely why the chair is the global minimum. Look down any C–C bond in a Newman projection (see figure) and the H's sit in the gaps, exactly like staggered ethane.

False — the boat keeps good $s{p}^3$ angles too. Its extra energy comes from eclipsing (torsional) strain along its two sides plus the steric flagpole H···H clash — not angle strain.

True — twisting slightly relieves the flagpole clash and some eclipsing, so the twist-boat sits a little below the pure boat, though still well above the chair.

False — axial bonds alternate up, down, up, down as you walk around the six carbons. A carbon whose axial points up has its equatorial tilting gently down, and vice versa.

False — the whole ring inverts. Every axial bond becomes equatorial and every equatorial becomes axial simultaneously; nothing stays put.

False — cis/trans is fixed by connectivity (geometry), not conformation. A flip swaps axial↔equatorial but a cis pair stays cis and a trans pair stays trans.

False — it is genuinely accurate for the small rings (cyclopropane, cyclobutane) that physically cannot pucker away their strain. It only fails once rings (five carbons and up) can escape into 3-D.

True — flat $d$ favours cyclopentane ($+1.5°$), but real cyclopentane puckers into an envelope that still carries some torsional strain, while chair cyclohexane has essentially none, so cyclohexane wins per CH₂ (compare via heat of combustion).

The error is assuming the ring is a flat hexagon. Real cyclohexane is a puckered chair with ≈ $111°$ angles, so no stretching and no instability.

Wrong — they are the same molecule but different energies. Axial-CH₃ suffers two 1,3-diaxial clashes, so equilibrium favours equatorial ≈ 95:5, driven by ΔG = −RT ln K.

Wrong — they are conformers. You only rotate about C–C single bonds (no bonds broken), and interconversion is fast at room temperature.

Wrong — flagpole strain is steric (van der Waals): two H atoms at the prow and stern of a boat point at each other and crowd. Angles stay near $109.5°$.

Backwards — axial points into the crowded 1,3-diaxial region shared with two other same-face axial groups. Bulky groups prefer equatorial, which points safely outward.

Wrong sign-handling — a negative $\Delta G$ makes the exponent $-\Delta G/RT$ positive, so $K>1$, correctly favouring the equatorial product.

Wrong — three points always define a flat plane; cyclopropane cannot pucker. That's exactly why it stays severely strained (flat $d=+49.5°$) and Baeyer's theory nails it.

It combines two wins at once — every bond angle sits near the ideal $109.5°$ (no angle strain, thanks to tetrahedral geometry) AND all adjacent C–H bonds are staggered (no torsional strain), with no flagpole clashes.

An axial group points into the same space as the two other axial bonds on the same face (1,3-diaxial positions); a large group there suffers steric repulsion, which it escapes by going equatorial.

There is no smooth zero-strain path directly between the two chairs; the twist-boat is the lowest-energy bridge (barrier ≈ $45\text{kJ/mol}$), so the flip routes through it.

Different rings have different numbers of CH₂ units, so total combustion heat scales with size. Dividing by CH₂ removes the size effect and isolates the strain-per-unit, giving a fair stability comparison.

His polygon geometry and the subtraction $109.5°-{\theta }_{\text{internal}}$ were correct; the flaw was assuming rings stay flat. Once rings fold into 3-D, the flat internal angle no longer describes the real bond angle.

On a chair, 1,4 carbons sit so that identical up/down "tags" (cis) force one methyl axial and one equatorial, while opposite tags (trans) let both point equatorial — the most stable arrangement.

Formally $d\to 109.5°-180°=-70.5°$, a large negative number. It is meaningless because giant rings pucker freely, keeping real angles near $109.5°$ — the flat model breaks completely.

No — although flat $d$ is small ($+1.5°$), a flat pentagon would eclipse all its C–H bonds (torsional strain). It puckers into an "envelope" to stagger them, trading a hair of angle strain for less torsional strain.

The preference shrinks toward zero — tiny groups cause negligible 1,3-diaxial strain, so both chairs are nearly equally populated. The equatorial bias is a size effect, not an absolute rule.

No — with all substituents being identical H's, the two chairs are indistinguishable and equal in energy. The equilibrium is 50:50 and the "flip" produces the same thing.

No — it puckers slightly into a "butterfly" to relieve eclipsing, accepting a tiny bit more angle strain in exchange for less torsional strain. Small rings still make trade-offs, just limited ones.

No — the chair is always the global minimum for unstrained cyclohexane. The boat/twist-boat only appear transiently during ring flips or when unusual bridging forces the geometry.