Exercises — Types of organic reactions — addition, substitution, elimination, rearrangement

Type: Addition (hydrogenation).

• Two molecules (${\text{C}}_3{\text{H}}_6+{\text{H}}_2$) became one (${\text{C}}_3{\text{H}}_8$).
• The $\text{C=C}$ $\pi$ bond opened; two $\text{H}$ atoms added across it.
• Degree of unsaturation dropped from $1\to 0$.
• Nothing left the molecule. → Addition confirmed by the classifier's box 2.

Type: Substitution (nucleophilic).

• ${\text{Cl}}^{-}$ left and ${\text{CN}}^{-}$ (a nucleophile) took its exact place.
• Atoms in ($\text{CN}$) = atoms out ($\text{Cl}$); no $\pi$ bond born or destroyed.
• This is box 4 of the classifier — a group swap.

Type: Elimination (dehydration).

• $\text{-OH}$ and a $\beta$-$\text{H}$ left as ${\text{H}}_2\text{O}$ from adjacent carbons.
• A new $\text{C=C}$ $\pi$ bond was born — unsaturation rose $0\to 1$.
• One molecule split into two. Box 3.

Major product: ${\text{CH}}_3{\text{-CHBr-CH}}_3$ (2-bromopropane).

• Step 1 (slow): the $\pi$ electrons grab ${\text{H}}^{+}$. $\text{H}$ can land on C1 (terminal) or C2.
• Landing on C1 puts the $+$ charge on C2, giving a secondary carbocation.
• Landing on C2 would leave a primary cation — much less stable.
• By Carbocation stability ($3^{\circ }>2^{\circ }>1^{\circ }$, via Hyperconjugation and Inductive effect), the mechanism takes the $2^{\circ }$ path.
• Step 2 (fast): ${\text{Br}}^{-}$ adds to $\text{C2}$. So $\text{Br}$ sits on the more substituted carbon → Markovnikov.

Major product: but-2-ene, ${\text{CH}}_3{\text{-CH=CH-CH}}_3$.

• Two $\beta$-hydrogens are available: on C1 (the terminal ${\text{CH}}_3$... actually the far ${\text{CH}}_2$) giving but-1-ene, or on C3 giving but-2-ene.
• But-2-ene is disubstituted ($2$ alkyl groups on the double bond); but-1-ene is monosubstituted.
• More alkyl groups → more hyperconjugation → lower-energy alkene → Saytzeff major.

Mechanism: $S_{N}2$. Rate $=k[{\text{CH}}_3\text{Br}][{\text{OH}}^{-}]$.

• Substrate is methyl (least hindered) — no stable carbocation possible, so $S_{N}1$ is ruled out.
• ${\text{OH}}^{-}$ is a strong nucleophile; acetone is polar aprotic (doesn't cage the nucleophile).
• Both favour the one-step backside attack → inversion (see left panel of figure). See SN1 vs SN2 mechanisms.

Mechanism: $S_{N}1$. Rate $=k[{\text{(CH}}_3{\text{)}}_3\text{C-Br}]$; outcome = racemisation.

• Tertiary carbon → too crowded for backside attack ($S_{N}2$ blocked), but forms a very stable $3^{\circ }$ carbocation.
• Polar protic solvent (water/ethanol) stabilises that cation.
• The planar cation is attacked from both faces equally → racemic mixture (right panel of figure).

Elimination, E2.

• A bulky base is too fat to reach the carbon for substitution but can still pluck an exposed $\beta$-$\text{H}$.
• Strong base + one concerted step → E2, rate $=k[\text{sub}][\text{base}]$.
• See E1 vs E2 mechanisms. Bulky base also steers toward the Hofmann (less substituted) alkene, but the classification is firmly E2.

Product: 2-methylbutan-2-ol, ${\text{(CH}}_3{\text{)}}_2{\text{C(OH)-CH}}_2{\text{-CH}}_3$. Types: Substitution ($S_{N}1$) with Rearrangement (1,2-methyl shift).

• Step 1: ${\text{Br}}^{-}$ leaves the ${\text{CH}}_2$, giving a primary neopentyl cation ${\text{(CH}}_3{\text{)}}_3{\text{C-CH}}_2^{+}$ — very unstable.
• Step 2 (rearrangement): a methyl group migrates with its bonding pair (1,2-methyl shift) to convert the $1^{\circ }$ cation into a $3^{\circ }$ cation ${\text{(CH}}_3{\text{)}}_2\stackrel{+}{C}{\text{-CH}}_2{\text{-CH}}_3$. Formula unchanged (${\text{C}}_5{\text{H}}_{11}^{+}$).
• Step 3: water attacks the $3^{\circ }$ carbon, then loses ${\text{H}}^{+}$ → the tertiary alcohol.
• The rearranged product dominates because energy drops going $1^{\circ }\to 3^{\circ }$.

Major product: 2-chloro-2-methylbutane, ${\text{CH}}_3{\text{-CCl(CH}}_3{\text{)-CH}}_2{\text{-CH}}_3$. Types: Addition + Rearrangement.

• ${\text{H}}^{+}$ adds to C1 (terminal) → a $2^{\circ }$ cation on C2: ${\text{CH}}_3\text{-}\stackrel{+}{C}{\text{H-CH(CH}}_3{\text{)}}_2$.
• A 1,2-hydride shift from the adjacent $\text{CH}$ turns the $2^{\circ }$ cation into a $3^{\circ }$ cation on C3.
• ${\text{Cl}}^{-}$ then adds to the $3^{\circ }$ carbon → the "unexpected" Markovnikov-plus-rearranged product.
• Lesson: whenever a more stable cation is one shift away, expect rearrangement even in simple additions.

Type: Aromatic Electrophilic Substitution ($S_E$Ar).

• The electrophile ${\text{NO}}_2^{+}$ attacks the ring $\pi$ cloud, forming a resonance-stabilised arenium ion (Wheland intermediate) — momentarily an addition-like species.
• But instead of a nucleophile adding (which would destroy aromaticity), a ring ${\text{H}}^{+}$ is lost, restoring the aromatic sextet.
• Net: one $\text{H}$ out, one ${\text{NO}}_2$ in, ring $\pi$ system preserved → substitution. See Aromatic Electrophilic Substitution.
• Addition is avoided because keeping aromaticity ($\sim 150$ kJ/mol resonance energy) is worth far more than the two extra $\sigma$ bonds addition would buy.

(a) Rate law: Rate $=k[\text{substrate}]$ (first order), because nucleophile concentration has no effect — consistent with a rate-determining ionisation step (classic $S_{N}1$). (b) For a first-order reaction, half-life $t_{1/2}=\frac{\ln 2}{k}$, so $t_{1/2}\propto 1/k$.

• The $3^{\circ }$ substrate has $k$ larger by $10^4$, so its half-life is smaller by $10^4$: $t_{1/2}(3^{\circ })=\frac{200\text{s}}{10^4}=0.02\text{s}=2\times 10^{-2}\text{s}.$
• The huge rate jump is Carbocation stability in action: the $3^{\circ }$ cation forms $10^4\times$ faster because it is so much lower in energy.

Rule: Saytzeff — the more substituted (but-2-ene) is major.

• Major:minor $=60:40=3:2=1.5$.
• Consistent with Saytzeff since the disubstituted alkene (but-2-ene) is favoured by hyperconjugation. See E1 vs E2 mechanisms and Leaving groups (${\text{Br}}^{-}$ is a good leaving group, enabling the elimination).

L1.1 type? ::: Addition (hydrogenation). L1.2 type? ::: Nucleophilic substitution. L1.3 type? ::: Elimination (dehydration). L2.1 major product? ::: 2-bromopropane (Markovnikov). L2.2 major alkene? ::: but-2-ene (Saytzeff). L3.2 stereochemical outcome? ::: Racemisation ($S_{N}1$). L4.1 product & extra step? ::: 2-methylbutan-2-ol via $S_{N}1$ + 1,2-methyl shift. L5.2(b) tertiary half-life? ::: $0.02$ s. L5.3 major:minor ratio? ::: $3:2=1.5$.