(a) (i) The frequencies of vibration of the following molecules in their v = 0 states are HCl : 2885 cm⁻¹; D₂ : 2990 cm⁻¹; DCl …

(a)(i) Energy change of HCl + D₂ → DCl + HD

Given: the v = 0 wavenumbers are HCl 2885, D₂ 2990, DCl 1990 and HD 3627 cm⁻¹. In the v = 0 state each molecule has only its zero-point energy, E = ½hc·ν̃.

The reaction energy is the zero-point energy of the products minus that of the reactants, so the common factor ½hc can be taken out:

ΔE = ½hc [(ν̃_DCl + ν̃_HD) − (ν̃_HCl + ν̃_D₂)]

Δν̃ = (1990 + 3627) − (2885 + 2990) = 5617 − 5875 = −258 cm⁻¹

Per mole: N_A·h·c = 6.022 × 10²³ × 6.626 × 10⁻³⁴ J s × 2.998 × 10¹⁰ cm s⁻¹ = 11.96 J mol⁻¹ cm.

ΔE = ½ × 11.96 × (−258) J mol⁻¹ = −1543 J mol⁻¹ ≈ −1.54 kJ mol⁻¹

The value is negative, so the products have lower zero-point energy than the reactants and energy is liberated. This is only the zero-point contribution to the energy change, as the data given allow.

(a)(ii) IR carbonyl absorptions of acid, ester and anhydride

The acid and the ester each have one C=O group, so each shows one strong band. The acid absorbs lower (1725 cm⁻¹) than the ester (1740 cm⁻¹) because its carbonyl is hydrogen-bonded in the dimer.

Butyric anhydride has two C=O groups joined through one oxygen. The two oscillators couple and give two bands, a symmetric stretch (higher, about 1825 cm⁻¹) and an asymmetric stretch (lower, about 1750 cm⁻¹). The bridging oxygen lone pair is shared between two carbonyls, so donation into each C=O is weaker than in an ester. The C=O bonds are therefore stiffer and the bands appear at higher wavenumber than for an ester. Hence the anhydride shows a doublet and the acid and ester a singlet.

(b)(i) Products of the three reactions

A: NaBH₄ reduces the ketone and leaves the ester, and the acid work-up protonates the alkoxide. A is methyl 4-hydroxycyclohexane-1-carboxylate.

B: the substrate is estrone (phenolic OH and a 17-ketone). Butyllithium, in excess to also deprotonate the phenol, forms lithium acetylide, which adds to the C-17 carbonyl. Work-up with H₃O⁺ gives the tertiary propargylic alcohol and restores the phenol. B is 17α-ethynylestradiol (ethinylestradiol).

C: Na/NH₃(l)/EtOH is a Birch reduction. The electron-donating OMe group stays on an sp² carbon and the ring is protonated at the ortho and meta positions, leaving the double bonds 1,4 to each other. C is 1-methoxycyclohexa-1,4-diene.

(b)(ii) Tacticity of polymers

Tacticity is the regularity of the relative stereochemical arrangement of the substituents on the stereocentres along a vinyl polymer chain, for example polypropylene. In an isotactic polymer all substituents lie on the same side of the zig-zag chain. In a syndiotactic polymer they alternate regularly from one side to the other. In an atactic polymer they are placed at random. Isotactic and syndiotactic polymers pack well and are crystalline and strong; atactic polymers are amorphous and soft.

(c)(i) Structure of C₁₆H₂₅NO

The formula gives 5 degrees of unsaturation. The IR band at 1690 cm⁻¹ is an aryl ketone C=O. The doublets at δ 7.21 and 7.81 (2H each) show a para-disubstituted benzene ring, the 7.81 pair being ortho to the C=O. The doublet at 1.29 (6H) with the septet at 3.12 (1H) is an isopropyl group on the ring. The triplet at 1.11 (6H) with the quartet at 2.40 (4H) is N(CH₂CH₃)₂. The two triplets at 2.55 and 2.65 (2H each) are a CH₂CH₂ unit between the carbonyl and nitrogen. Unsaturation is benzene (4) plus C=O (1) = 5, and the H count is 25.

The structure is 3-(diethylamino)-1-[4-(propan-2-yl)phenyl]propan-1-one, p-(CH₃)₂CH–C₆H₄–CO–CH₂CH₂–N(C₂H₅)₂.

(c)(ii) Order of chemical shifts of the lettered protons

The compound is a 4H-oxepine bearing a formyl and an acetyl group. Hd is the acetyl CH₃ (δ about 2.2). Hb is the enol-ether β-vinyl H, shielded by the oxygen lone-pair donation (about 5). Ha is the enol-ether α-vinyl H on the carbon bonded to O (about 6.3). He is also on an O-bearing vinyl carbon but is β to the acetyl C=O, so it is strongly deshielded (about 7.5). Hc is the aldehyde proton (about 9.7).

The increasing order is Hd < Hb < Ha < He < Hc. The δ values are typical estimates.