 Solution

The two carbon skeletons are allene, $\mathrm{C}{\mathrm{H}}_2=\mathrm{C}=\mathrm{C}{\mathrm{H}}_2$, and propyne, $\mathrm{C}{\mathrm{H}}_3-\mathrm{C}\equiv \mathrm{CH}$. “Linear” describes the three-carbon skeleton; it does not mean every hydrogen lies on the same line.

For allene, use the contributor ${}^{2-}\mathrm{C}=\mathrm{C}={\mathrm{C}}^{2-}$. A terminal lone pair attacks a water hydrogen while the O–H pair returns to oxygen, giving $\mathrm{H}{\mathrm{C}}^{-}=\mathrm{C}={\mathrm{C}}^{2-}$ and hydroxide. Repeat at the still-dianionic end, then protonate each remaining terminal carbanion. The four successive proton transfers givewith two hydrogens placed on each terminal carbon in this branch.

For propyne, the resonance contributor ${}^{3-}\mathrm{C}-\mathrm{C}\equiv {\mathrm{C}}^{-}$ makes the alternative electron flow clear. Three successive protonations of the singly bonded terminal carbon convert its three lone pairs into C–H bonds; protonation of the acetylide end gives $\mathrm{C}{\mathrm{H}}_3-\mathrm{C}\equiv \mathrm{CH}$. These are formal protonation pathways for the multiply charged anion, not a claim that the highly charged resonance contributors are separately isolable species. Each transfer produces $\mathrm{O}{\mathrm{H}}^{-}$; overallAllene has one proton resonance integrating to 4H, ideally a singlet because its four hydrogens are chemically equivalent. Proton-decoupled carbon NMR has two resonances, in ratio two terminal carbons to one central carbon: approximately $75$ and $210$ ppm, respectively. The unusually downfield central cumulene carbon is not a carbonyl.

Propyne has two proton resonances, integrating 3H near $1.8$–$2.0$ ppm and 1H near $2$–$3$ ppm. If the small four-bond coupling is resolved, they are a methyl doublet and an acetylenic quartet; if unresolved, each can look like a singlet. Proton-decoupled carbon NMR has three resonances: one methyl carbon near $5$ ppm and two distinct sp carbons around $65$–$85$ ppm. These are approximate predictions, not supplied measured shifts.