Domain: Organic synthesis

An organic compound, tert-butyl 3-methylenepyrrolidine-1-carboxylate, is subjected to a multi-step transformation. In the first step, it is treated with osmium tetroxide (OsO₄) and N-methylmorpholine N-oxide (NMO) in a THF–water mixture at 40 °C, resulting in the formation of intermediate X. In the second step, intermediate X reacts with 3-chloro-2-(chloromethyl)prop-1-ene in the presence of sodium hydride (NaH) in THF at 60 °C for 72 hours, yielding organic product A. In the third step, product A is again treated with OsO₄ and N-methylmorpholine N-oxide in THF–water at 40 °C to form intermediate Y. Finally, intermediate Y is reacted with sodium periodate (NaIO₄) in methanol–water, leading to the formation of the final organic product. Determine the molecular formula of the final organic product.

Grading rubric:
criterion: Does the response identify Intermediate X as tert-butyl 3-hydroxy-3-(hydroxymethyl)pyrrolidine-1-carboxylate?
weight: 10
criterion: Does the response identify the reaction in Step 2 as a double alkylation?
weight: 10
criterion: Does the response identify Product A as tert-butyl 8-methylene-6,10-dioxa-2-azaspiro[4.6]undecane-2-carboxylate?
weight: 10
criterion: Does the response identify step 3 as dihydroxylation of the exo-methylene group of Product A?
weight: 10
criterion:  Does the response identify the intermediate Y as tert-butyl 8-hydroxy-8-(hydroxymethyl)-6,10-dioxa-2-azaspiro[4.6]undecane-2-carboxylate?
weight: 10
criterion: Does the response identify the final step involving oxidative cleavage of a 1,2-diol?
weight: 10
criterion:  Does the response identify the final organic product as tert-butyl 8-oxo-6,10-dioxa-2-azaspiro[4.6]undecane-2-carboxylate?
weight: 20
criterion: Does the final answer explicitly state the molecular formula as C13H21NO5?
weight: 20

Answer:
C13H21NO5