Domain: Organic synthesis

Determine the molecular formula of the final product obtained when naphthalene undergoes sequential transformations: initial reaction with \(sodium(Na)\) and \(ammonia(NH_{3})\) in \(ethanol(EtOH)\) and \(diethyl\ ether(Et_{2}O)\), subsequent treatment with \(Potassium\ tert-butoxide(t-BuOK)\) in \(chloroform(CHCl_{3})\) at -30 to \(0^\circ\)C, followed by reaction using \(sodium(Na)\) and \(ammonia(NH_{3})\) in \(diethyl\ ether(Et_{2}O)\), and concluding with reaction using  (2,3-Dichloro-5,6-dicyano-1,4-benzoquinone(DDQ) and \(acetic\ acid(HOAc)\) in \(dioxane\) on heating to yield the final product.

Grading rubric:
criterion: Correct identification first step of naphthalene with sodium in liquid ammonia as a reduction of two aromatic π-bonds

weight: 10
criterion: Correctly identifies the first intermediate as 1,4,5,8-tetrahydronaphthalene

weight: 10
criterion: Correctly identifies the second intermediate as 9,9-dichloro-1,4,5,8-tetrahydro-4a,8a-methanonaphthalene


weight: 10
criterion: Correctly identifies the third step as a reductive dehalogenation of gem-dichlorocyclopropane to form a methylene bridge

weight: 10
criterion: Correctly identifies the third intermediate as 1,4,5,8-tetrahydro-4a,8a-methanonaphthalene

weight: 20
criterion: Correctly identifies the final product as bicyclo[4.4.1]undeca-1,3,5,7,9-pentaene
weight: 20
criterion: Gives the IUPAC molecular formula of the final product exactly as \\(C_{11}H_{10}\\)
weight: 20

Answer:
C11H10