Chemistry - Reaction between a carbene and n-pentane

Solution 1:

n-Hexane is one of the 3 products formed. Carbenes are high-energy, reactive intermediates. Due to their extreme reactivity they usually react indiscriminately. In the case of methylene (the carbene in your diagram), it will insert into each of the different $\ce{C-H}$ bonds that are present in n-pentane. Because of its reactivity, the 3 products will be formed in a statistical ratio that is roughly equivalent to the number of different hydrogens present in the starting n-pentane, 6:4:2.

If you'd like to learn more about carbenes, for example

• singlet and triplet carbenes
• their addition to carbon-carbon double bonds

then take a look at these earlier answers - ref_1, ref_2

Solution 2:

Carbenes:

The reactions of carbenes with alkenes are well documented (e.g., cyclopropane formation by intramolecular cycloadditions to alkenes). Yet, the reactions of carbenes with alkanes have different story. Carbenes can undergo insertion into a $\ce{C-H}$ bond. The the mechanism involves hydrogen transfer to carbene from alkane through cyclic intermedeate of $\ce{C*-H--CH2--C*}$ to substitute $\ce{-H}$ by $\ce{-CH3}$ (read). That mechanism has close resemblance to the mechanism suggested for the intramolecular cycloaddition of carbenes to alkene (ref 1). However, the reactivity of carbenes is depend on whether the excited state of the carbenes at singlet or triplet state 1 (courtesy from Ref.1)

Singlet carbenes can insert in a concerted manner, with the orbitals overlapping constructively provided the carbene approaches side-on, whereas triplet carbenes insert via a two-step radical pathway. However, very few triplet carbene insertions have been observed. Nonetheless, insertion between two carbons are unlikely, according to two separate groups from Yale and Princeton Universities (ref 2). Accordingly, when bicyclo[1.1.0]butane (also 1,3-dimethyl version) was treated with carbene, it did not insert between bridged carbon atoms, which is the most unstable bond, to give expected bridged methylene group (e.g., ref 3). Princeton group has very interesting on different approach, but similar result: see ref 4.

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References:

1. Carbenes: Synthesis, properties, and organometallic chemistry: Coord. Chem. Rev., 2009, 253(7-8), 862–892; https://doi.org/10.1016/j.ccr.2008.05.018
2. Bicyclo[1.1.0]butane: Tetrahedron, 1965, 21(10), 2749-2769; https://doi.org/10.1016/S0040-4020(01)98361-9
3. 1,3-Dimethylbicyclo[1.1.0]butane: Tetrahedron Lett, 1965, 6(15), 991-995; https://doi.org/10.1016/S0040-4039(01)99513-9
4. Reaction of carbenes with bicyclo[2.1.0]pentane: Tetrahedron Lett, 1985, 26(44), 5399-5402 https://doi.org/10.1016/S0040-4039(00)98218-2