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Well I was studying organic chemistry, and I came across this reaction for increasing the length of the carbon chain. Upon asking my teacher about the following reaction, she said she was unsure about it. Is this a valid reaction? And if it is, can you please provide the name of the reagent and the actual mechanism?

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I think the reagent you're talking about is ketene (R=H in the figure below). It is a linear molecule (the central carbon is $\ce{sp}$ hybridized) and very reactive.

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When mixed with an alkane and heated it dimerizes to form diketene rather than react with the alkane.

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However, when irradiated with light, ketene will produce the reactive carbene "methlylene" ($\ce{CH2:}$). When this photolysis is performed in the presence of an alkane, the methylene will insert itself into the various $\ce{C-H}$ bonds like you've drawn. However the reaction is not synthetically useful for a number of reasons. For example, the $\ce{C-H}$ insertion reaction is very indiscriminate and a variety of products will be formed if different $\ce{C-H}$ bonds exist in the molecule.

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  • $\begingroup$ Oh, so it is not the best way to increase the length of the carbon chain? Then what is a better reaction to do so? Is there a way to only increase the chain one at a time? $\endgroup$ – Gummy bears Jan 17 '15 at 7:03
  • $\begingroup$ @Gummybears That's right, the ketene method is not a synthetically useful way to extend a carbon chain. Starting with an alkane, there is no good way to extend the chain by one carbon at a time. You could do something like free radical bromination of the alkane, separate (ugh!) all of the resulting isomers, then form a Grignard reagent and react it with carbon dioxide to generate the one carbon longer carboxylic acid. In the lab, you would actually just buy the alkyl bromide and skip the messy bromination step. BTW, if the above answer was helpful, please mark it as accepted, thanks! $\endgroup$ – ron Jan 17 '15 at 14:41
  • $\begingroup$ Well I really don't want it for a lab process. Hmm... then what is the best way to increase the length of the carbon chain of an alkane? $\endgroup$ – Gummy bears Jan 17 '15 at 16:42
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    $\begingroup$ @Gummybears If you have to start with the alkane (like on a test), then free radical bromination (as described in my earlier comment) is probably the way to go. I'm not aware of any method that can selectively target a specific C-H bond in an alkane where many different C-H bonds might exist. C-H bond activation is an active area of current research. There are some organometallic reagents that can select certain C-H bonds in non-alkanes. You might want to post this as a new question. $\endgroup$ – ron Jan 17 '15 at 17:04
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I would describe the reaction as a C-H insertion reaction of the carbene generated in situ from ketene. The reaction starts with an initial release of carbon monoxide to generate the highly electrophilic 6 electrons carbene species, which is then involved in a C-H insertion process. The C-H insertion can proceed through two mechanism: via singlet state or triplet state of the carbene. The carbene is a very electrophilic sp2 hybridized species with 6 electrons: a lone pair and two pairs in bond orbitals (with H atoms). Singlet carbenes have the lone pair of electrons in a nonbonding sp2 orbital and have an empty p orbital, while triplet carbenes have two unpaired electrons, one in a sp2 and the other in a p orbital. C-H insertion mediated by singlet carbenes is believed to proceed through a concerted mechanism, with the side-on approach of the carbene which provide constructive orbitals overlapping. Triplet carbene insertions should follow a two-step radical pathway, but it is generally accepted that the reaction proceed through singlet state carbenes (supported by retention of stereochemistry observed when if the C-H bond is at a stereogenic center).

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