Which of the following reactions give an alkyne? (a) sodium fumarate \(\frac{\text { Kolbe's }}{\text { electrolysis }}\) (b) \(\mathrm{CH}_{3} \mathrm{CBr}_{2} \mathrm{CHBr}_{2} \longrightarrow \underset{\mathrm{Zn} \text { /alcohol } / \Delta}{\longrightarrow}\) (c) \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CHBr}_{2} \stackrel{\mathrm{NaNH}_{2} / \Delta}{\longrightarrow}\) (d) \(\mathrm{CH}_{3} \mathrm{CHBr}-\mathrm{CH}_{2} \mathrm{Br} \stackrel{\mathrm{NaNH}_{2}}{\longrightarrow}\)

Kolbe's electrolysis is an electrochemical reaction that plays a significant role in chemistry. It is typically used to convert salts of carboxylic acids into alkanes. When a direct electric current is passed through an aqueous solution of a sodium or potassium salt of a carboxylic acid, the carboxylate ions undergo decarboxylation – which means that they lose their carbon dioxide groups. Since this technique involves removal of CO2 rather than the formation of carbon-carbon triple bonds, it does not lead to alkyne formation.

It's essential to understand that Kolbe's electrolysis does not involve the creation or breaking of carbon-carbon double or triple bonds, so it does not provide a pathway to create alkynes. This makes it clear why reaction (a) does not yield an alkyne but rather, if anything, an alkane or related structure.

The Corey-Fuchs reaction is a powerful method for transforming geminal dihalides into alkynes. In this process, a compound with two halogen atoms on the same carbon (a geminal dihalide) is converted into an alkyne through the use of a phosphonium ylide. It operates through a two-step mechanism which first forms a dibromoalkene intermediate that is then dehydrohalogenated to form the alkyne.

As the solution indicates, reaction (b) involves a geminal dihalide, making the Corey-Fuchs reaction applicable. It's a great example of how starting with a compound having two halogens on the same carbon can lead to the formation of an alkyne, thanks to the specific reagents and conditions used.

Dehydrohalogenation is a crucial reaction in organic chemistry where a halogen atom and a hydrogen atom are removed from adjacent carbon atoms – referred to as vicinal dihalides – resulting in the formation of an unsaturated bond. This reaction is often driven by bases such as sodium amide (NaNH2).

When applied to vicinal dihalides, as seen in reactions (c) and (d), dehydrohalogenation removes hydrogen and halogen to create a double or triple bond. In reaction (c), we already start with an alkene, which after two dehydrohalogenation steps can lead to the formation of an alkyne. However, reaction (d) will stop at the alkene stage since we begin with an alkane and would need additional steps to arrive at an alkyne.

Geminal dihalides are organic compounds where two halogen atoms are connected to the same carbon atom. This specific arrangement makes them attractive starting materials for several reactions, notably the formation of alkynes through the Corey-Fuchs reaction.

Geminal dihalides, due to the strain and instability caused by having two halogen atoms on a single carbon, are prone to elimination reactions, leading to the formation of multiple bonds between carbon atoms. The reaction (b) from the exercise perfectly illustrates a situation where a geminal dihalide is a key reactant that, under suitable conditions, can be converted into an alkyne.

Vicinal dihalides contain two halogen atoms attached to adjacent or neighboring carbon atoms. These compounds are particularly interesting in synthesis because of their susceptibility to dehydrohalogenation – a reaction that can yield alkenes or alkynes, depending on the starting material.

The exercise's reactions (c) and (d) showcase vicinal dihalides. While both are subject to dehydrohalogenation, only (c), which starts with an alkene, will proceed to generate an alkyne after the elimination of two molecules of HX (halogen hydrogen). In reaction (d), the starting alkane only undergoes a single elimination to become an alkene, which would need to undergo a further elimination to form an alkyne.