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The hydrocarbon with seven carbon atoms containing a neopentyl and a vinyl group is:
a.) 4,4-dimethylpentane
b.) 2,2-dimethyl-3-pentene
c.) 2,2-dimethyl-4-pentene
d.) Isopropyl-2-butene

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Answer
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Hint: The structure of vinyl and neopentyl groups are \[ - CH = C{H_2}\] and \[ - C{\left( {C{H_3}} \right)_3}\] respectively. Among the options given to us, only 4,4-dimethylpentane contains both the vinyl and the neopentyl groups.

Complete step by step answer:
Let’s first look at neopentyl and vinyl groups.
Neopentane is a double-branched-chain alkane with five carbon atoms, also called 2,2-dimethylpropane or \[ - C{\left( {C{H_3}} \right)_3}\] . Neopentane is a flammable gas at room temperature and pressure which on a cold day or in an ice bath, or when compressed to a higher pressure, may condense into a highly volatile liquid.
Neopentane has achiral tetrahedral symmetry and is the simplest alkane with quaternary carbon.
With the molecular formula \[{C_5}{H_{12}}\] (pentane), it is one of the three structural isomers, the other two being n-pentane and isopentane.
In chemistry, the functional group with the formula \[ - CH = C{H_2}\] is vinyl or ethenyl (abbreviated as Vi). It is the molecule of ethylene (IUPAC ethene) \[\left( {{H_2}C{\text{ }} = {\text{ }}C{H_2}} \right)\] with one less hydrogen atom. The name vinyl is also used for compounds that contain the group \[R - CH = C{H_2}\] where R is any other group of atoms. Vinyl is among the alkenyl functional groups. The \[s{p^2} - \] hybridized carbons on the carbon skeleton are vinylic.

So among the following compounds, only 4,4-dimethylpentane contains both the neopentyl group and a vinyl group. The structure of 4,4-dimethylpentane is shown below
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As you can see in the diagram the left part in the diagram of 4,4-dimethylpentane contains a vinyl group and the right highlighted part is the neopentyl group.
So, the correct answer is “Option A”.

Note: In these kinds of problems we just have to check the structural formula of the given options. Then define and make the structure of the groups that have to be in the structure (in this case vinyl group and neopentyl group). Then check in which of the given molecules contain the groups vinyl and neopentyl (they can vary from problem to problem).