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The IUPAC name of:
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A.$3,4 - $ dimethylpentanoyl chloride
B.$1 - $ chloro-$1 - $ oxo $2,3 - $ dimethyl pentane
C.$2 - $ ethyl $3 - $ methylbutanoyl chloride
D.$2,3 - $ dimethylpentanoyl chloride

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Answer
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Hint: Functional group: In the hydrogen the atoms or groups which are other than carbon and hydrogen, are known as function groups. For example: chloride if chlorine is present in the compound.

Complete answer:
First of all we will talk about the alkanes, alkenes and alkynes.
Alkanes: The compounds which are formed by carbon and hydrogen and have only a single bond between the carbon-carbon atoms, are known as alkanes. For example: The first member of the alkane family is ethane $({H_3}C - C{H_3})$. The general formula of the alkane group is ${C_n}{H_{(2n + 2)}}$.
Alkenes: The compounds which are formed by carbon and hydrogen and have at least one double bond along with a single bond between the carbon-carbon atoms, are known as alkenes. For example: The first member of the alkene family is ethene $({H_2}C = C{H_2})$. The general formula of the alkene group is ${C_n}{H_{2n}}$.
Alkynes: The compounds which are formed by carbon and hydrogen and have at least one triple bond along with a single bond between the carbon-carbon atoms, are known as alkynes. For example: The first member of the alkyne family is ethyne $(HC \equiv CH)$. The general formula of the alkyne group is ${C_n}{H_{(2n - 2)}}$.
Number of carbon atom in alkaneName of the parent chain
OneMethane
Two Ethane
Three Propane
Four Butane
Five Pentane
Six Hexane
Seven Heptane

Functional group: In hydrogen the atoms or groups which are other than carbon and hydrogen, are known as function groups. For example: chloride if chlorine is present in the compound.
The first step in the IUPAC naming system is to identify the longest carbon chain containing the groups. Here in the given compound the largest chain contains five carbons. So the name of the parent chain will be pentane. Now here one function group is attached to the parent chain i.e. –oyl chloride group which is $ - COCl$ . And two branches are there in which methyl groups are present in the compound. Now we will number the carbon such that the carbon which contains functionality gets lower. So we will do the numbering from the right side. So the carbon containing the -oyl chloride group will get number one and the two branching carbon atoms will get number as two and three. So the IUPAC name will be as: $2,3 - $ methylpentanoyl chloride. Because of the presence of –oyl chloride group in the compound the suffix -oyl chloride is used in the IUPAC name of the molecule.

Hence option C is correct.

Note:
Suffix to some functional groups are as: for carboxylic acid suffix used is –oic acid, for alcohols suffix used is alkyl alcohol. For example: if an alcohol group is present in methane then the IUPAC name of the compound will be methyl alcohol.