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Write formulas for the first five members of each homologous series beginning with HCOOH.

Answer
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Hint: HCOOH is formic acid. It belongs to the class of organic compounds called carboxylic acids. Each compound which is part of the homologous differs from its next compound with $-C{{H}_{2}}$group. You can now add a $-C{{H}_{2}}$to formic acid to identify the homologous series.

Complete step by step answer:
Homologous series is a sequence of compounds with the same functional group and similar chemical properties in which the members of the series are branched or unbranched.
Compounds within a homologous series typically have fixed functional groups that give them similar chemical and physical properties.
These properties typically change gradually along with the series, and the changes are explained by mere differences in molecular size and mass of the compounds.
From the above understanding we will now write the formulas for the members of the homologous series starting with HCOOH:
First member: $HCOOH$ ( methanoic acid )
Second member: $C{{H}_{3}}COOH$( ethanoic acid)
Third member: $C{{H}_{3}}C{{H}_{2}}COOH$( propanoic acid)
Fourth member: $C{{H}_{3}}C{{H}_{2}}C{{H}_{2}}COOH$ (butanoic acid)
Fifth member: $C{{H}_{3}}C{{H}_{2}}C{{H}_{2}}C{{H}_{2}}COOH$(pentanoic acid)

From the above series we see that as mentioned in the hint, the compounds differ from each other by a $-C{{H}_{2}}$ group.

Note: The homologous series of compounds have similar properties which are limited only to the starting members of the group. As the number of carbon atoms increases, we see a significant change in their properties, both physical and chemical. For example methane, ethane and propane exist as gases however higher members like hexadecane exist as a liquid. Alkanes having a number of carbon atoms greater than 14 exist as solids at room temperature although they are part of the same homologous series.