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I have to tell the name of the following compound

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The name is cyclopropylmethyl cyclobutanecarboxylate. All of it makes sense but I don't understand why the suffix carboxylate comes? Why are we writing the single carbon left unaccounted for by using carboxyl ? Kindly clarify.

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The group -COO- is called "carboxylate" if it is included in a molecule with some organic radicals attached on its left and on its right-hand side. It is a definition, due to the fact that there is a carbon atom bound to an oxygen atom. Joined together, it makes carboxy. This terminology is used when no simpler way of naming this structure exists.

Examples. The structure CH3-COO- may be called methylcarboxylate. But usually it is called acetate. It is shorter.

The structure C6H5COO- may be called phenylcarboxylate. But usually it is called benzoate, as it is a shorter name.

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The names of esters are usually formed by placing the alcoholic component in front of the name of the acid component as a separate word. The corresponding rules in the current version of Nomenclature of Organic Chemistry – IUPAC Recommendations and Preferred Names 2013 (Blue Book) read as follows.

P-65.6.1 General methodology

Neutral salts and esters are both named using the name of the anion derived from the name of the acid. Anion names are formed by changing an ‘-ic acid’ ending of an acid name to ‘-ate’ and an ‘-ous acid’ ending of an acid name to ‘-ite’. Then, salts are named using the names of cations, and esters the names of organyl groups, cited as separate words in front of the name of the anion.

Since the acid component of the ester that is given in the question is cyclobutanecarboxylic acid, the corresponding ester is named as … cyclobutanecarboxylate.

However, that does not completely answer your question why the extra carbon atom is named using the ‘carboxy’ part.

Simple carboxylic acids are named substitutively using the suffix ‘oic acid’ as follows.

P-65.1.2.1 Carboxylic acid groups, $\ce{-COOH}$, that conceptually replace a $\ce{-CH3}$ group of methane or terminate an unbranched hydrocarbon chain are named by replacing the final ‘e’ of the name of the corresponding hydrocarbon by the suffix ‘oic acid’. No locants are necessary to denote the positions of the carboxylic acid groups in a hydrocarbon chain; locants are used when hydrocarbon chains are modified by skeletal replacement, as shown in P-15.4.3.2.3. Except for formic acid, acetic acid, oxalic acid (see P-65.1.1.1), and oxamic acid (see P-65.1.1.1), systematically formed names are preferred IUPAC names; the names given in P-65 .1.1.2 are retained names for use in general nomenclature.

Thus, the ‘carboxy’ part is not used in such simple cases. For example, pentanoic acid is not named ‘butanecarboxylic acid’.

However, the acid component of the ester that is given in the question is not such a simple case since the $\ce{-COOH}$ group does not terminate the chain of the parent structure (the cyclobutene ring). In such cases, the suffix ‘carboxylic acid’ is used instead.

P-65.1.2.2 The suffix ‘carboxylic acid’ is used for all carboxylic acids not covered by P-65.1.2.1, except for benzoic acid, a retained name (see P-65.1.1.1). The carboxy group can be attached to any atom, carbon or heteroatom, of any parent hydride; (…).

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