yes. particularly in organic chemistry, molecules are often made up of groups of atoms that are common to many chemicals. these groups often behave in similar ways regardless of what they’re stuck to.
“COOH” specifically is the carboxyl group. acetic acid is similarly CH3COOH
so for butyric acid, C4H8O2 is easier to calculate bulk properties, like molecular weight, from. this is also likely the least useful overall, because isomers (chemicals with the same formula but the atomcs arranged differently) exist and can have radically different properties.
C3H7COOH emphasizes that it is a carboxylic acid. in some cases, what the acid was specifically isn’t very relevant. the rest of the molecule doesn’t participate in the relevant reaction.
CH3CH2CH2CO2H has lots of information. butyric acid is a methyl group, two methyene bridges, and a carboxyl group. from that you also know what the molecule looks like. it’s long and mostly straight. but writing it out like that is rather cluttered, particularly if you don’t care about most of that.
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