Naming compounds

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shefv

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How would you name this compound? Which alkyl group gets priority?

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My chem book said that since they are all alkyl substituents, the priority here is based on alphabetical order so ethyl would get the priority. But the answer key gives 3 ethyl 1 methyl 5 propylcyclooctane as the answer.

Since the priority here based on alphabetical order or size of the substituents (i.e. methyl is smallest so it is on C1)?

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for cycloalkanes the alkyl substituents should be chosen with the group that comes first in the alphabet as c1, in this case it would be ethyl, which then gives 1-ethyl, 3-methyl, 7-propyl.

BUT Priority is always given first to the lowest combination of substituent numbers, in this case 1-methyl 3-ethyl 5-propyl (1,3,5 is lower than 1,3,7), so the methyl group is chosen as c1.
 
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notice that the propyl group could have also been chosen as c1 to give 1,3,5, but p comes after m in alphabet so propyl is lower priority. The general rule would be, lowest combination of substituents first, then alphabetical order
 
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