Final answer:
The criterion for assigning numbers to carbon atoms in a parent chain is to provide the lowest numerical locators to substituents. The sequence is chosen to yield the smallest set of numbers overall, considering both substituent quantity and alphabetical order if necessary.
Step-by-step explanation:
When numbering carbon atoms in the parent chain of a molecule containing a functional group, the criterion used is to assign the lowest possible numbers to carbon atoms that have substituents attached. This ensures that the substituents (branches or functional groups) receive the lowest numerical locators. For molecules with multiple substituents, numbers are further assigned in such a way to give the lowest sequence of numbers overall.
For instance, in a molecule with the longest chain being eight carbon atoms, like octane, and with branches on the third and fifth carbon when numbered from the left, that numbering is preferred. If numbered from the right, the branches would appear on the fourth and sixth carbons, which would be less preferable due to the higher locator numbers. When multiple substituents are present on a molecule, such as on a benzene ring, the substituent that comes first in alphabetical order is also considered in determining the starting point for numbering.