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According to the lowest locant rule shouldn't the numbering of the compound 1 start from the carbon at the 4th position, thus giving the IUPAC name as 1,2-dimethyl-4-hydroxybenzene?

For compound 2 they could have prioritized the functional group, but they have prioritized the lowest locant rule instead.

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    $\begingroup$ The functional group has the highest priority. $\endgroup$ – RBW Jun 11 '16 at 14:03
  • $\begingroup$ Agreed. But i can also find some other examples where the functional group is'nt given the priority. $\endgroup$ – Tajammul Saleem Jun 11 '16 at 14:23
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    $\begingroup$ Halides and nitro groups aren't considered to be functional groups in nomenclature, they are substituents, while a hydroxy group is a functional group e.g. you would never say phenyl chloride or hydroxybenzene, while chlorobenzene and benzenol (phenol) are preferred names. Understand the difference? $\endgroup$ – RBW Jun 11 '16 at 15:40
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There are several criteria for the numbering of locants. The most important simplified criteria for the numbering for substituted benzene compounds are:

  1. lower locants for the principal characteristic groups, which are expressed as a suffix or implied by the name of the functional parent compound (If there is a choice, the principal characteristic groups are assigned in accordance with the order of seniority of classes of compounds.)
  2. lower locants for prefixes
  3. lower locants for substituents cited first as a prefix in the name

The corresponding actual wording of the nomenclature rules (taken from Nomenclature of Organic Chemistry – IUPAC Recommendations and Preferred Names 2013 (Blue Book)) reads as follows:

P-14.4 NUMBERING

When several structural features appear in cyclic and acyclic compounds, low locants are assigned to them in the following decreasing order of seniority:

(…)

(c) principal characteristic groups and free valences (suffixes);

(…)

(f) detachable alphabetized prefixes, all considered together in a series of increasing numerical order;

(g) lowest locants for the substituent cited first as a prefix in the name;

(…)

The first compound given in the question has the functional parent compound phenol. The name ‘phenol’ implies the presence of the characteristic group $\ce{-OH}$. Since there are no other characteristic groups and low locants are assigned first to the principal characteristic group, the locant ‘1’ is assigned to the substituent group $\ce{-OH}$. Therefore, the systematic name for this compound is 3,4-dimethylphenol.

3,4-dimethylphenol

The second compound given in the question does not have any principal characteristic group – neither expressed as a suffix nor implied by the name of a functional parent compound. Therefore, low locants are assigned to the prefixes ‘chloro’, ‘methyl’, and ‘nitro’, all considered together as a set in a series of increasing numerical order. Thus, the systematic name for this compound is 2-chloro-1-methyl-4-nitrobenzene and neither ‘1-chloro-2-methyl-5-nitrobenzene’ nor ‘3-chloro-4-methyl-1-nitrobenzene’ since the locant set ‘1,2,4’ is lower than ‘1,2,5’ or ‘1,3,4’.

2-chloro-1-methyl-4-nitrobenzene

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  1. Lowest set locant rule is considered after prioritising the functional group (i.e. giving it the first position). so answer of the first question is 3,4-dimethylphenol.
  2. In the second question the answer given in the book is wrong . It should have been 3-chloro-4-methylnitrobenzene
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