What is the degree of polymerization of a sample of polyester prepared from 4-hy

Question

What is the degree of polymerization of a sample of polyester prepared from 4-hydroxybenzoic acid if the acid number, determined with standard KOH solution is 11.2?

11.2 mg x (1g/1000mg) x (1mol/56.1g) = 2.00E-4 moles

MW(polymer) = g/mol = 1g/2.00E-4 moles = 5000g/mol

The degree of polymerization is equal to the MW of the polymer / MW of the structure. For some reason the answer to this question is 42 using 120 as the MW of the structure. The MW of 4-hydroxybenzoic acid is 138.12g/mol yielding a DP of 36.2

The only way I can get the answer of 42 is by using a basic carboxyclic acid functional group of C2O2H4 (MW =120). Can anyone explain a different reason as to why I am not getting the correct answer?

Explanation / Answer

Answer-

as you stated that after putting its actual molar mass (4-hydroxybenzoic acid) i.e. 138.12 g/mol

degree of polymerisation =5000/138.12

=36.24

i would say  there is no possibily of taking basic carboxylic acid fuctional group of CH3COOH

since it cannot formed during the concerned reaction with KOH while finding acid number

but yes there is possiblity of elimination of water from the 4-hydroxybenzoic acid

so after elimination of one water molecule there is reduction of molecular mass by 18.01528

so mass of 4-hydroxybenzoic acid = 138.12-18.01528

mass of dehydrated acid =120.104

so degree of polymerisation =5000/120.104

=41.6

so it can be most probable reason.

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