here's a question that i don't understand the answer. please give me a right answer to this~~~?

This has to do with the preparation of crosslinked polyesters. The question is asking, “at what conversion of the carboxylic acid and hydroxyl functional groups of this particular reaction mixture will the resultant polyester have an infinite molecular weight?” The gel point, or critical conversion, Pc, is that conversion.

There are a number of theories out there that calculate this. You don’t say which theory you are to use. The easiest approach is the Carothers theory, but it is somewhat inaccurate and tends to underestimate Pc. The other approaches are very complicated, so I’ll stick to Carothers.

For a step growth polymerization the critical conversion in the Carothers theory is:

Pc = 2 / f(avg),

Where f(avg) is the average functionality of the reaction mixture, regardless if they are acids or hydroxyls. So,

f(avg) = ∑Nifi / ∑Ni.

For phthalic acid, f = 2; for glycerol, f = 3; for ethylene glycol, f = 2. (Ethanol has f = 1). Ni are the number of moles of monomer i.

a) f(avg) = ((1 mole)(2 COOH) + (1 mole)( 3 –OH)) / ((1 mole) + (1 mole))

f(avg) = 2.5; so

Pc = 2 / 2.5 = 0.8, or 80% conversion to get a gel.

b) f(avg) = (1.2*2+0.96*3)/(1.2+0.96) = 2.44

Pc = 2 / 2.44 = 0.81, or 81% conversion to get a gel.

c) f(avg) = (1.2*2+0.96*3+0.002*2)/(1.2+0.96+.002) = 2.43

Pc = 2 / 2.43 = 0.82, or 82% conversion to a get a gel.

As I said before, these will be underestimates.