polycondensation reaction takes place between 1.2 moles of a dicarboxylic acid, 0.4 moles of glycerol (a triol) and 0.6 moles of ethylene glycol (a diol). A.Calculate the critical extents of reaction for gelation using (i) the statistical theory of Flory and (ii) the Carothers theory.B.Comment on the observation that the measured value of the critical extent of reaction is 0.866.

(b). When the value for the critical extent of reaction is 0.866, then the number of moles of glycerol and the number of moles of di-carboxylic acid is the same. But, in this case the number of moles of glycerol is not the same with the number of moles of di-carboxylic acid.

Explanation:

So, without mincing words let's get straight into the solution to the question above.

(a). Using the (i) statistical theory of Flory to Determine the critical extent of reaction gelation, one has to make use of the two equations given below;

P(1) = [ v + vb ( n - 2)^-1/2 ------------------(1).

P(2) = v^1/2 [ 1 + b ( n - 2)^-1/2 ----------(2).

The value for v = 1.2 + 1.2/ 1.2 × 2 = 1.

The value of b = (1.2 + 1.2)/ 1.2 = 0.5.

Thus, putting the values into the equation (1) and (2) above gives;

NB: n = 3.

P(1) = [ 1 + 1 × 0.5 ( 3 - 2)^-1/2 = 0.816.

P(2) = 1^1/2 [ 1 + 0.5 ( 3 - 2)^-1/2 = 0.816.

Using the (ii) carother's theory to Determine the critical extent of reaction gelation.

We have the following values for glycerol: k = 0.4, n = 3.

For ethylene glycol; k = 0.6, n = 2.

Therefore, the critical extent of reaction gelation =2/[ (0.6 × 2) + (0.4 × 3) + (1.2 × 2)/ (0.6 + 0.4 + 1.2)] = 2/ 2.18 = 0.917

(b). When the value for the critical extent of reaction is 0.866, then the number of moles of glycerol and the number of moles of di-carboxylic acid is the same. But, in this case the number of moles of glycerol is not the same with the number of moles of di-carboxylic acid.