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.

(a). (I). 0.816; 0.816

(ii). 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.

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.

most historians agree that gabriel mouton, the vicar of st. paul’s church in lyons, france, is the “founding father” of the metric system. he proposed a decimal system of measurement in 1670. mouton based it on the length of one minute of arc of a great circle of the earth (now called a nautical mile, 1852 meters). he also proposed the swing-length of a pendulum with a frequency of one beat per second as the unit of length (about 25 cm). a pendulum beating with this length would have been fairly easy to produce, thus facilitating the widespread distribution of uniform standards. over the years, his work was revised, improved, and extended by a number of french scientists.

the political sponsor of weights and measures reform in the french revolutionary national assembly was the bishop of autun, better known as talleyrand. under his auspices, the french academy appointed several committees to carry out the work of developing a usable system of weights and measures for france. one of the committees recommended a decimalized measurement system based upon a length equal to one ten-millionth of the length of a quadrant of the earth’s meridian (i.e., one ten-millionth of the distance between the equator and the north pole).