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.

c- cold periods in earth's history during which glaciers covered much of the surface.

explanation:

pre-sliced bread is a relatively recent development in baking technology. previous to that, it was always sold in a bakery in daily-made contiguous loaves with no wrapping, and was moderately perishable, usually being used with a day or two (which is why every bakery had a discounted “day-old” bread table.) therefore, pre-sliced bread would grow stale quickly. the hard crust provided a protective layer, and once the exposed dry slice left from the previous cut was removed, the interior was still soft.

what keeps bread soft is the moisture retained in the crumb (the light spongy part that’s not crust). the reason the crust develops is the surface of the dough gets exposed to hot dry air during baking which browns the outer layer and seals it, preventing all the moisture from escaping the dough. longer exposure to air will also eventually cause your bread to lose flavor and become stale.

people were used to cutting slices as they needed them and storing bread in a specially-made wooden or metal breadbox or pail with a lid to preserve it longer, but the first automatically sliced commercial loaves were produced on july 6, 1928, in chillicothe, missouri, using a machine invented by otto rohwedder, an iowa-born, missouri-based jeweler.[1] pre-sliced bread would indeed dry out, were it not for another 20th century technology: the plastic bag. bread could now be pre-sliced, and if the enclosing bag remains sealed as much as possible, the bread will remain soft and fresh for longer than if sitting unwrapped on a shelf or enclosed in a bread box that is not air-tight. sealed packaging meant bread could also be sold on store shelves and eliminate frequent trips to a bakery.

sealing bread in a plastic bag had another effect: the moisture in the loaf will re-distribute into the crust and soften it, which is sometimes more pleasing in a sandwich - especially for children whose teeth might not yet be strong enough to tear through a hard crust. a homemade loaf of bread can be sealed in a bag overnight and the crust will become soft like store-bought sandwich bread.

these were novel changes in how bread was produced and sold, which led to the coining of the phrase “the greatest thing since sliced bread.”