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HW3 Solutions

# HW3 Solutions - ChE178:ProblemSet#3Solutions 1 Glycerol can...

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Ch E 178: Problem Set #3 Solutions  1. Glycerol can react with octadecanedioic acid to form a crosslinked polymer. HO OH ethylene glycol O OH O HO octadecanedioic acid OH HO OH glycerol a. Describe the chemical reactions that would occur when the above reagents are mixed. Condensation reactions occur. The functional groups on e E thylene glycol is an f=2 base, and glycerol would react with the functional groups on o is an f=3 base, and ctadecanedioic acid is a f=2 acid. but not which each other. This will lead to chains made up of octadecanedioic acid as well as ethylene glycol and/or glycerol monomers. Glycerol reacting will lead to crosslinking. The described schemes are depicted below: HO OH O O 7 + OH HO O O O O 7 * O * O O O O 7 O O O O 7 * O O O O 7 O O O O O 7 O n O 7 O O O m (for example)

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HO OH O O 7 + HO OH OH O O O O 7 O O O 7 O O O O O 7 * * + OH HO HO OH O O 7 + HO OH OH O O O O 7 O O O O 7 * * * O O O O 7 O * b. Calculate the extent of reaction (p –also called degree of conversion) at which gelation occurs for: i. Stoichiometric amounts of octadecanedioic acid and glycerol Assume there are a basis of 1mol each 1mol octadecanedioic acid and 1mol glycerol . Since glycerol has a base functionality and is f=3, we will now call all OH groups “A” and all acids=B. (as a reference amount). Call the carboxylic acid groups B groups and the OH groups A groups. Then to start, we have: 1mol octadecanedioic acid * 2 B groups/octadecanedioic acid = 2mol B groups 1mol glycerol * 3 A groups/glycerol = 3mol A groups Since there is not a stoichiometric balance among the mutually reactive functional groups, Carothers theory (described in your book on pages 39-40) does not work. We must use Flory Statistical Theory (discussed in class and described in your book on pages 40-42): f=3 (from glycerol, the triol) r = initial # A . groups initial # B . groups = 3 2 1 . # ) . . . .( . . # = = groups A total case our in glycerol molecules RA from groups f ρ
Since B groups are limiting present in smaller quantity , they will be completely consumed before the A groups. So we use the equation for So the degree of conversion of B is most important (p B ) c , since it is the limiting groups’ critical extent of reaction (equation derived in book on pages 41-42 , related to the equation for p Ac derived in class ). 866 . 0 )] 2 3 ( 1 1 [ 2 3 )] 2 ( 1 [ ) ( 2 1 2 1 2 1 2 1 = - + = - + = - - f r p c B ρ ii. Molar ratio 1.500:0.950 octadecanedioic to glycerol 1.500mol octadecanedioic acid * 2 B groups/octadecanedioic acid = 3.000mol B groups 0.950mol glycerol * 3 A groups/glycerol = 2.850mol A groups Again, use Flory Statistical Theory: f=3 (from glycerol, the triol) 950 . 0 000 . 3 850 . 2 . # . # = = = groups B initial groups A initial r 1 . # ) . . . .( . . # = = groups A total case our in glycerol molecules RA from groups f ρ Since A groups are limiting, they will be completely consumed before the B groups. So we use the equation for (p A ) c , since it is the limiting groups’ critical extent of reaction .

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HW3 Solutions - ChE178:ProblemSet#3Solutions 1 Glycerol can...

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