HW3_Solutions - Ch E 178: Problem Set #3 Solutions 1....

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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 OO O HO H octadecanedioic acid OH HO OH glycerol a. Describe the chemical reactions that would occur when the above reagents are mixed. Condensation reactions occur. Ethylene glycol is an f=2 base, glycerol is an f=3 base, and ctadecanedioic acid is a f=2 acid. Glycerol reacting will lead to crosslinking. O O O O 7 O O O O 7 * O O O O 7 O O O O O 7 O n (for example) O O 7 O O m 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 a basis of 1mol each 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. 1mol octadecanedioic acid * 2 B groups/octadecanedioic acid = 2mol B groups
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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 present in smaller quantity, they will be completely consumed before the A groups. So the degree of conversion of B is most important (p B ) 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 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 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. 725 . 0 )] 2 3 ( 1 * 950 . 0 950 . 0 [ )] 2 ( [ ) ( 2 1 2 1 = + = + = f r r p c A iii. Molar ratio 1.500:0.980:0.750 octadecanedioic: glycerol: ethylene glycol 1.500mol octadecanedioic acid * 2 B groups/octadecanedioic acid = 3.000mol B groups
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0.980mol glycerol * 3 A groups/glycerol = 2.940mol A groups 0.750mol ethylene glycol * 2 A groups/ethylene glycol = 1.500mol A groups Total B groups to start = 3.000mol Total A groups to start = 4.440mol Again, use Flory Statistical Theory: f=3 (from glycerol, the triol) 480 . 1 000 . 3 440 . 4 . # . # = = = groups B initial groups A initial r 662 . 0
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This note was uploaded on 12/09/2011 for the course CHEM ENG 178 taught by Professor Segalman during the Fall '08 term at Berkeley.

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HW3_Solutions - Ch E 178: Problem Set #3 Solutions 1....

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