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Unformatted text preview: Homework #4 Solutions 1. In free radical polymerization, the important rate constants depend on temperature as: k init = A init exp( E init RT ) . (initiation) k p = A p exp( E p RT ) (propagation) k term = A term exp( E term RT (termination) where T is temperature (K), the E's are activation enthalpies and the A's are constants. The free radical polymerization of styrene in benzene is carried out using AIBN as the initiator at both 50°C and 90°C . Compute the ratio of the polymerization rates and number average polymerizations of polystyrene produced at the two temperatures given that: E init = 126 kJ/mol E p = 34 kJ/mol E term = 10 kJ/mol ______________________________________________________________________________ The rate of polymerization is given by the following equation: [ ][ ] 2 / 1 2 / 1 I M k fk k R t d p p = For 50°C: [ ][ ] ( ) [ ][ ] 2 / 1 50 2 / 1 50 , 50 , 50 , 2 / 1 50 , 2 / 1 50 2 / 1 50 , 50 2 / 1 50 , 2 / 1 50 50 , 50 , 2 2 exp 2 exp 2 exp exp I M RT E E E A A A f R I M RT E A RT E A f RT E A R p d t t d p p t t d d p p p  =    = Similarly, for 90°C: ( ) [ ][ ] 2 / 1 90 2 / 1 90 , 90 , 90 , 2 / 1 90 , 2 2 exp I M RT E E E A A A f R p d t t d p p  = Homework #4 Solutions ( ) [ ][ ] ( ) [ ][ ] 2 / 1 90 2 / 1 90 , 90 , 90 , 2 / 1 2 / 1 50 2 / 1 50 , 50 , 50 , 2 / 1 90 , 50 , 2 2 exp 2 2 exp I M RT E E E A A A f I M RT E E E A A A f R R p d t t d p p d t t d p p p   = Assuming the f is the same for both systems and the initial concentrations of the monomer and initiator are same for both systems, ( ) [ ][ ] ( ) [ ][ ] ( ) ( ) ( ) ( )  =  =   =   = 15 . 363 * 314 . 8 * 2 000 , 184 15 . 323 * 314 . 8 * 2 000 , 184 exp 2 2 2 2 exp 2 2 exp 2 2 exp 2 2 exp 2 2 exp 90 , 50 , 90 50 90 50 90 , 50 , 2 / 1 90 2 / 1 90 , 90 , 90 , 2 / 1 2 / 1 50 2 / 1 50 , 50 , 50 , 2 / 1 90 , 50 , p p p d t p d t p d t p d t p p p d t t d p p d t t d p p p R R RT E E E RT E E E RT E E E RT E E E R R I M RT E E E A A A f I M RT E E E A A A f R R 0230 ....
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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.
 Fall '08
 SEGALMAN

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