Question

A second order polycondensation reaction involving diol and diacid was performed. Initial concentration of each monomer was 0.5 M (1M concentration of functional groups of each type). After 8 hours an aliquot is removed from the reaction media and it was determined that extent of reaction of carboxylic acid groups is 0.53.

(a) Calculate the number-average degree of polymerization and polydispersity of the polymer at this stage of the process.

(b) Determine the number average degree of polymerization after 13 hours of reaction.

Answer 1

Ans:-Xn is the number average degree of polymerisation.

Xn=1/1-p

p=extent of reaction

here p=0.53

SO Xn = 1/.47 = 2.12

polydispersity= Mw/Mn { where Mw= wieght avg mol. weight, Mn= number avg mol. weight.

polydispersity =1+ Kp/Kexch(2/p-1) (Kp=rate pf propagation , Kexch: rate of exchange)

The above data has not been provided.

Now because it is second -order polycondesation.

so accordingly ,

-d[A]/dt = k[A][B]

Since [A]=[B], d[A]/dt = k[A]²

1/[A]-1/[A₀]=Kt

p=([A₀]kt)/(1+[A₀]kt)

Xn=1+[A₀]kt

2.12=1+[.5* k* 8]

k=.28

now Xn after 13 hours is

Xn= 1+[.5*.28*13]= 2.82