Rate constants for termination kt may be of the order of 1x108 L/mol s in free r

Question

Rate constants for termination kt may be of the order of 1x108 L/mol s in free radical polymerizations. Consider the polymerization of styrene initiated by ditert -butyl peroxide at 60. ?C. For a solution of 0.01 M peroxide and 1.0 M styrene in benzene, the initial rate of polymerization is 1.5x10-7 mol/L s and <Mn> of the polymer produced is 138,000. (a) From the above information estimate kp for styrene at 60. ?C. (b) What is the average lifetime of a macroradical during initial stages of polymerization in this system?

Explanation / Answer

A.) To find Kp at 60oC

The formula for Kp is Kp=Kc(RT)?n or Kp = PcC PdD / PaA PbB

Using the first formula Kc= (0.01 * 1.0) / (1.5 * 10-7) [ 0.01 M peroxide with 1.0 M styrene is formed]

Kc = 6.7 * 104

so Kp = (6.7 * 104 ) x (0.0821 * 333)?n here ?n = (1.5 * 10-7) - (0.01 * 1.0) = -9.99 * 10-3

Hence, Kp = 6.48 * 104 at 60oC

B.)   Average life (t) =1.44×t1/2

t1/2 = 0.693 / k

t1/2 = 0.693 / (1.5 * 10-7) = 4620000 sec

so,

  Average life (t) =1.44× 4620000 = 6652800 sec

  t1/2 = 4620000 sec

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