# Solution

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The following relationship was derived for the gross reaction rate.

$rbr=kp(kdkt)12[I.]12[M.]rbr = Gross reaction speedkp = Rate constant of the growth reactionkd = Rate constant of initiator decaykt = Rate constant of the termination[I.] = Initiator concentration[M.] = Monomer concentration$

As the gross reaction rates for the polymerizations with full initiator concentration $[I.]1$and 25% initiator concentration $[I.]2=14[I.]1$should be the same, the following equation must apply.

$kp(kdkt)12[I.]112[M.]1=kp(kdkt)12[I.]212[M.]2[M.]1= original monomer concentration[M.]2 = wanted monomer concentration$

It follows:

$[I.]112[M.]1=[I.]212[M.]2=(14[I.]1)12[M.]2=12[I.]112[M.]2$

Dissolve after $[M.]2$results

$[M.]2=2[M.]1$

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