The Probability of Finding an X-mer

If you didn t say p, then you re really lost when it comes to probabilities and you should give up polymer science and become a sociologist. Moving on, what is the individual probability that the second group has reacted Another p, of course. But, and this is the crux, what is the probability that both groups taken together have reacted  

Do you think we ve finished No, there s still one B left unaccounted for. We ve got to the end of the chain and there s still one B group hanging out, unreacted. We can t ignore it. The probability that this group has not reacted is 1 - p. 

So the overall probability of finding a 5-mer after p groups have reacted is p 1 -p). Now we can simply generalize this to the probability of finding an x-mer. Piece of cake. If the probability of finding an x-mer is P, then we obtain Equation 5-12. 

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The probability of finding an x-mer at random must be equal to the number or mole fraction of x-mers present, X, so we have our first answer (Equation 5-13). 

The probability of finding an x-mer, or, equivalently, the mole fraction of jc-mers polymerized at some instant of time, is then given by exactly the same expression as that obtained in dealing with condensation polymerizations (Equation 5-19). 

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