Question

Can someone show me the steps to derive carother equation and explain to me the process or what it is? I am confused with what it is and how to apply it. Thanks!

Answer 1

What is Carother equation-

for the step growth polymerization reactions , W.H. Carother, proposed an equation, that's gives the degree of polymerization Xn ,for a given fractional monomer conversion P.

Steps to derive Carother equation.

step 1- initially ,Let us consider ,a monomer system A-B.

in which , we assume-

N0 = No. Of molecules present initially ,and

N= No .Of molecules remaining at time t

And then ,we calculate,

The total number of functional groups of either A or B which have reacted = N0 - N

step-2 . I​​​​​​n this step, we calculate the extent of reactions P at time t ,

Extent of reaction p is defined as-

P= total number of function group of either A or B that have reacted/No. Of group initially present.

= (N0 - N) / N0 ( putting values from step 1)

P =N0/N0 - N/N0 (distributing)

P= 1 - N/N0

Or N/N0 = 1- 1/P ---------------- equation A

here We shall introduce , the degree of polymerization Xn ,which is numerically equal to N0/N

therefore,

From equation A , putting , N0/N =Xn , and rearranging equation.

Xn = 1/1-P ------- this equation is Carother equation.

HOW TO APPLY CAROTHER EQUATION--

Let us assume, we have given a problem--

we have to calculate Xn, the degree of polymerization ,if a monomer conversion is 99.5 %.

we shall apply Carother equation to find out the value of Xn.

Xn = 1/1-P

P is given = 99.5% =0.995.

Xn = 1/1-0.995

Xn=200.

thus the required value is 200.

​​​​​​

​​​​