The polydispersity index of a polymer contain | vedclass

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(A) The polydispersity index $(PDI)$ is defined as the ratio of weight average molecular mass $(M_w)$ to number average molecular mass $(M_n)$.$PDI =

Vedclass · Accepted Answer

$1.67$

Vedclass · Answer

(A) The polydispersity index $(PDI)$ is defined as the ratio of weight average molecular mass $(M_w)$ to number average molecular mass $(M_n)$.$PDI = \frac{M_w}{M_n}$Given: $N_1 = 10$,$M_1 = 1.0 	imes 10^4 = 10,000$; $N_2 = 10$,$M_2 = 1.0 	imes 10^5 = 100,000$.Number average molecular mass $(M_n)$: $M_n = \frac{\sum N_i M_i}{\sum N_i} = \frac{(10 	imes 10,000) + (10 	imes 100,000)}{10 + 10} = \frac{100,000 + 1,000,000}{20} = \frac{1,100,000}{20} = 55,000$.Weight average molecular mass $(M_w)$: $M_w = \frac{\sum N_i M_i^2}{\sum N_i M_i} = \frac{10 	imes (10,000)^2 + 10 	imes (100,000)^2}{(10 	imes 10,000) + (10 	imes 100,000)} = \frac{10^9 + 10^{11}}{1,100,000} = \frac{101,000,000,000}{1,100,000} \approx 91,818$.$PDI = \frac{91,818}{55,000} \approx 1.67$.

The polydispersity index of a polymer containing $10$ molecules with molecular mass $1.0 \times 10^4$ and $10$ molecules with molecular mass $1.0 \times 10^5$ is approximately.

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