A $50g$ sample of poly$($amide$6)[$Nylon $6]$ produced by "ideal" step$-$growth polymerization

of the monomer $P$ is found to contain $3{10}^{-3}$mol of $-\frac{C}{O}OH$ end groups by nuclear

magnetic resonance $($NMR$).$

a$.$ Calculate the number$-$average molecular weight of this sample of Nylon $6.$

b$.$ Calculate the extent of reaction $p$ of the step$-$growth polymerization.

c$.$ Assuming "ideal" step$-$growth polymerization statistics, calculate the weight$-$

average molecular weight.

d$.$ Estimate the weight fraction of chains in this sample that have a molecular weight

less than $8000gmo{l}^{-1}.($HINT: integration may be necessary$)$ Molar mass of P is $132$ g$/$mol$.$ It is C$6$H$13$O$2$N