Problem $1\mathrm{.}3$:

For a step$-$growth polymerization, the rate of polymerization is given by:

$R_o=\frac{d}{dt}[AA]=k[AA][BB]$

$k$ is the polymerization rate constant

$[AA{]}_o=$ initial monomer concentration at $t=0$

$p=$ the fractional conversation

$($i$)$ Show the number$-$average degree of polymerization: $x_n=[AA{]}_{0}kt+1$

$($ii$)$ Calculate the weight$-$average degree of polymerization $($Xw$)$