Methyl methacrylate $($shown below$)$ was polymerised at an initial concentration of $200gd{m}^{-3}$ using azobisisobutyronitrile $[(CH{)}_3{)}_{2}C(CN)$ as initiator at an initial concentration of $1\mathrm{.}64{10}^{-2}gd{m}^{-3}$ and a reaction temperature of $60C.$ The relevant rate coefficients at $60C$ are:

Initiation kinetics coefficient, $k_i=8\mathrm{.}5{10}^{-6}{s}^{-1}$

Propagation kinetics coefficient, $k_p=833d{m}^{3}mo{l}^{-1}{s}^{-1}$

Termination kinetics coefficient, $k_t=9\mathrm{.}3{10}^{6}d{m}^{3}mo{l}^{-1}{s}^{-2}$

$($a$)$ Assume that the initiator efficiency $f=0\mathrm{.}7,$ and termination only by disproportionation. Calculate the followings for this batch regactor after $0\mathrm{.}5h.($Assuming $[$I$]$ is a constant as discussed in the Tutorial$)$

$($I$)$ the concentration of the monomer left

$($II$)$ number average molecular weight of the poly$($methyl methacrylate$)$ formed

$($b$)$ Assuming the above rate coefficients for initiator dissociation, propagation, and termination can be replaced by the appropriate Arrhenius expressions:

$k_2=A_i$exp$(-\frac{E_i}{R}T)$

$k_p=A_p$exp$(-\frac{E_p}{R}T)$

$k_1=A_1$exp$(-\frac{E_1}{R}T)$

And the activation energies for the three steps are known as:

$($b$)$ Assuming the above rate coefficients for initiator dissociation, propagation, and termination can be replaced by the appropriate Arrhenius expressions:

$k_1=A_i$exp$(-\frac{E_i}{R}T)$

$k_p=A_p$exp$(-\frac{E_p}{R}T)$

$k_1=A_1$exp$(-\frac{E_1}{R}T)$

And the activation energies for the three steps are known as:

$E_p=34kJmo{l}^{-1}$

$E_1=12kJmo{l}^{-1}$

$E_i=128kJmo{l}^{-1}$

When the temperature changed from $60C$ to $70C,$ with initial monomer and initiator concentrations unchanged, $f=0\mathrm{.}7,$ and termination only by disproportionation. Calculate the followings for this batch reactor after $0\mathrm{.}5h.($Assuming $[$I$]$ is a constant as discussed in the Tutorial$)$

$($III$)$ the concentration of the monomer left

$($IV$)$ number average molecular weight of the poly$($methyl methacrylate$)$ formed

$($c$)$ By comparing the two value sets above, comment on the origin of such changes from temperature.