$(1)(20$p$.)$ The recombination of iodine atoms $(2I{I}_2)$ in a particular solvent is believed to be

diffusion controlled. At $298K,$ the rate constant is observed to be $1\mathrm{.}3{10}^{10}$ liter mole $e^{-1}{s}^{-1}.$

$($a$)$ If the reaction distance $(\{$:$r_{AB})$ is taken to be $2\mathrm{.}2,$ estimate the diffusion coefficient of I

atoms in this solvent at $298K.$

$(10$p$.)$

$($b$)$ The temperature dependence of diffusion coefficients in liquids is roughly given

by $D=D_o(\frac{T}{})$ where $$ is the $($temperature dependent$)$ viscosity of the solvent. The

viscosity of the solvent vs$.$ temperature is

Create an Arrhenius plot of the rate constant for the I $+$ I reaction for temperatures from $273$

to $373K.$ What is the apparent activation energy for this diffusion controlled reaction?

$(10$p$.)$