Problem $2.$

A pure particle of solid malachite $(CuC{O}_3*Cu(OH{)}_2),0\mathrm{.}3mm$ in diameter dissolves completely in a wellstirred acid bath according to the reaction:

$CuC{O}_3$:$Cu(OH{)}_2+4H^{+}$harr$2C{u}^{2+}+3H_{2}O+C{O}_2$

Assuming acid depletion is negligible and that the rate of reaction is completely controlled by diffusion, calculate:

i$)$ the time required for a particle to be $95\%$ reacted if the required time for $50\%$ reaction is $5000s,$ and

ii$)$ the time required to leach $98\%$ of a particle that is three times the size of the original particle for which leaching data is available. $($Assume the particle is relatively large by kinetic model standards.$)$

iii$)$ Using the following data from column leaching tests for the ore, determine if the reaction is chemical or diffusion controlled.

$\backslash$table$[[$Time$,d,$Fraction Reacted$],[1\mathrm{.}5,0\mathrm{.}12],[3,0\mathrm{.}21],[4,0\mathrm{.}27],[5\mathrm{.}6,0\mathrm{.}36],[9\mathrm{.}8,0\mathrm{.}45],[16\mathrm{.}5,0\mathrm{.}6],[27\mathrm{.}2,0\mathrm{.}71],[35\mathrm{.}6,0\mathrm{.}75]]$