Electropolishing is a well$-$known method for improving the surface finish of a metallic component.

Through detailed electrochemical studies, it has been found that during electropolishing of

copper parts in a phosphoric acid$-$based solution, the diffusion of copper phosphate species

determines the rate of electropolishing.

The following results were obtained in one such test:

In these results:

i is the corrosion $($electropolishing$)$ current density $(A{m}^{-2})$

$t$ is the time of electropolishing $($s$),$ and

$$ is the dynamic viscosity of the electropolishing solution $(Ns{m}^{-2})$

The following are relationships that relevant to this system:

$($a$)\frac{i}{\sqrt[\phantom{2}]{?}}$ t bears an Arrhenius relationship to the temperature of the electropolishing solution

$($b$){}^{-\mathrm{.}5}$ bears an Arrhenius relationshig to the temperature of the electropolishing solution

$($c$)$ the diffusion coefficient of the copper phosphate species in the electropolishing

solution $($D$)$ is given by the expression

$D=\frac{kT}{6r},$

where

k is the Boltzmann's constant $(=1\mathrm{.}3805{10}^{-23}J{K}^{-1}),$

$T$ is the temperature of the electropolishing solution $(K),$ and

r is the atomic radius of copper $=1\mathrm{.}28{10}^{-10}m$

$($d$)$ the thickness of the diffusion layer $(8)$ is obtained from the expression

$i=(DzFA)(),$

where

D is the diffusion coefficient $($see item $($c$)$ above$),$

$z$ is the number of electrons involved in the electropolishing process,

$A$ is the concentration of the electropolishing solution $($in $mo{l}^{-3}).$

Calculate the diffusion laver thickness for the system when

$($i$)$ electropolishing solution temperature $=55C$

$($ii$)$ electropolishing time $=3$min, and

$($iii$)$ concentration of the electropolishing solution $=35$ umol liter ${?}^{-1}.$

NOTES:

Copper corrodes thus: $,CuC{u}^{2+}+2e$

$1$ liter $=1000c{m}^3.$