$1.$ Plot the appropriate polarization curves for the following half$-$cell reactions and determine the corrosion potential and corrosion rate $($current density$)$ assuming activation control of both the anodic and cathodic processes. $(4$ points$)$

M $=$ M$++$ e$-,$ e $=-0\mathrm{.}8$ V$,$ io $=10-12$ A$/$cm$2$

H$++$ e$-=$ H$,$ e $=+0\mathrm{.}2$ V$,$ io $=10-9$ A$/$cm$2$

Ba$/$c $=+/-0\mathrm{.}1$ V$/$dec

If the reduction reaction is current limited at $10-6$ A$/$cm$2,$ recalculate the potential and corrosion rate by plotting on the attached sheet $(1$ point$).$

$2.$ Calculate the corrosion rate $($current density$)$ of iron in deaerated acidic water at pH $=0$ and pH$2=1$ atm; BactC is $-0\mathrm{.}20$ V dec$-1.$ io for H$2$ reduction on Fe is $10-12$ A$/$m$2$; Ecorr is $-0\mathrm{.}80$ V$.(5$ points$).$

$3.$ Electrorefining of copper using acidic copper sulfate solution is carried out at a current of $25$ kA and $0\mathrm{.}4$ V$.$ If the output per day is $500$ kg on a total cathode area of $15$ m$2$ calculate $(12$ points$)$:

$($a$)$ Current efficiency, $($b$)$ energy efficiency, kWh$/$kg$,($c$)$ Current density, $($d$)$ thickness of deposit

$4.$ If the corrosion current is $1$ mA from a sample of copper with a surface area of $1$ cm$2,$ what is the corrosion rate in mm$/$y$?$ Corrosion product is Cu$2$O$.$ Density of copper $=9$ g$/$cc; At$.$ Wt$.63\mathrm{.}5(6$ points$)$

$5.$ Rank the following ions in order of their thermodynamic difficulty of plating out of a solution: $(5$ points$)$

Cu$2+,$ Co$2+,$ Fe$2+,$ Fe$3+,$ Na$+,$ Pb$2+,$ Cu$+$

HINT: Use the EMF Table for Probs. $5.$

$6.$ Calculate the corrosion rate of iron in oxygen$-$free acid, pH $=3$; if the reaction is: $(7$ points$)$

Fe $+2$H$+=$ Fe$2++$ H$2$

eo $($Fe$/$Fe$2+)=-0\mathrm{.}44$ V; eo $(2$H$+/$H$2)=0\mathrm{.}00$ V; aFe$2+=10-8$;

io $($Fe$/$Fe$2+)=10-6$ A m$-2$; io $(2$H$+/$H$2$ on Fe$)=10-4$ A m$-2$;

$$a $=0\mathrm{.}05$ V dec$-1$c $=-0\mathrm{.}10$ V dec$-1$; pH$2=1\mathrm{.}0$ atm.