a$.$ A polymer electrolyte membrane fuel cell $($PEMFC$),$ producing liquid water, operates at $80C$ on air $(1$atm$)$ on the cathode side with the volume fraction given in Table $1.$ The anode side is fed with pure hydrogen $(1$atm. Calculate the cell voltage for this cell when there is no current drawn. Write the half$-$cell reactions at the cathode and anode, together with the overall cell reaction. Will this cell voltage remain constant when the current starts to flow? Discuss your answer.

Table $1.$ Composition of air

Table $2$ Variation of $G_r$ of $H_2+\frac{1}{2}{O}_2{H}_{2}O$ as a function of temperature

b$.$ If the anode of the PEMFC is now directly supplied with syngas composed of

$13$mol$\%H_2,1$mol$\%C{H}_4,16$mol$\%CO,5$mol$\%C{O}_2,36$mol$\%H_{2}O$ and $29$

mol$\%N_2,$ with the same operating conditions and oxidant as in $Q(a),$ how does

the performance of this PEMFC compare to the one given in Q$($a$).$ Discuss your

answer and suggest detailed and specific methods, considering gas mixtures fed

into the cell anode, to improve the cell performance.