A $40\mathrm{.}00-mL$ aliquot of $0\mathrm{.}0500MHN{O}_2$ is diluted to $75\mathrm{.}0mL$ and titrated with $0\mathrm{.}0800MC{e}^{4+}.$ Assume the hydrogen ion concentration is at $1\mathrm{.}00M$ throughout the titration. $($Use $1\mathrm{.}44V$ for the formal potential of the cerium system.$)$

$($a$)$ Calculate the potential of the indicator cathode with respect to a saturated calomel reference electrode after addition of $10\mathrm{.}0,25\mathrm{.}00,40\mathrm{.}00,49\mathrm{.}00,49\mathrm{.}90,50\mathrm{.}10,51\mathrm{.}00,55\mathrm{.}00,60\mathrm{.}00,70\mathrm{.}00,$ and $90\mathrm{.}00mL$ of cerium$($IV$)$

$($b$)$ Draw a titration curve for these data.