Consider a fully charged, $6-$cell lead$-$acid battery that is nominally $12V.$

a$)$ What is the maximum theoretical charge that this battery can discharge if the total mass of the

lead anodes is $10kg$ and there is excess $H_{2}S{O}_4$ and $Pb{O}_2?$ Assume that it is possible to reach a

state of charge of zero.

b$)$ What is the theoretical maximum amount of work that can be obtained from this battery?

c$)$ Derive an expression for the open cell voltage of the battery as a function of charge.

d$)$ Using the expression from part c$),$ what is the $pH$ and sulfate ion concentration $[\{$:$S{O}_4^{2-}]$ at

complete discharge? Assume a total electrolyte volume of $16\mathrm{.}5L,$ a fully$-$charged starting

concentration of a $[S{O}_4^{2-}]=6M,$ and an initial $pH=-1\mathrm{.}08?$

please solve all parts