$(60$ pts$)$ Under standard conditions, suppose a $C{r}_2{O}_7^{2-}|C{r}^{3+}$ half$-$cell combined with a

$C{d}^{2+}|Cd$ half$-$cell to form a galvanic cell.

a$.$ Write half reactions at the anode and the cathode.

b$.$ Write the balanced equation for the overall cell reaction.

c$.$ Calculate the cell voltage $E$ at $25C$ if this cell is operated at $pH=3\mathrm{.}50$ and $25C$ with

$[C{r}_2{O}_7^{2-}]=0\mathrm{.}105M,[C{r}^{3+}]=0\mathrm{.}022M,$ and $[C{d}^{2+}]=0\mathrm{.}020M.$