What type of a battery is lead storage battery? Write the anode and cathode reactions and the overall cell reaction occurring in the operation of a lead storage battery.
(b) Calucluate the potential for half-cell containing.
0.10 M `K_(2)Cr_(2)O_(7)(aq), 0.20 M Cr^(3+) (aq) and 1.0 xx 10^(-4) M H^(+) (aq)`
The half -cell reaction is
`Cr_(2)O_(7)^(2-) (aq) + 4H^(+) (aq) + 6 e^(-) to 2 Cr^(3+) (aq) + 7H_(2)O(l)`
and the standard electron potential is given as `E^(o) = 1.33V`.

Explanation

(a). The lead storage battery is the most important secondary cell.
cell reactions when the battery is in use are given below.
At anode: `Pb(s)+SO_(4)^(2-)(aq)toPbSO_(4)(s)+2e^(-)`
at At cathode: `PbO_(2)(s)+SO_(4)^(2-)(aq)+4H^(+)(aq)+2e^(-)toPbSO_(4)(s)+2H_(2)O(l)`
The overall cell reaction is
`Pb(s)+PbO_(2)(s)+2H_(2)SO_(4)(aq)to2PbSO_(4)(s)+2H_(2)O(l)`
(b). the cell reaction for the cell
`Cr_(2)O_(7)^(2-)(a)+14H^(+)(aq)+6e^(-)to2Cr^(3+)(aq)+7H_(2)O(l)`
`E=E_(cell)^(0)-(0.059)/(n)log(([Cr^(3+)(aq)]^(2))/([Cr_(2)O_(7)^(2-)(aq)][H^(+)]^(14))`
`E=1.33-(0.0591)/(6)log(((0.2)^(2))/(0.1xx(10^(-4))^(14)))`
`E=1.33-0.5476=0.7824V`.