(a) Write the anode and cathode reactions and the overall reaction occuring in a lead storage battery.
(b) A copper - silver cell is set up. The copper ion concentrations is `0.10` M. The concentration of silver ion is not known. The cell potential when measured was `0.422` V. Determine the concentration of silver ions in the cell.
`Given " "E^(@)Ag^(+)//Ag=+0.80 V,E^(@)Cu^(2+)//Cu=+0.34 V`

Explanation

(a)Anode reaction : `Pb+SO_(4)_^(2-) rightarrow Pb SO_(4) (s)+ 2 " " e^(-)"`
Cathode reaction : `Pb" "O_(2) +4 H^(+)+ SO_(4)^(2-) + 2e^(-) rightarrow Pb" "SO_(4)+2H_(2)O`
Overall reaction : `Pb+Pb" "O_(2)+2 " "SO_(4)^(2-)+ 4H^(+)rightarrow 2Pb" "SO_(4)+2H_(2)O`
(b) The cell reaction is : `Cu (s)+2Ag^(+)(aq) rightarrow Cu^(2+)(aq) +2" "Ag(s)`
`therefore`" " `E_("cell")^(@)=0.80-0.34=0.46`
Using Nernst equation, we have
`E_(cell)=E^(@)._(cell)-0.529/n log. ([Cu^(2+)])/ ([Ag^(+)]^(2))`
`0.422=0.46-0.059/2log. 0.10/[Ag^(+)]^(2)`
`0.529/2log. 0.10/[Ag^(+)]^(2)=0.038`
`therefore`" "`log.(0.10)/([Ag^(+)]^(2))=1.288 rArr 0.10/([Ag^(+)]^(2))=anti-log 1.288`
`rArr`" "`0.10/([Ag^(+)]^(2)) =19.41rArr[Ag^(+)]^(2)`
`=0.005151=51.51xx10^(-4)`
`[Ag^(+)]=7.1xx10^(-2)M`.