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 copperion 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

The cell may be represented as :
`Cu (s) | Cu ^(2+) (0.10 M) || Ag^(+) (aq) | Ag(s)`
The cell reaction is
Cu (s) + ` 2 Ag^(+) (aq) to Cu^(2+) (aq) + 2 Ag (s)`
`E^(Theta) (Cu^(2+) |Cu) = + 0.34 V , E^(@) (Ag^(+) |Ag) = + 0.80 V`
`E_(cell)^(Theta) = E^(Theta) (Ag^(+) | Ag) - E^(Theta) (Cu^(2+) |Cu) = 0.80 - 0.34 = 0.46 V`
`[Cu^(2+)] = 0.10 M , [Ag^(+)] = ?`
`E_(cell) = E_(cell)^(Theta) - (0.059)/(2) "log" ([Cu^(2+)])/([Ag^(+)]^(2))`
`0.422 = 0.46 - (0.059)/(2) "log" (0.10)/([Ag^(+)]^(2)`
`(0.059)/(2) "log" (0.10)/[Ag^(+)]^(2)) = 0.46 - 0.422`
`(0.059)/(2) "log" (0.10)/([Ag^(+)]^(2)) = 0.038`
`log (0.10)/([Ag^(+)]^(2)) = ( 2 xx 0.038)/(0.059) = 1.2881`
`(0.1)/([Ag^(+)]^(2)) = 19.42`
`[Ag^(+)]^(2) = (0.1)/(19.42) = 5.15 xx 10^(-3)`
`[Ag^(+)] = 0.0717 M`