We have taken a saturated solution of `AgBr`, whose `K_(sp)` is `12xx10^(-14).` If `10^(-7)M` of `AgNO_(3)` are added to `1L` of this solutino, find the conductivity `(` specific conductance `)` of the solution in terms of `10^(-7)S m^(-1)` units.
Given `:`
`lambda^(@)._((Ag^(o+)))=6xx10^(-3)S m^(2) mol^(-1)`
`lambda^(@)._((Br^(c-)))=8xx10^(-3)S m^(2)mol^(-1)`
`lambda^(@)._((NO_(3)^(C-)))=7XX10^(-3)S m^(2) mol^(-1)`

Explanation

Solubility of `AgBr` in presence of `10^(-07)` mole of `AgNO_(3)` solution
`K_(SP_(AgBr)) = [Ag^(+)][Br^(-)]`
`12 xx 10^(-14) = [S + 10^(-7)] xx S`
`:. S = 3 xx 10^(-7)M`
`:. [Ag^(+)] = [3 xx 10^(-7) + 10^(-7)] = 4 xx 10^(-7) M`
`[Br^(-)] = 3 xx 10^(-7) M`
`[NO_(3)^(-)] = 3 xx 10^(-7)M`
`because kappa = (lambda^(@) xx M)/(1000)`
(`lambda` in `S m^(2) mol^(-1) = lambda xx 10^(4) s cm^(2) mol^(-1)`)
`:. kappa_(Ag^(+)) = (6 xx 10^(-3) xx 10^(4) xx 4 xx 10^(-7))/(1000)`
`= 24 xx 10^(-9) S cm^(-1)`
`kappa_(Br^(-)) = (8 xx 10^(-3) xx 10^(4) xx 3 xx 10^(-7))/(1000)`
`= 24 xx 10^(-9) S cm^(-1)`
`kappa_(NO_(3)^(-)) = (7 xx 10^(-3) xx 10^(4) xx 10^(-7))/(1000)`
`= 7 xx 10^(-9) S cm^(-1)`
`:. kappa_("total") = kappa_(Ag^(+)) + kappa_(Br^(-)) + kappa_(NO_(3)^(-))`
`= 24 xx 10^(-9) + 24 xx 10^(-9) + 7 xx 10^(-9)`
`= 55 xx 10^(-9) S cm^(-1) = 55 xx 10^(-7) S cm^(-1)`
in the unit of `1 xx 10^(-7) Sm^(-1)`, the conductivity is `55`.