At what `[Br^(-)]/sqrt(CO_(3)^(2-)]` does the following cell have its reaction at equilibrium?
`Ag(s) | Ag_(2)CO_(3)(s)| Na_(2)CO_(3)(aq)|| KBr(aq) | AgBr(s)| Ag(s)`
`K_z9sp) = 8 xx 10^(-12)` for Ag_(2)CO^(3)` and `K_(sp) = 4 xx 10^(-13)` for AgBr

Options

A. `sqrt1xx10^(-7)`
B. `sqrt2xx10^(-7)`
C. `sqrt3xx10^(-7)`
D. `sqrt4xx10^(-7)`

Answer

B

Explanation

`({:("Anode :",Ag(s)toAg^+(aq)+1 e^(-)),("Cathode:",Ag^+(aq)+1e^(-)toAg):})/`
`"net":Ag_((AgBr))^+overset(1e^(-))Ag_((Ag_2CO_3))^+`
`0=0+0.059/1 log(((K_(SP)AgBr)/([Br^(-)])))/sqrt((K_(SP)Ag_2CO_3)/([CO_3^(2-)]))implies(K_(SP)AgBr)/([Br^(-)])=sqrt((K_(SP)Ag_2CO_3)/([CO_3^(2-)]))`
`implies (4xx10^(-13))/sqrt(8xx10^(-12))=([Br^(-)])/sqrt([CO_3^(-2)]) implies ([Br^(-)])/sqrt([CO_3^(-2)])=sqrt2xx10^(-7)`