For the galvanic cell : `Ag|AgCl(s), KCl (0.2M)||KBr(0.001M), AgBr(s)|Ag,` calculate the EMF and assign correct polarity to each electrode for a spontaneous process after taking into account the cell reaction at `25^(@)C`. Given :
`K_(sp)(AgCl)=2.8xx10^(-10), K_(sp)(AgBr)=3.3xx10^(-13)`

Explanation

For the galvanic cell,
`Ag|AgCl(s), KCl(0.2M)||KBr(0.001M), AgBr(s)|Ag`
`E_("cell")=(0.591)/(n)log.([Ag^(+)]_(AgBr))/([Ag^(+)]_(AgCl))" …[1]"`
Given, `K_(ap)(AgCl)=2.8xx10^(-1)." Now, "[Cl^(-)]=0.2 (M)`
`therefore" "2.8xx10^(-10)=[Ag^(+)]_(AgCl)xx0.2`
`"or, "[Ag^(+)]_(AgCl)=(2.8xx10^(-10))/(0.2)=14xx10^(-10)(M)`
Givne, `K_(sp)(AgBr)=3.3xx10^(-13)." Here, "[Br^(-)]=0.001M`
`therefore" "3.3xx10^(-13)=[Ag^(+)]_(AgBr)xx0.001`
`"or, "[Ag^(+)]_(AgBr)=(3.3xx10^(-13))/(0.001)=3.3xx10^(-10)(M)`
`"Substituting in equation (1), "E_("cell")=(0.059)/(1)log.(3.3xx10^(-19))/(14xx10^(-10))`
`=0.059xx(-0.6274)=-0.037V`
The negative value of `E_("cell")` indicates that the cell reaction `[AgBr(s)+Cl^(-)(aq)rarrAgCl(s)+Br^(-)(aq)]` is not spontaneous but the reverse reaction is spontaneous as in this case `E_("cell")=+0.037V`. To carry out the reverse reaction, the polarity of the given cell should be reversed i.e., the anode should be made cathode, and vice - versa.