The fixing of photographic film involves film involves dissolving unexposed AgBr in a thiosulphate solultion.
`AgBr_((s))+2S_(2)O_(3(a.))^(2-)hArr[Ag(S_(2)O_(3))_(2)]_((aq.))^(3-)+Br_((aq.))^(-)`
Calculate the equilibrium constant K for the dissociation reaction of `[Ag(S_(2)O_(3))_(2)]^(3-)`.
`K_(SP)of AgBr=5.4xx10^(-13)` and `K_(f) for [Ag(S_(2)O_(3))_(2)]^(3-) = 4.7xx10^(-13))`

Explanation

`K_(f)=([Ag(S_(2)O_(3))_(2)]^(3-)xx[Br^(-)])/([S_(2)O_(3)^(2-)]^(2))`
`= 4.7xx10^(13)` …… (1)
`K_(SP)` of `AgBr= [Ag^(+)][Br^(-)]`
`=5.4xx10^(-13)` ………(2)
Also `[Ag(S_(2)O_(3))_(2)]^(3-)hArr Ag^(+)+2S_(2)O_(3)^(2-)`
`K_(d)= ([Ag^(+)][S_(2)O_(3)^(2-)]^(2))/([Ag(S_(2)O_(3))_(2)]^(3-))` .......(3)
By eqs. (2) and (3),
`:. K_(d)=(K_(SP))/(K_(f))=(5.4xx10^(-13))/(4.7xx10^(13))=1.15`