The solubility product `(K_(sp))` of the following compounds are given at `25^(@)C`
`{:("Compounds",K_(sp)),(AgCl,1.1 xx 10^(-10)),(AgI,1.0 xx 10^(-16)),(PbCrO_(4),4.0 xx 10^(-14)),(Ag_(2)CO_(3),8.0 xx 10^(-12)):}`
The most soluble and least soluble compounds are

Options

A. a) `AgCl and PbCrO_(4)`
B. b) `AgI and Ag_(2)CO_(3)`
C. c) `AgCl and Ag_(2)CO_(3)`
D. d) `Ag_(2)CO_(3) and AgI`

Answer

D

Explanation

(i) `AgCl(s) harr Ag^(+) (aq) + Cl^(-)(aq)`
`K_(sp) = [Ag^(+)][Cl^(-)]`
`= s xx s = s^(2)`
`K_(sp) = 1.1 xx 10^(-10)` (given)
`therefore" "s^(2) = 1.1 xx 10^(-10)`
or `s = 1.04 xx 10^(-5) "mol L"^(-1)`
(ii) `AgI harr Ag^(+) + I^(-)`
`K_(sp) = [Ag^(+)][I^(-)]`
`= s xx s = s^(2)`
`K_(sp) = s^(2) = 1.0 xx 10^(-16)`
or `s = 1.0 xx 10^(-8) "mol L"^(-1)`
(iii) `PbCrO_(4) harr Pb^(2+) + CrO_(4)^(2-)`
`K_(sp) = [Pb^(2+)][CrO_(4)^(2-)]`
`= s xx s = s^(2)`
`K_(sp) = s^(2) = 4.0 xx 10^(-14)`
or `s = 2.0 xx 10^(-7)"mol L"^(-1)`
(iv) `Ag_(2)CO_(3)harr 2 underset(2s)(Ag^(+)) + underset(s)(CO_(3)^(2-))`
`= 4s^(3)`
`K_(sp) = [Ag^(+)]^(2) [CO_(3)^(2-)]`
`= (2s)^(2) xx s = 4s^(3)`
`K_(sp) = 4s^(3) = 8.0 xx 10^(-12)`
or `s = 1.26 xx 10^(-4) "mol L"^(-1)`