The solubility product `(K_(sp))` of the following compounds are given at `25^(@)C`
`{:("Compound",,"K"_(sp)),("AgCl",,1.1xx10^(-10)),(Agl,,1.0xx10^(-16)),(PbCrO_(4),,4.0xx10^(-14)),(Ag_(2)CO_(3),,8.0xx10^(-12)):}`
The most soluble and least soluble compound are respectively

Options

A. `AgCl and PbCrO_(4)`
B. `Agl and Ag_(2)CO_(3)`
C. `AgCl and Ag_(2)CO_(3)`
D. `Ag_(2)CO_(3) and Agl `

Answer

D

Explanation

The solubility equilibrium is
`"AgCl" hArrAg_((aq))^(+) +Cl_((aq))^(-)`
`K_(sp) = [Ag^(+)][Cl^(-)]`
Let solubility of AgCl be S moles per litre, then the concentrations of various species at equilibrium are
`[Ag^(+)] = S, [Cl^(-)] = S `
`K_(sp) = [Ag^(+)][Cl^(-)] `
`1.1 xx10^(-10) = (S) xx (S) = S^(2)`
`S = (1.1 xx 10^(-10))^(1//2) = 1 xx 10^(-5)`
` {:("AgCl ",1xx10^(-5)),("Agl ",1xx10^(-8)),("PbCrO"_(4),2xx10^(-7)),(Ag_(2)CO_(3),1.26xx10^(-4)):}`
`Ag_(2)CO_(3)` is most soluble and Agl is least soluble.