Question

Which has the greater molarity in water, AgCl or $Mg(OH)_{2}$? ($(K_{sp} (AgCl) = 1.8 \times 10^{-10}$, $(K_{sp}(Mg(OH)_{2}) = 1.2 \times 10^{-11}$)

Answer 1

third option is the correct answer

Answer 2

$AgCl \rightleftharpoons { Ag }^{ + }+ { Cl }^{ - }$

Given,

${ k }_{ sp }=1.8\times { 10 }^{ -10 }\\ { [Ag }^{ + }][{ Cl }^{ - }]$

$Mg{ (OH })_{ 2 } \rightleftharpoons { Mg }^{ 2+ } + { 2OH }^{ - }$

${ k }_{ sp }=1.2\times { 10 }^{ -11 }\\{ k }_{ sp }= [{ Mg }^{ 2+ }{ { ][OH }^{ - }] }^{ 2 }\\=1.2\times { 10 }^{ -11 }$

Let ${ Mg }^{ 2+ }=x, [OH }^{ - }] }^{ 2}]=2x$

$x({ 2x }^{ 2 })=4{ x }^{ 3 }=1.2\times { 10 }^{ -11 }\\x=1.4\times { 10 }^{ -4 }M$

Since the ${ k }_{ sp }$ for Silver chloride AgCl is  greater than that of ${ k }_{ sp }$ for Magnesium Hydroxide $Mg{ (OH })_{ 2 }$ and also ${ k }_{ sp }$ for $Mg{ (OH })_{ 2 }$ is more soluble in water.

The ${ k }_{ sp }$ expressions are not comparable since Magnesium Hydroxide have a square term in it.