What is the molar solubility of silver sulfite in a 0.112 M silver nitrate solution?

What is the molar solubility of silver sulfite in a 0.112 M silver nitrate solution?

Given:

• {eq}\displaystyle \rm M = 0.112\ M {/eq} is the concentration of the silver nitrate

Since silver nitrate is a completely soluble compound, we can use its concentration as its amount that is soluble. That is, we can write:

{eq}\displaystyle \rm \Big[Ag^+_{aq}\Big] = \Big[AgNO_3\Big] = 0.112\ M {/eq}

We can write out the reaction of silver sulfite and silver nitrate as:

{eq}\displaystyle \rm Ag_2 SO_{3(s)}\ \to\ 2Ag^+_{(aq)} + SO_{3(aq)}^{-2} {/eq}

The solubility product constant for silver sulfite is:

• {eq}\displaystyle \rm K_{sp} = 1.5\ \times\ 10^{-14} {/eq}

So by using the equation:

{eq}\displaystyle \rm K_{sp} = \Big[Ag^+_{(aq)}\Big]\Big[SO_{3(aq)}^{-2}\Big] {/eq}

We can re-write this as:

{eq}\displaystyle \rm K_{sp} = \Big[0.112\ M\Big]^2 S {/eq}

We isolate the molar solubility S here and substitute our constant:

{eq}\displaystyle \rm S = \frac{1.5\ \times\ 10^{-14}}{(0.112\ M)^2} {/eq}

We get:

{eq}\displaystyle \rm \boxed{\rm S = 1.196\ \times\ 10^{-12}\ M} {/eq}