Question #659e1

Magnesium carbonate is considered insoluble in water, which implies that when you dissolve this salt in water, a dynamic equilibrium exists between the undissolved solid and the dissolved ions.

`"MgCO"_ (3(s)) rightleftharpoons "Mg"_ ((aq))^(2+) + "CO"_ (3(aq))^(2-)" "color(darkorange)((!))`

Some of the solid will dissolve to produce ions, but most of the salt will remain undissolved, i.e. this equilibrium lies to the left.

By definition, the solubility product constant, `K_(sp)`, is equal to

`K_(sp) = ["Mg"^(2+)] * ["CO"_3^(2-)]`

The expression for `K_(sp)` uses the equilibrium concentrations of the two ions.

In your solution, you know that

`["CO"_3^(2-)] = "0.25 M"`

You also know that

`K_(sp) = 6.82 * 10^(-6)`

Your goal here is to determine the concentration of magnesium cations that will satisfy equation `color(darkorange)((!))`.

Rearrange the equation to solve for `["Mg"^(2+)]`

`["Mg"^(2+)] = K_(ps)/(["CO"_3^(2-)])`

Plug in your values to find

`["Mg"^(2+)] = (6.82 * 10^(-6))/(0.25) = color(darkgreen)(ul(color(black)(2.7 * 10^(-5)color(white)(.)"M")))`