# Question 659e1

Apr 25, 2017

["Mg"^(2+)] = 2.7 * 10^(-5)"M"

#### Explanation:

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, ${K}_{s p}$, is equal to

${K}_{s p} = \left[{\text{Mg"^(2+)] * ["CO}}_{3}^{2 -}\right]$

The expression for ${K}_{s p}$ uses the equilibrium concentrations of the two ions.

In your solution, you know that

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

You also know that

${K}_{s p} = 6.82 \cdot {10}^{- 6}$

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

Rearrange the equation to solve for $\left[{\text{Mg}}^{2 +}\right]$

["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")))#