Question #659e1

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Question #659e1

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Answer 1 · 2017-04-25T00:47:25

$[{Mg}^{2 +}] = 2.7 \cdot 10^{- 5} M$ $["Mg"^(2+)] = 2.7 * 10^(-5)"M"$

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.

${MgCO}_{3 (s)} ⇌ {Mg}_{(a q)}^{2 +} + {CO}_{3 (a q)}^{2 -} (!)$ $"MgCO"_ (3(s)) rightleftharpoons "Mg"_ ((aq))^(2+) + "CO"_ (3(aq))^(2-)" "color(darkorange)((!))$

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, $K_{s p}$ $K_(sp)$ , is equal to

$K_{s p} = [{Mg}^{2 +}] \cdot [{CO}_{3}^{2 -}]$ $K_(sp) = ["Mg"^(2+)] * ["CO"_3^(2-)]$

The expression for $K_{s p}$ $K_(sp)$ uses the equilibrium concentrations of the two ions.

In your solution, you know that

$[{CO}_{3}^{2 -}] = 0.25 M$ $["CO"_3^(2-)] = "0.25 M"$

You also know that

$K_{s p} = 6.82 \cdot 10^{- 6}$ $K_(sp) = 6.82 * 10^(-6)$

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

Rearrange the equation to solve for $[{Mg}^{2 +}]$ $["Mg"^(2+)]$

$[{Mg}^{2 +}] = \frac{K_{p s}}{[{CO}_{3}^{2 -}]}$ $["Mg"^(2+)] = K_(ps)/(["CO"_3^(2-)])$

Plug in your values to find

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

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Question #659e1

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