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$K_{\mathrm{sp}}$ for magnesium carbonate, $\mathrm{MgCO}_{3},$ has a value $3.5 \times 10^{-8}$ at $25^{\circ} \mathrm{C}$ . Calculate the solubility of magnesium carbonate in mol $/ \mathrm{L}$ and $\mathrm{g} / \mathrm{L}$ at $25^{\circ} \mathrm{C}$ .

$1.73 \times 10^{-5} \frac{g}{L}$

Chemistry 102

Chapter 17

Equilibrium

Section 9

Solubility Equilibria

Chemical Equilibrium

Rice University

University of Maryland - University College

Brown University

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this question here is asking us about the association of a museum carbonate, which two solid in water, and this is only partially soluble M G two plus acquis and see a three to minus. And so this could be an equilibrium reaction that is governed by the chaos. P that is given to us, which is 3.5 times cents a day instead of some of this problem were to use a nice table and so initial change equilibrium situation because we always want to a nice table Enough. We're getting chaos speeds because we want to understand what's happening at equal. But that's the case. Be really described. So remember solids are ignored during the mass action expression, so we don't care what's happening over here on this side. In the initial demonstration of my museum. To possibly carbonate are both zero. The change is gonna be the same for each them plus X plus X, because their story geometrical equal, there's a one coefficient. Technically, they're both of these, so you deliver and we have accidents. And so remember with them to rewrite the mass action expression. Casspi equals the concentration of magnesium. Two plus times a concentration of carbonate. This is the product of all the concentrations of each of the reactors area to the products over the reactors. But we ignore the solids, and so this equals X squared. Just taking the X from here in the X from there, and we're gonna use this plug that in for the task T She was 3.5 times sentiment. And when you solve them, you're gonna answer for X, which is equal to 1.87 times 10 sent forth Moller because this is a concentration, as we know from here. And so dash answers our first question because were asked to find the soluble iti in terms of moles per liter. And remember, um, Capital M is actually the same saying moles per liter. And this is defining how much of this magnesium carbonate is going to react to dissolve and become that amount of nine museum two plus and carbonate. And so that answers the first question. Actually, next part the question were intercepted. Multiply this by the molecular weight of magnesium carbonate, so I'm gonna rewrite it 1.87 time since the negative fourth moles per liter will be multiplied by 84 0.3 grams. Promote. That's the mark. Their weight of magnesium carbonate. I just looked it up and most will cancel out. When we do this, we're gonna get a final answer, which is? You go to 0.157 grasped her leader, and that's our answer.

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