### Video Transcript

What is the equation for the
solubility product, ๐พ sp, of yttrium carbonate, Y2(CO3)3? (A) ๐พ sp equals the concentration
of Y squared times the concentration of CO3 cubed. (B) ๐พ sp equals the concentration
of Y3+ times the concentration of CO32โ. (C) ๐พ sp equals the concentration
of Y3+ squared times the concentration of CO32โ cubed. (D) ๐พ sp equals the concentration
of Y3+ cubed times the concentration of CO32โ squared. Or (E) ๐พ sp equals the
concentration of Y3+ cubed divided by the concentration of CO32โ squared.

In this question, we want to
identify the correct equation for the given compoundโs solubility product, which is
the product of the concentrations of the ions in a saturated solution raised to the
power of their respective stoichiometric coefficients. In order to write this equation, we
need to determine the chemical formulas and the stoichiometric coefficients of these
ions when the compound dissolves.

The solid compound in question is
yttrium carbonate, which has the chemical formula Y2(CO3)3. In water, it will dissolve until it
reaches an equilibrium with its constituent ions in solution. Its chemical formula indicates that
for each unit of yttrium carbonate, there are three carbonate ions, which have a
charge of two minus. There are also two yttrium ions
present. For the compound to be neutral
overall, we know the yttrium ions must have a charge of three plus. We can write the balanced
equilibrium reaction as shown.

Now, we can write the ๐พ sp using
this reaction equation. The ๐พ sp will be equal to the
concentration of yttrium three plus ions times the concentration of the carbonate
ions. We use brackets to denote
concentration. We must remember to raise the ion
concentrations to the power of their respective stoichiometric coefficients. The ๐พ sp equation we have written
matches answer choice (C).

Therefore, the equation for the
solubility product, ๐พ sp, of yttrium carbonate is answer choice (C). ๐พ sp equals the concentration of
Y3+ ions squared times the concentration of CO32โ ions cubed.