### Video Transcript

The solubility of barium carbonate,
BaCO3, at room temperature is 5.08 times 10 to the negative five moles per cubic
decimeter. What is the solubility product of
barium carbonate at this temperature? Give your answer in scientific
notation to two decimal places. (A) 2.58 times 10 to the negative
nine moles squared times decimeters to the negative six. (B) 1.31 times 10 to the negative
13 moles squared times decimeters to the negative six. (C) 1.02 times 10 to the negative
four moles squared times decimeters to the negative six. (D) 5.16 times 10 to the negative
nine moles squared times decimeters to the negative six. Or (E) 2.54 times 10 to the
negative five moles squared times decimeters to the negative six.

In this question, we want to find
the solubility product, abbreviated K sp, of barium carbonate. The solubility product of a
compound is the product of the concentrations of the ions in a saturated solution
raised to the power of their respective stoichiometric coefficients. We can look at this using an
equilibrium equation of the generic solid compound, MA, dissociating into its
constituent ions.

The lowercase letters represent the
stoichiometric coefficients of the ions in solution. So, the K sp would be written as
shown. We use brackets to denote
concentration, which we can measure in units of moles per cubic decimeter. We are given from the problem the
solubility of barium carbonate at room temperature measured in moles per cubic
decimeter. We can use the generic equation to
write a balanced equilibrium equation for barium carbonate.

Barium carbonate would be in
equilibrium with barium cations and carbonate anions. Using this equation, we can write
the K sp expression. At equilibrium, all species are
stoichiometrically equivalent. As each unit of barium carbonate
dissolves, one barium ion and one carbonate ion are produced. Per cubic decimeter of water, 5.08
times 10 to the negative five moles of barium carbonate can dissolve. Thus, the concentrations of the
produced ions will also be 5.08 times 10 to the negative five moles per cubic
decimeter.

We can substitute these
concentrations into the K sp equation. We can multiply these
concentrations together to find the numerical value of the solubility product. To find the units, we multiply
moles times moles to get moles squared, and decimeters to the negative three times
decimeters to the negative three to get decimeters to the negative six. Our answer is already in scientific
notation. But we need to round it to two
decimal places, to get 2.58 times 10 to the negative nine moles squared times
decimeters to the negative six.

Therefore, the solubility product
of barium carbonate at room temperature is answer choice (A), 2.58 times 10 to the
negative nine moles squared times decimeters to the negative six.