Why is it that copper (II) sulfate with barium hydroxide --> copper hydroxide (solid) + barium sulfate (solid)? According to the solubility rules given to me by my professor, both are insoluble, and therefore should be labeled as solids. Is there something I'm missing here? I'm in a first semester college chemistry class.

Frankly I don't understand your question. You're right. Both Cu(OH)2 and BaSO4 are solids and you have labeled them correctly. According to the solubility rules, a reaction proceeds when ONE of the products is a solid. This doesn't change when BOTH products are solids.

Should've phrased it differently. I meant, why is CuSO4 and Ba(OH)2 given as aqueous solutions in the beginning? That's the problem I was given. I'm not sure why they're soluble when they're not "supposed" to be, according to my solubility rules.

An unknown compound contains only C, H, and O. Combustion of 3.70 g of this compound produced 9.03 g of CO2 and 3.70 g of H2O.

Im so confused.

In the reaction between copper (II) sulfate and barium hydroxide, copper hydroxide and barium sulfate are formed as solids. You are correct that both copper hydroxide and barium sulfate are considered insoluble, based on the solubility rules provided by your professor. However, there is a key concept you may be missing.

Solubility rules provide a general guide for predicting the solubility of ionic compounds, but they do not always account for the entire context of a reaction. While copper hydroxide and barium sulfate are indeed insoluble, the reaction between copper (II) sulfate and barium hydroxide involves a double replacement reaction, also known as a precipitation reaction.

In a precipitation reaction, two soluble compounds react to form an insoluble compound, called a precipitate. In this case, copper (II) sulfate is soluble in water, as it dissociates into copper ions (Cu²⁺) and sulfate ions (SO₄²⁻). Barium hydroxide is also soluble in water, dissociating into barium ions (Ba²⁺) and hydroxide ions (OH⁻).

When copper (II) sulfate and barium hydroxide are mixed together, the copper ions from copper (II) sulfate combine with hydroxide ions from barium hydroxide to form insoluble copper hydroxide (Cu(OH)₂). Similarly, the sulfate ions from copper (II) sulfate combine with the barium ions from barium hydroxide to form insoluble barium sulfate (BaSO₄).

As a result, a double replacement reaction occurs, where the cations and anions switch partners to form the precipitates. The balanced chemical equation for the reaction is:
CuSO₄ (aq) + Ba(OH)₂ (aq) → Cu(OH)₂ (s) + BaSO₄ (s)

In summary, while copper hydroxide and barium sulfate are individually considered insoluble according to solubility rules, they do not dissolve in water when combined in this reaction due to a double replacement reaction, resulting in the formation of solid precipitates.