Write net ionic equations for the formation of (a) a precipitate when solutions of magnesium nitrate and potassium hydroxide are mixed. (b) two different precipitates when solutions of silver(I) sulfate and barium chloride are mixed.

Precipitation reactions occur when two aqueous solutions combine to form a solid, known as a precipitate. These reactions are a subclass of exchange reactions where the anions and cations of the reactants trade places, resulting in the formation of at least one insoluble product.

For example, when magnesium nitrate and potassium hydroxide solutions are mixed, magnesium hydroxide, an insoluble compound that precipitates out of the solution, is formed. This can be illustrated by the chemical equation: \( Mg(NO_3)_2 + 2KOH \rightarrow Mg(OH)_2 + 2KNO_3 \).

Understanding precipitation reactions is crucial not just in chemistry, but also in environmental science and engineering, where they play a role in water treatment and the natural formation of mineral deposits.

Spectator ions are ions that do not participate in the chemical reaction and remain unchanged on both the reactant and the product sides of the equation. They are present in the same form throughout the reaction process and can be observed in ionic equations.

In the net ionic equation process, these spectator ions are omitted to simplify the equation and focus on the actual chemical change taking place. For instance, in the reaction between magnesium nitrate and potassium hydroxide, potassium (\( K^+ \)) and nitrate (\( NO_3^- \)) ions are spectator ions. They can be eliminated to leave the net ionic equation: \( Mg^{2+} + 2OH^- \rightarrow Mg(OH)_2 (solid) \).

Spectator ions can help in understanding reaction mechanisms and are key to calculating the concentrations of various species in a solution after a reaction has occurred.

Solubility rules are guidelines that help predict whether a compound will dissolve in water, forming an aqueous solution, or form a precipitate. These rules are based on empirical observations and tend to generalize the solubility of ionic compounds.

For example, most nitrates (\( NO_3^- \)) and alkali metal compounds are soluble in water, which means they won't form a precipitate when dissolved. However, compounds like silver chloride (\( AgCl \)) and barium sulfate (\( BaSO_4 \)) are generally insoluble and will precipitate out of the solution when the corresponding ions are mixed.

The solubility rules dictate that in reaction between silver(I) sulfate and barium chloride, both silver(I) chloride and barium sulfate are formed as precipitates. These rules are vital for predicting the outcomes of reactions and are used by chemists to design synthetic routes and by environmental scientists to understand the mobility of ions in natural waters.