Determine the concentration of \(\mathrm{NO}_{3}{ }^{-}\)in each aqueous solution. (Assume complete dissociation of each compound.) (a) \(0.10 \mathrm{M} \mathrm{KNO}_{3}\) (b) \(0.10 \mathrm{M} \mathrm{Ca}\left(\mathrm{NO}_{3}\right)_{2}\) (c) \(0.10 \mathrm{M} \mathrm{Cr}\left(\mathrm{NO}_{3}\right)_{3}\)

Molarity is a central concept in chemistry, referring to the concentration of a solution. It is defined as the number of moles of a solute dissolved in one liter of solution. When you see a chemical formula with a 'M' next to it, such as '0.10 M KNO_{3}', it's telling you that in every liter of that solution, there are 0.10 moles of potassium nitrate.

Dissociation is what happens when ionic compounds like KNO_{3}, Ca(NO_{3})_{2}, or Cr(NO_{3})_{3} dissolve in water. They split into their constituent ions. For example, KNO_{3} dissociates into K^{+} and NO_{3}^{-}. The extent of this separation is vital because it affects the final concentration of ions in the solution, which impacts many properties, including conductivity and reactivity.

It’s crucial to remember that the dissociation assumed in this exercise is complete. This means every single unit of the compound splits apart in water, which is an ideal situation often used for simplicity in calculations.

Stoichiometry is the math behind chemistry. It's about the relationships between the amounts of reactants and products in a chemical reaction. In the context of solutions, stoichiometry helps us understand the ratio of the different ions that result from dissociation.

You apply stoichiometry to determine how many nitrate ions come from each compound. For instance, if one formula unit of Ca(NO_{3})_{2} produces two NO_{3}^{-} ions, then a 0.10 M solution of Ca(NO_{3})_{2} will result in a nitrate concentration that's double the original molarity of the compound. Understanding the stoichiometric ratios of compounds is essential for accurately calculating ion concentrations in solutions, as you need to know how many of each type of ion you have.

The final step in our exploration is to apply what we've learned about molarity and stoichiometry to calculate specific ion concentrations. Using the given examples, we can determine the concentration of nitrate ions by considering the stoichiometric coefficients from the dissociation formula.

For KNO_{3}, which dissociates into K^{+} and NO_{3}^{-}, the ratio of nitrate to compound is 1:1, so the nitrate concentration remains 0.10 M. For Ca(NO_{3})_{2}, the ratio is 2:1, resulting in a doubled nitrate concentration of 0.20 M. Finally, for Cr(NO_{3})_{3}, with a ratio of 3:1, the nitrate concentration is tripled to 0.30 M. Each calculation requires carefully applying the correct stoichiometric ratios, as these details directly impact the outcome and accuracy of your results.