(a) Which will have the highest concentration of potassium ion: \(0.20 M \mathrm{KCl}, 0.15 M \mathrm{K}_{2} \mathrm{CrO}_{4},\) or 0.080\(M \mathrm{K}_{3} \mathrm{PO}_{4} ?\) (b) Which will contain the greater number of moles of potassium ion: 30.0 \(\mathrm{mL}\) of 0.15 \(\mathrm{M} \mathrm{K}_{2} \mathrm{CrO}_{4}\) or 25.0 \(\mathrm{mL}\) of 0.080 \(\mathrm{M} \mathrm{K}_{3} \mathrm{PO}_{4} ?\)

Molarity is a measure of concentration, expressing the number of moles of a solute per liter of solution. It's signified by the letter 'M' and is calculated using the formula:
\[ Molarity = \frac{moles \text{ of solute}}{volume \text{ of solution in liters}} \]
In simpler terms, it tells us how 'strong' or 'concentrated' a solution is with respect to a particular solute. In the context of potassium ion concentration in various compounds like KCl, K₂CrO₄, and K₃PO₄, molarity directly affects the number of available potassium ions in the solution. When comparing solutions with different molarities, the ion concentration is not just about the stated molarity of compounds, but also about the stoichiometry, which is the ratio of ions released per formula unit of the compound. A higher molarity usually means a higher concentration of ions up to the point where the solution becomes saturated and no more solute can be dissolved.

Understanding the relationship between moles and volume is crucial for many chemistry problems, including calculating ion concentrations in solutions. A mole is a unit of measurement that represents a set number of particles, usually atoms or molecules. The volume is the space that the solution occupies, typically measured in liters or milliliters.
For dilute solutions, where the solute-solvent interactions don't significantly change the volume, the relationship between moles, molarity, and volume is linear and is given by the straightforward formula:
\[ moles = Molarity \times Volume \]
This relationship allows us to determine the number of moles of any component in a solution if we know the molarity and the volume. The accurate conversion between the units of volume (milliliters to liters) is critical, as molarity is defined per liter of solution. To avoid common mistakes, always check that the volume used in calculations is in liters.

Stoichiometry deals with the quantitative relationships of the elements within compounds and the calculations based on these relationships. When it comes to ionic compounds, stoichiometry becomes particularly important in understanding how many ions are produced when the compound dissolves in water.
For each compound such as KCl, K₂CrO₄, and K₃PO₄, the proportion of potassium to the other elements is determined by the chemical formula. For example, KCl has 1 potassium ion for every chloride ion, while K₂CrO₄ and K₃PO₄ have 2 and 3 potassium ions, respectively, for each formula unit. When these compounds dissolve in water, each unit dissociates to release multiple potassium ions, impacting the concentration. The stoichiometric coefficients tell us the exact number of moles of ions released from one mole of ionic compound, playing a vital role in the calculations of ion concentration in solution.