What are the final concentrations of all the ions when following are mixed? \(50 \mathrm{~mL}\) of \(0.12 \mathrm{M} \mathrm{Fe}\left(\mathrm{NO}_{3}\right)_{3}, 100 \mathrm{~mL}\) of \(0.10 \mathrm{M} \mathrm{FeCl}_{3}\) and \(100 \mathrm{~mL}\) of \(0.26 \mathrm{M} \mathrm{Mg}\left(\mathrm{NO}_{3}\right)_{2}\)

Molarity is a term used in chemistry to describe the concentration of a solution. It's defined as the number of moles of solute (the substance to be dissolved) per liter of solution. The unit for molarity is moles per liter ((M/L) or molar ((M)). To calculate molarity, you can use the following formula:
\( \text{Molarity} = \frac{\text{Moles of solute}}{\text{Volume of solution in liters}} \).
In the context of the exercise provided, molarity assists in understanding how much of each ion is present in a given volume of solution before and after mixing. For instance, a solution having a molarity of 0.12 M implies that there are 0.12 moles of the solute in every liter of the solution. Accurate molarity calculations are essential for the proper execution of stoichiometric calculations in chemistry.

Stoichiometry is the area of chemistry that pertains to the quantitative relationships between the substances as they participate in chemical reactions. In essence, it's like a recipe for a reaction: telling you how much of each reactant you need and what amount of product you can expect.
When performing stoichiometric calculations, balance between the reactants and products in a chemical equation is crucial. This balance is based on the conservation of mass and the principle that atoms are neither created nor destroyed in a chemical reaction.
For the given exercise, stoichiometry is used to determine the moles of each ion in the solutions. By understanding the stoichiometric relationships in the compounds (for example, \( \mathrm{Fe(NO_{3})_{3}} \) has three \( \mathrm{NO_{3}^{-}} \) ions for every one \( \mathrm{Fe^{3+}} \) ion), we can accurately calculate the final concentrations of ions after mixing the solutions.

Solution concentration refers to the amount of solute present in a given quantity of solvent or solution. It's a measure of how 'concentrated' a solution is. There are several ways to express concentration, including molarity, molality, mass percent, and volume percent. Molarity, the measure used in the provided exercise, is one of the most common methods, especially in aqueous solutions, which are solutions where water is the solvent.
In practice, understanding solution concentration is paramount when preparing solutions for experiments, as well as when combining solutions, as seen in the exercise. Knowing the concentration of each solution helps to predict how the concentrations will change upon mixing. For instance, mixing equal volumes of solutions with different molarities will result in a final molarity that is the average of the two initial molarities.
The exercise precisely uses the concept of solution concentration to determine the final concentration of ions when the initial solutions are mixed. By calculating the final concentrations, we can predict the behavior of the ions in the new combined solution and use this knowledge for further chemical analysis or reactions.