Question

What is the molarity of \(\mathrm{NO}_{3}^{-}\) in each solution? a. 0.150 \(\mathrm{M} \mathrm{KNO}_{3}\) b. 0.150 \(\mathrm{M} \mathrm{Ca}\left(\mathrm{NO}_{3}\right)_{2}\) c. 0.150 \(\mathrm{M} \mathrm{Al}\left(\mathrm{NO}_{3}\right)_{3}\)

Short answer

a. 0.150 M NO_3^-, b. 0.300 M NO_3^-, c. 0.450 M NO_3^-

Step-by-step solution

Identify the Number of Nitrate Ions per Formula Unit

For each compound, determine the number of nitrate ((NO_3^-)) ions per formula unit. For KNO_3, there is 1 nitrate ion per unit. For Ca(NO_3)_2, there are 2 nitrate ions per unit. For Al(NO_3)_3, there are 3 nitrate ions per unit.

Calculate Molarity of NO_3^- for Each Compound

Calculate the molarity of NO_3^- based on the number of nitrate ions and the initial molarity of each compound. Multiply the initial molarity by the number of NO_3^- ions in each compound’s formula unit.a. For KNO_3: 0.150 M KNO_3 * 1 NO_3^- = 0.150 M NO_3^-b. For Ca(NO_3)_2: 0.150 M Ca(NO_3)_2 * 2NO_3^- = 0.300 M NO_3^-c. For Al(NO_3)_3: 0.150 M Al(NO_3)_3 * 3 NO_3^- = 0.450 M NO_3^-

Key concepts

Nitrate Ion Concentration

Understanding nitrate ion concentration is crucial for students tackling problems in chemistry, specifically when dealing with solutions that involve salts of nitric acid. Nitrate, represented by the chemical notation (NO_{3}^{-}), is a polyatomic ion comprised of one nitrogen atom and three oxygen atoms. When dissolved in water, compounds containing nitrate ions dissociate, and the nitrate ions become solvated by the water molecules. The concentration of nitrate ions is determined by both the molarity of the original compound and the number of nitrate ions released upon dissociation.

For example, in a solution of potassium nitrate (KNO_{3}), for every one formula unit of KNO_{3} that dissolves, one nitrate ion is released into the solution. Therefore, if the solution has a molarity of 0.150 M, this represents the concentration of nitrate ions as well. In compounds with multiple nitrate groups like Ca(NO_{3})_{2} and Al(NO_{3})_{3}, you must account for each nitrate ion when determining their concentrations in solution.

Chemical Formula Unit

A chemical formula unit refers to the simplest whole-number ratio of ions present in an ionic compound that indicates the composition of the compound. It provides critical information about the ratio and types of atoms that constitute the compound. For salts containing the nitrate ion, such as KNO_{3}, Ca(NO_{3})_{2}, and Al(NO_{3})_{3}, the numbers and parentheses in their formulas are clues for determining the nitrate ion concentration in solution.

Let's break down Ca(NO_{3})_{2} as an example. The chemical formula indicates that each formula unit consists of one calcium ion and two nitrate ions. When such an ionic compound dissolves, it separates into its constituent ions, meaning one formula unit of Ca(NO_{3})_{2} will yield two nitrate ions in solution. This knowledge is central to correctly calculating the molarity of ions in solution, as omitting these details leads to inaccuracies in understanding the solution's composition.

Solution Concentration

The concentration of a solution typically refers to the amount of solute present in a given volume of solvent. Molarity (M) is a common unit of concentration, defined as moles of solute per liter of solution. It's important to note that in a solution containing ionic compounds, the total molarity of the solution reflects the concentration of all the ions present, not just the compound itself.

When dissolving ionic compounds like KNO_{3}, Ca(NO_{3})_{2}, or Al(NO_{3})_{3}, the total solution concentration changes based on the number of ions each formula unit contributes. For instance, in a 0.150 M Al(NO_{3})_{3} solution, we understand this to mean there are 0.150 moles of the Al(NO_{3})_{3} formula units in one liter of solution. However, since each formula unit contributes three nitrate ions to the solution, we must multiply the compound molarity by three to find the molarity of nitrate ions, resulting in a 0.450 M NO_{3}^{-} concentration in the solution. Understanding this concept is fundamental in accurately determining concentrations within chemical solutions.