Question

What is the molar concentration of ions in a \(1.5 M \mathrm{KNO}_{3}\) solution? What is the molal concentration of ions in a \(1.5 \mathrm{~m} \mathrm{KNO}_{3}\) solution?

Short answer

The molar concentration of ions in a 1.5M \(\mathrm{KNO}_{3}\) solution is 3.0M and the molal concentration of ions in a 1.5m \(\mathrm{KNO}_{3}\) solution is 1.5m.

Step-by-step solution

Determine the molar concentration of ions

The molar concentration of ions in the solution is determined by multiplying the given molar concentration by the number of ions formed per formula unit of solute. For every mole of \(\mathrm{KNO}_{3}\) dissolved, one mole of \(\mathrm{K}^{+}\) ions and one mole of \(\mathrm{NO}_{3}^{-}\) ions are formed. Therefore, the total molar concentration of ions is \(1.5 M \times 2 = 3.0 M\).

Determine the molal concentration of ions

The molal concentration of ions is equal to the molal concentration of the solute. This means that the molality \(\mathrm{KNO}_{3}\) would be equipoise to the molality of ions in the solution. Therefore, the molal concentration of ions is \(1.5m\).

Key concepts

Molal Concentration

Molal concentration, also referred to as molality, is a measure of the concentration of a solute in a solution. Unlike molarity, which is dependent on the volume of the solution, molality is based on the mass of the solvent. It's calculated as the number of moles of solute per kilogram of solvent. This concentration measure is particularly valuable when dealing with temperature changes because, unlike volume, mass does not change with temperature.

When you encounter an exercise asking for the molal concentration of ions, like in the \(1.5 \mathrm{~m} \mathrm{KNO}_{3}\) solution example, you must understand that the molality provided refers to the entire compound, not just the individual ions. Since \( \mathrm{KNO}_{3}\) dissociates into two types of ions, \( \mathrm{K}^{+}\) and \( \mathrm{NO}_{3}^{-}\), it's easy to wrongly assume you need to adjust the value for individual ions. However, the concept of molality holds true regardless of dissociation. Thus, a \(1.5 \mathrm{~m}\) molal concentration of \( \mathrm{KNO}_{3}\) means that the total molal concentration of ions is also \(1.5m\), as the molecular association doesn't influence the molality.

Ions in Solution

Understanding the behavior of ions in solution is critical for comprehending many chemical processes. When ionic compounds like \( \mathrm{KNO}_{3}\) (potassium nitrate) dissolve in water, they dissociate into their constituent ions. Each unit of \( \mathrm{KNO}_{3}\) yields one \( \mathrm{K}^{+}\) ion and one \( \mathrm{NO}_{3}^{-}\) ion.

When calculating the concentration of ions in a solution, it's essential to consider the total number of ions produced. In our example, the molar concentration of \( \mathrm{KNO}_{3}\) is \(1.5 M\), but since it dissociates into two ions, the actual molar concentration of ions in the solution is doubly large, amounting to \(3.0 M\). This idea is pivotal when discussing properties such as the conductivity and freezing point depression of the solution, which depend on the total concentration of ions.

KNO3

Potassium nitrate, with the chemical formula \( \mathrm{KNO}_{3}\), is a salt composed of potassium and nitrate ions. It's commonly used in fertilizers, preservatives, and even fireworks due to its oxidizing properties. When it dissolves in water, it fully dissociates to form \( \mathrm{K}^{+}\) and \( \mathrm{NO}_{3}^{-}\) ions.

Understanding the dissolving process of \( \mathrm{KNO}_{3}\) not only helps in calculating ion concentrations but also assists in predicting the behavior of the solution. For instance, since \( \mathrm{KNO}_{3}\) dissociates into two ions, it can significantly affect the boiling and freezing points of water due to the colligative properties of solutions. Such effects are directly proportional to the number of dissolved particles, in this case, ions, in the solution. By knowing that one mole of \( \mathrm{KNO}_{3}\) produces two moles of ions, you can use this information to calculate changes in physical properties such as osmotic pressure, vapor pressure lowering, and melting or boiling point changes.