Question

A solution is \(0.126 \mathrm{M} \mathrm{KCl}\) and \(0.148 \mathrm{M} \mathrm{MgCl}_{2} .\) What are \(\left[\mathrm{K}^{+}\right],\left[\mathrm{Mg}^{2+}\right],\) and \(\left[\mathrm{Cl}^{-}\right]\) in this solution?

Short answer

The concentrations of the ions in the solution are: [K+] = 0.126 M, [Mg2+] = 0.148 M, [Cl-] = 0.422 M.

Step-by-step solution

Identify the ions and their ratios

When KCl is dissolved in water, it dissociates into K+ and Cl- ions in a 1:1 ratio. Therefore, the concentration of each ion will be equal to the molarity of KCl. Similarly, when MgCl2 is dissolved, it dissociates into Mg2+ ions and Cl- ions but in a 1:2 ratio because there are 2 chloride ions for each magnesium ion. This means that the concentration of Cl- ions from the MgCl2 will be twice the molarity of MgCl2.

Calculate the concentration of K+ and Mg2+ ions

Given that the solution is 0.126 M KCl and 0.148 M MgCl2, the concentration of K+ ions will be 0.126 M while the concentration of Mg2+ ions will be 0.148 M.

Calculate the concentration of Cl- ions

The concentration of Cl- ions will be the sum of the concentration of Cl- from KCl and twice the concentration from MgCl2 since it dissociates into two Cl- ions. Therefore, the concentration of Cl- ions will be 0.126 M + 2*0.148 M = 0.422 M.

Key concepts

Understanding Molarity

Molarity is a key concept in chemistry that helps us understand how concentrated a solution is. It is defined as the number of moles of a solute dissolved in one liter of solution and is expressed in moles per liter (M). For instance, in this exercise, the molarity of the potassium chloride (KCl) solution is 0.126 M. This means there are 0.126 moles of KCl dissolved in every liter of solution. Similarly, the magnesium chloride (MgCl2) solution has a molarity of 0.148 M. This is crucial because molarity directly influences the concentration of ions present, which we aim to calculate here.
Molarity allows chemists to predict the behavior of solutions in reactions. It's directly related to properties like conductivity or the rate of a reaction. Therefore, understanding molarity gives us insight into how solutions interact at the molecular level.

The Process of Dissociation

Dissociation refers to the process where ionic compounds separate into their component ions when dissolved in water. Ionic compounds like KCl and MgCl2 dissociate upon mixing with water due to the polar nature of water molecules. In the case of KCl, it dissociates into potassium ions (K+) and chloride ions (Cl-). This happens in a 1:1 ratio, which means that for each KCl molecule dissolved, one K+ and one Cl- ion are formed.
MgCl2, however, dissociates differently because its structure contains two chloride ions per magnesium ion (Mg2+). Thus, when MgCl2 dissolves, it results in one Mg2+ ion and two Cl- ions. This 1:2 ratio is significant as it doubles the concentration of chloride ions compared to the concentration of magnesium ions from the same source. Dissociation is a fundamental concept for understanding reactions in aqueous solutions as it provides the ions necessary for further chemical interactions.

Calculating Ion Concentration

Ion concentration is determined by how fully the solute dissociates in the solution, and it's often related back to the molarity of the initial solution. The concentration of ions like K+, Mg2+, and Cl- relies on both the molarity of their respective compounds and the stoichiometry with which they dissociate.
Given that the molarity of the KCl solution is 0.126 M, the concentration of K+ ions is equally 0.126 M, as they dissociate in a 1:1 ratio.

• For MgCl2, the concentration of Mg2+ ions remains 0.148 M because for every mole of MgCl2 that dissociates, one mole of Mg2+ ions is produced.
• However, for chloride ions, both KCl and MgCl2 contribute. From KCl, we have 0.126 M Cl- ions, and from MgCl2, we have twice the molarity, giving us 2 * 0.148 M = 0.296 M Cl- ions. When combined, this results in a total chloride ion concentration of 0.422 M.

This approach to calculating ion concentration is vital in determining the reactivity and properties of the solution.