Question

A lab technician mixes a solution of \(0.015 \mathrm{M} \mathrm{Mg}(\mathrm{OH})_{2}\). Is the resulting \(\mathrm{OH}^{-}\) concentration greater than, equal to, or less than 0.015 M? Explain your answer.

Short answer

The \(\mathrm{OH}^-\) concentration is greater than 0.015 M.

Step-by-step solution

Understand the Problem

We have a solution of magnesium hydroxide, \(\mathrm{Mg(OH)}_2\), with a concentration of \(0.015 \mathrm{M}\), and we need to find the concentration of \(\mathrm{OH}^-\) ions in the solution to determine if it is greater than, less than, or equal to \(0.015 \mathrm{M}\).

Write the Dissociation Equation

Write the dissociation equation for magnesium hydroxide: \[ \mathrm{Mg(OH)}_2 \rightarrow \mathrm{Mg}^{2+} + 2 \mathrm{OH}^- \] This indicates that each molecule of \(\mathrm{Mg(OH)}_2\) produces two \(\mathrm{OH}^-\) ions in solution.

Calculate the \(\mathrm{OH}^-\) Concentration

Since 1 mole of \(\mathrm{Mg(OH)}_2\) produces 2 moles of \(\mathrm{OH}^-\), the concentration of \(\mathrm{OH}^-\) ions is given by \(2 \times 0.015 \mathrm{M} = 0.030 \mathrm{M}\).

Compare the \(\mathrm{OH}^-\) Concentration

Compare \(0.030 \mathrm{M}\) to \(0.015 \mathrm{M}\). The concentration of \(\mathrm{OH}^-\) (\(0.030 \mathrm{M}\)) is greater than \(0.015 \mathrm{M}\).

Key concepts

OH- concentration

In chemistry, the concentration of hydroxide ions, \(\mathrm{OH}^{-}\), is an essential factor when studying bases like magnesium hydroxide, \(\mathrm{Mg(OH)}_2\). When dissolved, \(\mathrm{Mg(OH)}_2\) dissociates to release hydroxide ions into the solution. The concentration of \(\mathrm{OH}^{-}\) ions determines the solution's basicity.

Specifically, for \(\mathrm{Mg(OH)}_2\), the dissociation equation shows that each molecule contributes two \(\mathrm{OH}^{-}\) ions. This means that for every mole of magnesium hydroxide dissolved, you will find two moles of \(\mathrm{OH}^{-}\) in the solution. If the starting molarity of \(\mathrm{Mg(OH)}_2\) is \(0.015\ \text{ M}\), the resulting \(\mathrm{OH}^{-}\) concentration will be twice that amount, at \(2\times 0.015\ \text{ M} = 0.030\ \text{ M}\).

This multiplication occurs because the dissociation releases two hydroxide ions per formula unit of \(\mathrm{Mg(OH)}_2\). Understanding how compounds like \(\mathrm{Mg(OH)}_2\) break down in a solution is crucial for calculating pH and other properties. Knowing the \(\mathrm{OH}^{-}\) concentration helps determine whether a solution is more or less basic based on the activity of these ions.

molarity

Molarity is a fundamental concept in chemistry that describes the concentration of a solute in a solution. It is expressed as moles of solute per liter of solution, often abbreviated as M. When dealing with magnesium hydroxide, \(\mathrm{Mg(OH)}_2\), knowing its molarity helps predict how much it will dissociate in water.

To calculate the molarity, divide the mass of the substance by its molar mass, then divide by the volume of the solution in liters. For \(\mathrm{Mg(OH)}_2\) at \(0.015\ \text{ M}\), this means there are \(0.015\ \text{ moles}\) of \(\mathrm{Mg(OH)}_2\) in every liter of the solution. Once dissolved, this initial molarity influences the amount of hydroxide ions released.

Understanding molarity helps balance chemical equations and predict the extent of reactions. It tells us how concentrated a solution is, impacting how it interacts with other substances and its saturation level.

dissociation equation

The dissociation equation is essential in understanding how ionic compounds like magnesium hydroxide dissolve in water. For \(\mathrm{Mg(OH)}_2\), the dissociation equation is \[ \mathrm{Mg(OH)}_2 \rightarrow \mathrm{Mg}^{2+} + 2\,\mathrm{OH}^{-} \] This shows that when \(\mathrm{Mg(OH)}_2\) dissociates, it forms one magnesium ion \(\left(\mathrm{Mg}^{2+}\right)\) and two hydroxide ions \(\left(\mathrm{OH}^{-}\right)\).

Dissociation equations help predict the concentrations of each ion in a solution, which means knowing the dissociation behavior directly influences calculations related to concentration, pH, and chemical reactivity. Since \(\mathrm{Mg(OH)}_2\) releases two \(\mathrm{OH}^{-}\) ions, understanding this equation allows chemists to determine that even if \(\mathrm{Mg(OH)}_2\) itself is sparingly soluble, its capacity to release multiple hydroxide ions can still significantly increase \(\mathrm{OH}^{-}\) concentration.

When tackling problems involving bases like \(\mathrm{Mg(OH)}_2\), grasping the dissociation equation enables more accurate predictions about behavior in chemical reactions and how these substances alter environmental pH.