Problem 6 - General Chemistry: Principles and Modern Applications

Question

Which of the following saturated aqueous solutions would have the highest \(\left[\mathrm{Mg}^{2+}\right]\): (a) \(\mathrm{MgCO}_{3} ;\) (b) \(\mathrm{MgF}_{2};\) (c) \(\mathrm{Mg}_{3}\left(\mathrm{PO}_{4}\right)_{2} ?\) Explain.

Step-by-Step Solution

Answer

The exact answer depends on the \(K_{sp}\) values for the three compounds, which may vary between different sources. The student must find these values from a reliable source to complete the exercise.

Step 1: Find the Ksp values

Search for the solubility product constants (\(K_{sp}\)) for the given compounds. \(K_{sp}\) values are typically listed in chemistry textbooks or online sources.

Step 2: Compare the Ksp values

Compare the \(K_{sp}\) values of the three compounds. The compound with the highest \(K_{sp}\) will have the highest concentration of \( \mathrm{Mg}^{2+}\) ions in a saturated solution.

Step 3: Identify the compound

The compound with the highest \(K_{sp}\) value is the one that will produce the highest [\(\mathrm{Mg}^{2+}]\) concentration in solution.

Key Concepts

Saturated Solutions

A saturated solution is a type of solution where no more solute can dissolve at a given temperature and pressure. Saturation means that the dissolved ions and undissolved solute are in a state of equilibrium. For example, if you continuously add sugar to a cup of tea and eventually see sugar settling at the bottom, you've reached saturation.
This concept is important because it defines the maximum concentration of ions in that solution. When we refer to a saturated solution of a compound like \(\text{MgCO}_3\), it indicates that the solution holds the maximum amount of dissolved magnesium and carbonate ions possible at that condition.
The notion of a 'saturated solution' is critical in assessing solubility because it marks the threshold beyond which no additional ions can dissolve unless the conditions change.

Concentration of Ions

The concentration of ions in a solution refers to the amount of ions in a given volume of solution. This is usually measured in moles per liter (M). In a saturated solution, this concentration reaches a point where additional solute no longer dissolves.
To determine the concentration of ions, one can use the solubility product constant (\(K_{sp}\)). Each ionic compound dissociates into its constituent ions in solution. The \(K_{sp}\) is the product of the concentrations of these ions, each raised to the power of their coefficients in the balanced chemical equation.
For example, if a compound \(AB\) dissociates as \(A^+ + B^-\), and its \(K_{sp}\) is given, you can set up the equation \([A^+] \times [B^-] = K_{sp}\) to solve for the concentration of either ion in a saturated solution.

Comparing Solubility

Comparing the solubility of different compounds indicates how much of each compound can dissolve in solution to form a saturated solution. The concept helps in determining which compound can produce the highest ion concentration under the same conditions.
The simplest way to compare solubility among compounds is by examining their \(K_{sp}\) values. A higher \(K_{sp}\) value generally means greater solubility, translating to a higher concentration of dissolved ions.

• If two compounds have different stoichiometries, direct comparison of \(K_{sp}\) may not be straightforward, and reaction equations need to be considered.
• Check the dissociation equations: For example, \(\text{MgCO}_3\) dissolves to form one \(\text{Mg}^{2+}\) and one \(\text{CO}_3^{2-}\), while \(\text{Mg}_3(\text{PO}_4)_2\) yields three \(\text{Mg}^{2+}\) and two \(\text{PO}_4^{3-}\).
• It's important to factor in the number of ions each compound produces to accurately compare their effective solubilities for determining concentrations.

By comparing them, one can predict which compound in a saturated solution will have the highest concentration of a specific ion, such as \(\text{Mg}^{2+}\), as asked in the original exercise.