Problem 28 - Chemistry Matter and Change

Question

Explain how to use the solubility product constant to calculate the solubility of a sparingly soluble ionic compound.

Step-by-Step Solution

Answer

To calculate the solubility of a sparingly soluble ionic compound using the solubility product constant (Ksp), follow these steps: 1. Write the balanced dissociation equation for the compound's dissolution in water. 2. Write the Ksp expression by multiplying the concentrations of the ions, each raised to the power of their stoichiometric coefficients. 3. Let the solubility be represented by 'x' and determine equilibrium concentrations of the ions. 4. Substitute the equilibrium concentrations into the Ksp expression. 5. Solve for 'x' by finding the value of Ksp (either provided or from a table) and performing the necessary operations to isolate 'x'. 6. 'x' represents the solubility of the ionic compound in mol/L.

Step 1: Understand the solubility equilibrium and Ksp

A sparingly soluble ionic compound can dissolve in water, but only to a small extent. When the compound begins to dissolve, it forms a saturated solution where the dissolved ions are in equilibrium with the solid compound. The solubility product constant, Ksp, is the equilibrium constant for this solubility equilibrium. It represents the product of the concentrations of the ions in the saturated solution raised to the power of their stoichiometric coefficients.

Step 2: Write the balanced dissociation equation

Write the balanced equation for the dissociation of the ionic compound in water. For example, let's consider the dissolution of a generic compound, AB, where A and B represent positive and negative ions, respectively: \[ AB_{(s)} \rightleftharpoons A^{+}_{(aq)} + B^{-}_{(aq)} \]

Step 3: Write the Ksp expression

Write the expression for the solubility product constant, Ksp. It is obtained by multiplying the concentrations of the ions in the saturated solution, each raised to the power of their stoichiometric coefficients. For our example, the Ksp expression would be as follows: \[ K_{sp} = [A^{+}][B^{-}] \]

Step 4: And use 'x' to represent the solubility

We can represent the solubility of the ionic compound as 'x.' To determine the equilibrium concentrations of the ions in the saturated solution, we let the molar solubility represented by x. In our example, as each molecule of AB produces one A+ ion and one B- ion: \[ [A^{+}] = x \] \[ [B^{-}] = x \]

Step 5: Plug in the concentrations into the Ksp expression

Substitute the equilibrium concentrations represented by 'x' into the Ksp expression derived in Step 3: \[ K_{sp} = x^2 \]

Step 6: Solving for solubility 'x'

To determine the solubility of the compound, first, find the Ksp value (either provided or obtained from a table). Then, solve for 'x' in Ksp expression. Taking a square root of Ksp gives us the solubility. \[ x = \sqrt{K_{sp}} \] This value of 'x' is the solubility of the ionic compound in mol/L.

Key Concepts

Sparingly Soluble Ionic Compounds

Sparingly soluble ionic compounds are those that dissolve in water, but only to a limited extent. They form saturated solutions where the dissolved ions are in dynamic equilibrium with the undissolved solid. In such cases, you'll find that only a small amount of the compound is dispersed as ions in solution. These compounds are important because their solubility is not significant, yet they follow the rules of chemical equilibrium.
Understanding the behavior of sparingly soluble compounds is essential in fields like chemistry and environmental science.
When calculating their solubility, we use the concept of equilibria which describes the maximum amount of solute that can dissolve in a solvent without any precipitate forming. This is where the solubility product constant, or Ksp, becomes crucial.

Equilibrium Concentrations

In a saturated solution containing a sparingly soluble ionic compound, equilibrium concentrations refer to the balance between the dissolved ions and the undissolved solid. When the compound dissolves, it releases its ions into the solution until no more can dissolve.

• This is the point at which the ions achieve equilibrium concentrations.
• The concentrations of these ions directly relate to the solubility of the compound.

By knowing the equilibrium concentrations, particularly when expressed in terms of solubility 'x', you can determine how much of the compound has dissolved.
Conceptually, this represents the maximum concentration of ions that can coexist with the undissolved solid in a stable, steady state.

Solubility Calculation

Solubility calculation involves determining how much of the sparingly soluble compound can ultimately dissolve in a solution. By expressing the solubility in terms of 'x', you can represent the molar solubility of the compound.
To compute solubility, follow these steps:

• Write the dissociation equation for the compound.
• Express the concentrations of ions formed using 'x'.
• Plug these into the solubility product constant equation, Ksp.

The value obtained will highlight how much of the compound dissolves without causing the solution to become saturated or the ions to precipitate.

Dissociation Equation

A dissociation equation describes how a sparingly soluble ionic compound separates into its constituent ions in solution. Writing this equation is crucial for understanding how to derive the Ksp expression.

• Take a generic compound AB which dissociates into one A⁺ and one B^- ion.
• The dissociation is represented as: \[ AB_{(s)} \rightleftharpoons A^{+}_{(aq)} + B^{-}_{(aq)} \]

This equation shows the stoichiometry of the ions produced. Knowing this allows one to set up the expression for Ksp, where the concentrations of A⁺ and B^- are crucial. The Ksp equation, such as \[ K_{sp} = [A^{+}][B^{-}] \], relies on these equations to evaluate equilibrium conditions.