Lesson 6: Solubility Equilibria and K_sp

_{Corresponding Textbook Chapter - 7.6}

Lesson Instructions

- Review the learning goals for Lesson 6: Solubility Equilibria and Ksp.
- Review the minds on, action, and consolidation sections of the lesson, completing any tasks as outlined.
- Complete the fill-in-the-blanks handouts that have been provided to you.
- Practice and apply what you've learned by completing the practice tasks outlined at the end of the lesson.

Learning Goals

By the end of this lesson, I will be able to ...

- write a K_sp equation
- calculate the value of K_sp
- calculate the molar solubility of an ionic compound
- calculate the molar solubility with a common ion present

Minds-On

Watch this video from Professor Dave, introducing the solubility product constant, K_sp.

"We've learned that some ionic solids are totally water insoluble, but in fact this is a slight oversimplification. Even such solids will dissolve to some minuscule degree, and we can measure this, and do calculations with it. Let's learn about solubility product constants!"

Action

Solubility of Ionic Compounds

- when a solid ionic compound dissolves in water, ions are removed from the crystal lattice structure as they become surrounded by water molecules
- the reverse reaction also takes place, eventually reaching equilibrium in a saturated solution

Solubility Product, K_sp

- the mathematical product of a compound’s dissolved ion concentrations raised to the power of their stoichiometric coefficients

Example 1. Write the chemical equation for the dissolving of copper (II) phosphate.

Example 2. Write the Ksp equation.

Calculating the Ksp and Molar Solubility

- the concentration of the solution at its saturation point
- identify the x-value

Example 3. The molar solubility of CaF₂ is 2.1 x 10^-4 mol/L at 25°C. Calculate K_sp for calcium fluoride.

Step 1: Write a balanced chemical equation for the dissolving of calcium fluoride (see Example 1 above).

Step 2: Identify the the x-value for the question provided. The x-value is the molar solubility value in mol/L. The x-value for calcium fluoride in Example 3 is 2.1 x 10^-4 mol/L.

Step 3: Use mole ratios to identify the x-values for each of the products in the dissolution.

Step 4: Write the K_sp equation for the dissolution of calcium fluoride. Using the newly calculated x-values, calculate the value of K_spfor the dissolution of calcium fluoride.

Step 5: Write a therefore statement for the K_sp of calcium fluoride.

Example 4. Calculate the molar solubility of Cu(OH)_{2 (s)} in water. (K_sp is 1.6 x 10^-19).

Step 1: Write a balanced chemical equation for the dissolving of copper (II) hydroxide.

Step 2: Determine the x-values using the coefficients from the balanced chemical equation.

Step 3: Write the K_spequation for the dissolution of copper (II) hydroxide.

Step 4: Using the K_spvalue given in the original question (see Example 4 above), K_sp1.6 x 10^-19, calculate the molar solubility value (x-value) for calcium (II) hydroxide.

Step 5: Write a therefore statement for the molar solubility of copper (II) hydroxide.

The Common Ion Effect

- in a saturated solution, the addition of either ion, from another compound, will shift the equilibrium

Example 5. KCl is added to a saturated solution of NaCl.

the [Cl^-] is increased
to consume excess Cl^-, equilibrium shifts to the left
more precipitate forms (NaCl becomes less soluble)
the presence of a common ion decreases the solubility of an ionic compound

Example 6. K_sp for PbI₂ is 9.8 x 10^-9. What is the molar solubility of PbI₂ in (a) pure water and (b) 0.10 M NaI?

Where did the +2x go when completing the solutions in blue? Don't forget that you can use the 100 rule to avoid using the quadratic formula.

(a) pure water

Step 1: Write a balanced chemical equation.
Step 2: Determine x-values using the coefficients of the balanced chemical equation.
Step 3: Write a K_spequation for the dissolution of lead iodide.
Step 4: Solve for x, aka the molar solubility of lead iodide.
Step 5: Write a therefore statement for the molar solubility of lead iodide.

(b) 0.10 M NaI

Step 1: Write a balanced chemical equation.
Step 2: Determine x-values using the coefficients of the balanced chemical equation. When calculating the x-values, make sure to account for the 0.10 M of NaI as outlined in part b) of the question above.
Step 3: Write a K_spequation for the dissolution of lead iodide.
Step 4: Solve for x, aka the molar solubility of lead iodide.
Step 5: Write a therefore statement for the molar solubility of lead iodide.

Predicting if a Precipitate Will Form

The Reaction Quotient can be used to determine whether a precipitate will form or not.

- a precipitate will form when the concentration of the ions is greater than its molar solubility

Q_sp > K_sp

[ions] is too large, the reaction will proceed to the left, resulting a precipitation

Q_sp < K_sp

[ions] is smaller than the molar solubility, no precipitation occurs, the solution is unsaturated

Q_sp = K_sp

the solution is saturated, no precipitation

Example 7. If 100. mL of 1.0 x 10^-3 mol/L solution of AgNO₃ is mixed with 100. mL of 5.0 x 10^-3 mol/L solution of KBr, will a precipitate form? The K_sp of AgBr = 5.4x10^-13(obtained from p.725 of your textbook).

Step 1: Write a balanced chemical equation for the reaction between silver nitrate and potassium bromide.

Step 2: Locate the solubility table provided to you at the beginning of the course as a reference sheet. Using the solubility table, we can see the potential precipitate will be AgBr_(s).

Step 3: Write an equation for the dissolution of the precipitate, silver bromide, AgBr_(s).

Step 4: We want to determine if the precipitate will form (i.e. will the reaction proceed to the left, or toward AgBr_(s).?). In order to determine this, we must compare Q and K, or Q_spand K_sp.

Step 5: Write the Q_spequation for the dissolution of AgBr_(s).

Step 5: In order to calculate Q_sp, determine the concentration values for [Ag⁺] and [Br ^-] by using the formula n = C x V and data from the original question (see Example 7 above).

Step 6: Now that you have determine the concentration values for [Ag⁺] and [Br ^-] you can solve for Q_sp.

Step 7: Compare Q_sp to K_sp:

Step 7: Consider what happens when Q_sp > K_{sp .} As mentioned above, when Q_sp > K_sp the concentration of ions is too large, and the reaction will proceed to the left, resulting a precipitate being formed.

Step 8: Write a therefore statement.

This lesson is now complete. Consolidate your learning by completing the self-check below and the assigned practice questions.

Self-Check

How prepared am I to start my homework? Can I ...

- write a K_sp equation?
- calculate the value of K_sp?
- calculate the molar solubility of a ionic compound?
- calculate molar solubility with a common ion present?

Practice

Using your textbook, complete the following questions:

- p. 464 # 1-4
- p. 468 # 1-4
- p. 470 # 2, 3

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Lesson 6: Solubility Equilibria and Ksp

Corresponding Textbook Chapter - 7.6