Unit 7 · Topic 7.11 Beta

Introduction to Solubility Equilibria

A slightly soluble salt reaches a dynamic equilibrium with its ions in a saturated solution.

Practice 5: Mathematical Routines

Question set for this topic

Part 1 · Hook

Why this matters

Doctors give patients a thick drink of barium sulfate before an X-ray of the gut. Barium ions are toxic, so why is this safe? Barium sulfate dissolves so little that a liter of water holds only a few thousandths of a gram of it. An equilibrium constant, Ksp, tells you exactly how little.

Part 2 · Before you start

What this builds on

Part 3 · Prerequisite check

Quick check before you start

1. What does "soluble" mean for an ionic compound in water?

  1. An appreciable amount dissolves to form ions
  2. It does not dissolve at all
  3. It reacts with water to form a gas
  4. It melts in water
Show the answer

Soluble salts dissolve and dissociate into ions.

  • Correct: An appreciable amount dissolves to form ions:
  • It does not dissolve at all:
  • It reacts with water to form a gas:
  • It melts in water:

2. When CaCl2 dissolves, how many Cl− ions form per formula unit?

  1. 2
  2. 1
  3. 3
  4. 0
Show the answer

CaCl₂ → Ca²⁺ + 2 Cl⁻.

  • Correct: 2:
  • 1:
  • 3:
  • 0:

3. Which species are left out of an equilibrium constant expression?

  1. Pure solids and pure liquids
  2. Gases
  3. Dissolved ions
  4. Products
Show the answer

Their concentrations are fixed, so they drop out.

  • Correct: Pure solids and pure liquids:
  • Gases:
  • Dissolved ions:
  • Products:

Part 4 · See it

See it first

Three panels. A 1 to 1 salt, AgCl, dissolves to Ag+ and Cl−, each at concentration s, so Ksp = s squared and s is the square root of Ksp, 1.3 times 10 to the minus 5 M. A 1 to 2 salt, CaF2, dissolves to Ca2+ at s and F− at 2s, so Ksp = s times (2s) squared = 4s cubed and s is the cube root of Ksp over 4, 2.1 times 10 to the minus 4 M. A warning panel: square the whole 2s, compare Ksp values only for salts with the same ion ratio, and never include the solid. CaF2 has the smaller Ksp but the larger molar solubility.
Write each ion concentration as s times its coefficient, then solve Ksp for s. Square the whole 2s. LevlPrep original diagram.

Part 5 · Step by step

How it works, step by step

  1. A slightly soluble salt is placed in waterions leave the solid, and some return to it
  2. Ions return as fast as they leavethe saturated solution is at equilibrium, with Ksp = product of ion concentrations
  3. Each formula unit releases ions in the ratio of its formulaevery ion concentration is s times its coefficient
  4. The ion concentrations are put into Ksp with their exponentsyou can solve for s, or calculate Ksp from a measured s
  5. The ion product Q is greater than Kspsolid precipitates until Q = Ksp

Part 6 · Key ideas

Key ideas

  • Ksp is the product of the ion concentrations in a saturated solution, each raised to its coefficient; the solid is left out.
  • Molar solubility s: mol of salt dissolved per liter. 1 : 1 salt: Ksp = s². MX2 salt: Ksp = s(2s)² = 4s³.
  • Rank solubility by Ksp only for salts with the same ion ratio.
  • Q > Ksp: precipitate forms. Q < Ksp: more can dissolve.

Part 7 · Misconception

A common mistake

The wrong idea: For Mg(OH)₂, Ksp = s × 2s, because there are two hydroxide ions.

What actually happens: [OH⁻] = 2s, and it is raised to the power 2 in Ksp: Ksp = s(2s)² = 4s³. Forgetting to square [OH⁻] is the most common Ksp error on the exam.

Part 8 · Check yourself

Check yourself

Exam-style questions. Anything you miss goes into your review queue.

Data table

Solubility products of four salts

A student looks up Ksp values (approximate, at 25 °C) for four slightly soluble salts.

Ksp at 25 °C
SaltIons formed per formula unitKsp
AgCl1 Ag+, 1 Cl−1.8 × 10−10
AgBr1 Ag+, 1 Br−5.0 × 10−13
Ag2CrO42 Ag+, 1 CrO42−1.1 × 10−12
CaF21 Ca2+, 2 F−3.9 × 10−11

1. Calculate the molar solubility of AgCl in pure water at 25 °C.

Type a number and its unit.

Show the answer

AgCl(s) ⇌ Ag⁺ + Cl⁻; [Ag⁺] = [Cl⁻] = s. Ksp = s² = 1.8 × 10⁻¹⁰, so s = √(1.8 × 10⁻¹⁰) = 1.3 × 10−5 M.

  • Answer: 1.3 × 10-5 M

2. Calculate the molar solubility of Ag2CrO4 in pure water at 25 °C.

Type a number and its unit.

Show the answer

Ag₂CrO₄(s) ⇌ 2 Ag⁺ + CrO₄²⁻; [Ag⁺] = 2s, [CrO₄²⁻] = s. Ksp = (2s)²(s) = 4s³ = 1.1 × 10⁻¹², so s³ = 2.75 × 10⁻¹³ and s = 6.5 × 10−5 M.

  • Answer: 6.5 × 10-5 M

3. Ag2CrO4 has a smaller Ksp than AgCl. Which salt has the greater molar solubility in water?

  1. Ag2CrO4
  2. AgCl
  3. They are equally soluble, because both are silver salts.
  4. It is undecided without the masses of the salts.
Show the answer

Ranking by Ksp works only for salts with the same ion ratio. Otherwise, calculate the molar solubility of each.

  • Correct: Ag2CrO4: Right: 6.5 × 10−5 M versus 1.3 × 10−5 M. With different ion ratios, the Ksp expressions have different forms, so Ksp alone cannot be compared.
  • AgCl: AgCl has the larger Ksp, but the expressions differ (s² vs 4s³). Calculate s for each.
  • They are equally soluble, because both are silver salts.: Sharing a cation does not make solubilities equal.
  • It is undecided without the masses of the salts.: It can: solve each Ksp expression for s.

4. Which pair of salts can be ranked by solubility just by comparing their Ksp values?

  1. AgCl and AgBr
  2. AgCl and Ag2CrO4
  3. AgBr and CaF2
  4. Ag2CrO4 and AgBr
Show the answer

When two salts produce the same number and ratio of ions, their Ksp expressions have the same form, so Ksp ranks solubility directly.

  • Correct: AgCl and AgBr: Right: both are 1 : 1, so Ksp = s² for each and a larger Ksp means a larger s.
  • AgCl and Ag2CrO4: These have different ion ratios (1 : 1 and 2 : 1), so their expressions differ.
  • AgBr and CaF2: Different ion ratios: s² versus 4s³.
  • Ag2CrO4 and AgBr: Different ion ratios: 4s³ versus s².

5. The molar solubility of Mg(OH)2 in water at 25 °C is 1.1 × 10−4 M. Calculate Ksp.

Type a number.

Show the answer

[Mg²⁺] = 1.1 × 10⁻⁴ M; [OH⁻] = 2(1.1 × 10⁻⁴) = 2.2 × 10⁻⁴ M. Ksp = (1.1 × 10⁻⁴)(2.2 × 10⁻⁴)² = 5.3 × 10−12.

  • Answer: 5.3 × 10-12

6. Equal volumes of 2.0 × 10−4 M AgNO3 and 2.0 × 10−4 M NaCl are mixed. Ksp of AgCl is 1.8 × 10−10. Does AgCl precipitate?

  1. Yes: Q = 1.0 × 10−8 > Ksp.
  2. No: Q = 1.0 × 10−8 < Ksp.
  3. Yes: Q = 4.0 × 10−8 > Ksp.
  4. No: both solutions are too dilute to form a solid.
Show the answer

Compare the ion product Q with Ksp. After mixing, [Ag⁺] = [Cl⁻] = 1.0 × 10⁻⁴ M; Q = 1.0 × 10⁻⁸ > Ksp, so solid AgCl forms until Q = Ksp.

  • Correct: Yes: Q = 1.0 × 10−8 > Ksp.: Right: mixing equal volumes halves each concentration to 1.0 × 10⁻⁴ M, and Q = (1.0 × 10⁻⁴)² = 1.0 × 10⁻⁸ > 1.8 × 10⁻¹⁰.
  • No: Q = 1.0 × 10−8 < Ksp.: Compare powers of ten: 10⁻⁸ is larger than 10⁻¹⁰.
  • Yes: Q = 4.0 × 10−8 > Ksp.: The conclusion is right but Q is wrong: mixing equal volumes halves each concentration before you multiply.
  • No: both solutions are too dilute to form a solid.: Dilution matters only through Q; here Q is still far above Ksp.

7. Put the steps for finding molar solubility from Ksp in order.

  1. Write the dissolving equation, with the ions in the ratio of the formula.
  2. Let s be the molar solubility and write each ion concentration as s times its coefficient.
  3. Write Ksp with each ion concentration raised to its coefficient, e.g. s(2s)2 = 4s3.
  4. Solve for s and report it in mol/L.
Show the answer

Equation, ion concentrations in terms of s, Ksp expression with exponents, solve.

  • Correct order: 1. Write the dissolving equation, with the ions in the ratio of the formula. 2. Let s be the molar solubility and write each ion concentration as s times its coefficient. 3. Write Ksp with each ion concentration raised to its coefficient, e.g. s(2s)2 = 4s3. 4. Solve for s and report it in mol/L.

Part 9 · Summary

Summary

A slightly soluble salt reaches a dynamic equilibrium with its ions in a saturated solution. Ksp is the product of the ion concentrations, each raised to its coefficient, with the solid left out. Writing each ion as s times its coefficient links Ksp to the molar solubility s (s² for a 1 : 1 salt, 4s³ for a 1 : 2 or 2 : 1 salt). Compare Ksp values directly only for salts with the same ion ratio; Q above Ksp means a precipitate forms.

Part 10 · Up next

What comes next

Part 11 · Connections

Connections