# Conversion of Solubility to Ksp

### Learning Objectives

• Define molar solubility.
• Perform calculations involving molar solubility and Ksp.

### How is baking soda made?

Baking soda (sodium bicarbonate) is prepared by bubbling carbon dioxide gas through a solution of ammonia and sodium chloride. Ammonium carbonate is first formed which then reacts with the NaCl to form sodium bicarbonate and ammonium chloride. The sodium bicarbonate is less soluble than the other materials, so it will precipitate out of solution.

## Conversion of Solubility to Ksp

Solubility is normally expressed in g/L of saturated solution. However, solubility can also be expressed as the moles per liter. Molar solubility is the number of moles of solute in one liter of saturated solution. In other words, the molar solubility of a given compound represents the highest molarity solution that is possible for that compound. The molar mass of a compound is the conversion factor between solubility and molar solubility. Given that the solubility of Zn(OH) 2 is 4.2 × 10 -4  g/L, the molar solubility can be calculated as shown below:

$frac{4.2 times 10^{-4} cancel{text{g}}}{text{L}} times frac{1 text{mol}}{99.41 cancel{text{g}}}=4.2 times 10^{-6} text{mol/L} (text{M})$

Solubility data can be used to calculate the Ksp for a given compound. The following steps need to be taken.

1. Convert from solubility to molar solubility.
2. Use the dissociation equation to determine the concentration of each of the ions in mol/L.
3. Apply the Ksp equation.

#### Sample Problem: Calculating Ksp from Solubility

The solubility of lead(II) fluoride is found experimentally to be 0.533 g/L. Calculate the Ksp for lead(II) fluoride.

Step 1: List the known quantities and plan the problem .

Known

• solubility of PbF 2 = 0.533 g/L
• molar mass = 245.20 g/mol

Unknown

• Ksp of PbF2 = ?

The dissociation equation for PbF 2 and the corresponding Ksp expression

$text{PbF}_2(s) rightleftarrows text{Pb}^{2+}(aq)+2text{F}^-(aq) && K_{sp}=[text{Pb}^{2+}][text{F}^-]^2$

The steps above will be followed to calculate the Ksp for PbF 2 .

Step 2: Solve .

$text{molar solubility} qquad frac{0.533 cancel{text{g}}}{text{L}} times frac{1 text{mol}}{245.20 cancel{text{g}}}=2.17 times 10^{-3} text{M}$

The dissociation equation shows that for every mole of PbF 2 that dissociates, 1 mol of Pb 2+ and 2 mol of F are produced. Therefore, at equilibrium the concentrations of the ions are:

$[text{Pb}^{2+}]=2.17 times 10^{-3} text{M} quad text{and} quad [text{F}^-]=2 times 2.17 times 10^{-3}=4.35 times 10^{-3} text{M}$

Substitute into the expression and solve for the $K_{sp}$ .

$K_{sp}=(2.17 times 10^{-3})(4.35 times 10^{-3})^2=4.11 times 10^{-8}$

The solubility product constant is significantly less than 1 for a nearly insoluble compound such as PbF 2 .

### Summary

• Molar solubility calculations are described.
• Calculations of Ksp using molar solubility are described.

### Practice

Read the material at ChemTeam.info and do the problems at the end.

### Review

1. What are the solution requirements for determining molar solubility?
2. Why do we need to convert mass to molarity to determine Ksp?
3. What Ksp values would you expect for very insoluble compounds?

## Glossary

• molar solubility: The number of moles of solute in one liter of saturated solution.