Problem Solving
Decision Making
Additional Problem Solving

Problem Solving

Calculations

1. The solubility of PbCrO4 is 1.34 x 10-7 mol/L at 25ºC. Calculate the value of Ksp.

Solution:
PbCrO4(s) <=> Pb2+(aq) + CrO42-(aq)
Ksp = [Pb2+][CrO42-]
Ksp = (1.34 x 10-7) (1.34 x 10-7)
Ksp = 1.80 x 10-14

2. The Ksp for Agcl is 1.7 x 10-10 at 25ºC. What is the solubility of AgCl?

Solution: Let's represent the concentration of Ag+ as "x". Since there will be an equal concentration of Cl-, this can be represented as "x" also. then,
AgCl(s) <=> Ag+(aq) + Cl-(aq)
Ksp = [Ag+][Cl-]
Ksp = [x] [x]
Ksp = x2
1.7 x 10-10 = x2
x = square root of 1.7 x 10-10
x = 1.3 x 10-5 mol/L

Decision Making

1. Taking both entropy and enthalpy into consideration, explain why a gas is less soluble in water, whereas certain solids are more soluble in warm water.
[When a gas dissolves in water it forms weak bonds to the water and occupies less space. It also has slightly more order than it would as a free gas. Thus dissolving of a gas is exothermic (bond forming) and decreases entropy. Solids also generally dissolve exothermically but become considerably disordered as they move freely in the water. Since processes are favored by increased entropy and lower energy, solids tend to dissolve in water. Gases dissolving are favored by energy but not by entropy, so lower solubility is expected.]

DG = DH - TDS
DG < 0 if DH < 0 and DS < 0
(Note that increasing T makes DG smaller)

2. Refer to the accompanying table of solubility product constants to answer these questions:

a. Although the ionic solids listed in the table are considered insoluble, which compound is the least soluble?
[CdS has the smallest Ksp and is therefore least soluble.]
Which is the most soluble?
[CaSO4 is largest, thus most soluble.]

b. Which three compounds are the most insoluble?
[PbS, CdS, ZnS have the lowest Ksp's]
Does this suggest a generalization?
[Sulfides in general have low solubility.]

NOTE: When a different number of ions per mole of slightly soluble salt form, the magnitude of the solubility product constant is not an immediately comparable value to determine relative solubility. For example, the K’s of CaCO3 and CaF2 are 4.95 x 10–9 and 1.61 x 10–10 , respectively, but their molar solubilities are 7.04 x 10–5 and 3.43 x 10–4, respectively.

Formula Ksp Formula Ksp
AgBr 7.7 x 10-13 CaSO4 6.1 x 10-5
AgCl 1.7 x 10-10 MgCO3 1 x 10-5
AgCN 2 x 10-12 MnS 1.4 x 10-15
AgI 8.3 x 10-17 PbCO3 1.6 x 10-13
BaCO3 4.9 x 10-9 PbCrO4 1.8 x 10-14
BaSO4 1.5 x 10-9 PbSO4 1.9 x 10-6
CdCO3 2.5 x 10-14 PbS 7 x 10-28
CdS 1 x 10-28 SrSO4 2.8 x 10-7
CaCO3 4.8 x 20 -9 ZnS 4.5 x 10-24

c. Certain toxic metal ions, including lead and mercury, are precipitated as a sulfide and then buried in an EPA approved landfill. Why is this an acceptable way to treat these toxic substances?
[Because these sulfides have such low solubility it is unlikely that they would dissolve and leach into the environment.]

Graph Interpretation

Refer to Figure 6 to answer the following questions:

  1. Which substance decreases in solubility with increasing temperature? [Ca(C2H3O2) * 2H20]
  2. Which substance has a solubility that is least affected by a change in temperature?
    [NaCl]

 

Additional Problem Solving

  1. Suppose you were given a bottle of a solution that contained either magnesium, mercury(II), or barium ions. If you only had solutions of sodium hydroxide, sodium sulfate, and sodium chromate in your laboratory, devise a scheme to determine which ion is present in the mystery solution. You may find the chart “What Dissolves and What Does Not” (see Pattern Recognition) useful.
    [Magnesium sulfate is soluble; barium hydroxide is soluble.]
  2. If you had a solution that contained a mixture of silver ions and strontium ions, devise four reactions that would allow you to precipitate one ion but leave the other in\par solution.
    [Combine with hydroxide, sulfate,\par sulfide, halide ions.]

(page 15, & 16)

TABLE OF CONTENTS TOPIC OVERVIEW CONCEPT/SKILLS DEVELOPMENT LINKS/ CONNECTIONS APPENDIX