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Chapter 15 - Applications of

Aqueous Equilibria

GCC CHM152

Neutralization: Strong Acid-Strong Base

Molecular: HCl(aq) + NaOH(aq) NaCl(aq) + H2O(l)

SA-SB rxn goes to completion (one-way )

• Write ionic and net ionic rxns

H+(aq) + Cl-(aq) + Na+(aq) + OH-(aq) H2O(l) + Na+(aq) + Cl-(aq)

• Net: H+(aq) + OH-(aq) H2O(l)

After neutralization, what’s in solution?

Do either of the salt ions react with water?

What is pH of the salt solution?

Neutralization: Weak Acid-Strong Base

HF (aq) + KOH (aq) KF (aq) + H2O (l)

Rxn goes to completion due to SB

Write ionic and net rxns:

HF(aq) + K+(aq) + OH-(aq) K+(aq) + F-(aq) + H2O(l)

Net: HF(aq) + OH-(aq) H2O(l) + F-(aq)

After neutralization, what’s in solution?

Do either of the salt ions react with water?

What will the pH of the solution be, roughly?

Neutralization: Strong Acid- Weak Base

HCl (aq) + NH3 (aq) NH4+

(aq) + Cl- (aq)

Rxn goes to completion because of strong acid

Write ionic and net rxns:

H+(aq) + Br-(aq) + NH3(aq) NH4+(aq) + Br-(aq)

Net Ionic: H+(aq) + NH3(aq) NH4+(aq)

After neutralization, what’s in solution?

Do either of the salt ions react with water?

What will the pH of the solution be, roughly?

Neutralization: Weak Acid-Weak Base

CH3COOH(aq) + NH3(aq) NH4CH3COO(aq)

Reaction does go to completion since no reactant is completely ionized.

Ionic: CH3COOH(aq) + NH3(aq) NH4+(aq) + CH3COO-(aq)

Net: same

The salt remaining after neutralization contains an acidic and a basic ion, so pH depends on their relative Ka and Kb values.

Neutralization Reactions

• Predict whether the pH after neutralization

will be greater than, less than, or equal to

7 for the following combinations:

• HNO2 and KOH

• HCl and LiOH

• HBr and NH3

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Common Ion effect

The shift in equilibrium caused by the

addition of a substance having an ion in

common with the equilibrium mixture.

Adding a common ion suppresses the

ionization of a weak acid or a weak base.

The source of the common ion is typically provided by adding a strong acid, a strong base or a soluble salt to the equilibrium reaction mixture.

Common Ion Concept Problem

Given this reaction:

CH3CO2H + H2O H3O+ + CH3CO2

-

What happens to the pH of the acetic acid

solution if we add NaCH3CO2?

[CH3CO2-]

Eq shifts

[H3O+] , thus pH

Common Ion Effect

CH3CO2H + H2O CH3CO2- + H3O

+

0.100 M CH3CO2H

• WA soln: pH = 2.879

Add common ion CH3CO2- , pH

0.100 M CH3CO2H, add 0.050 M NaCH3CO2

• Mix of WA and conj base: pH = 4.456

Common Ion Problem

• What is the pH of 1.00 M HF solution?

Ka = 7.0 x 10- 4

• What is the pH of 1.00 M HF solution after adding 0.500 M NaF? Ka = 7.0 x 10-4

16.3 Buffer Solution

Best buffer systems consist of either

a) a weak acid and its conjugate base

e.g. HC2H3O2 and NaC2H3O2

b) a weak base and its conjugate acid

e.g. NH3 and NH4Cl

A solution that resists changes in pH when a

small amount of acid or base is added.

•Buffers are used to control pHe.g. biological buffers maintain the pH of all body fluids

Which are buffer solutions?

• Identify the solutions below that would make

good buffer solutions (what criteria need to

be met?):

HF and NaF

NH3 and NH4Cl

KOH and KF

CH3COOH and LiCH3COO

NaNO3 and HNO3

NaOH and NaCl

HCl and NaCH3COO

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Buffer Capacity

• Buffers only work within a pH range set by

the value of Ka:

pH = pKa ± 1

• Outside this range, we see little buffering

effect.

• If you know the desired pH of a buffer

solution, you can choose an acid with a

pKa near the pH.

Buffer Range

• Select an appropriate acid-base pair to get

within the range of the desired pH.

• Look at table of Ka values (some are

shown on the next screen), calculate pKa,

and select an appropriate combination.

• How would you make a buffer solution with

pH = 4.10? What could you use to make

this?

Table of Ka values

• Acid Ka

3.5 x 10 –4

4.5 x 10 –4

3.0 x 10 –4

1.7 x 10 –4

8.0 x 10 –5

6.5 x 10 –5

1.8 x 10 –5

4.9 x 10 –10

1.3 x 10 –10

HF

HNO2

C9H8O4 (aspirin)

HCO2H (formic)

C6H8O6 (ascorbic)

C6H5CO2H (benzoic)

CH3CO2H (acetic)

HCN

C6H5OH (phenol)

Buffer Solutions

• HF(aq) + H2O(l) H3O+(aq) + F-(aq)

• Add HCl, which component of the buffer soln will HCl reaction with (acid or base)?

H+ will react with F- (conj. base)

• Add NaOH, which component of the buffer soln will NaOH react with (acid or base)?

OH- will react with HF (weak acid)

• There will be a pH change in each case, but not as

much as if the HCl (or NaOH) were added to water.

Buffer Solutions

• Figure 15.3

Buffers shockwave animation

Henderson-Hasselbalch Equation

• When solving for [H3O+] at equilibrium and

assuming x << [HA] & [A-] for good buffer action,

the equilibrium expression Ka = [H3O+][A-] / [HA]

can be rearranged to give a simplified calculation:

• pH = pKa + log ([A-] / [HA])

Can use moles or M – depending on given info

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Buffer Solutions + HCl

• What is the pH of 500.0 mL of 0.10 M formic acid combined with 500.0 mL of 0.20 M sodium formate? Ka = 1.8 x 10-4

• pH = pKa + log ([A-]/[HA]) = 4.05

• Now add 10.0 mL of 0.50 M HCl

calculate moles of substances, then calculate changes

Use a CHANGE Table (initial, change, final)

Buffer Solutions + HCl

• To find the new pH, first assume that all the added strong acid reacts with A- to form HA.

H3O+ + A-

H2O + HA How many moles of HA, A-, and H3O

+ are in solution?

• Initial mol HA = (0.10 M) (0.5000 L) = 0.050 mol

• Initial mol A- = (0.20 M) (0.5000 L) = 0.10 mol

• mol HCl = (0.0100 L) (0.50 M) = 0.0050 mol

• Final mol A- = 0.10 mol – 0.0050 mol = 0.095 mol

• Final mol HA = 0.050 mol + 0.0050 mol = 0.055 mol

• Can use final moles in H-H equation. Why?• pH = pKa + log ([A-]/[HA]) = 3.98

Buffer +NaOH

• What will happen when we add a strong base to a buffer system?

Added base reacts with HA to form A-:

HA and A-

HA + OH- H2O + A-

• Add 10.0 mL of 0.500 M NaOH to the formic acid/sodium formate buffer. What is the new pH?

Buffer Solutions + NaOH

• First assume that all OH- reacts with HF:

• HF + OH- H2O + F-

• How many moles of base were added? • mol OH- = (0.500 M) (0.0100 L) = 0.00500 mol OH-

• final mol HA = 0.050 mol - 0.00500 mol = 0.045 mol

• final mol A- = 0.10 mol + 0.00500 mol = 0.105 mol

• pH = pKa + log ([A-]/[HA]) = 4.11 (started at 4.05)

• In water, pH would change from 7 to 13.

Group Quiz #13

• 1) Calculate the pH of a 1.25 L buffer

solution made up of 0.50 M acetic acid

and 0.50 M sodium acetate.

• Ka = 1.8 x 10-5

• 2) What is the pH of the solution when

25.00 mL of 0.40 M NaOH is added to the

buffer?

pH Titration Curves

• Strong Acid-Strong Base Titrations:

• The equivalence point is the point at which equimolar amounts of acid and base have reacted (review 1st

semester notes on calcs).

• Graph generated with pH probe

• Figure 15.6

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pH Titration Curves

• 4 key points on a titration curve

At the beginning (before titrant is added)

Before the equivalence point

At the equivalence point

After the equivalence point

• Consider titrating 20.00 mL of 0.200 M HCl

with 0.100 M NaOH. Find equiv. pt. first!

M = mol

L =

1000 mmol

1000 mL =

mmol

mL

Strong Acid-Strong Base

• Draw 4 beakers.

• 1) Draw 2 moles HCl.

• 2) Draw what happens when 1 mole

NaOH is added.

• 3) Draw what happens when 2 moles

NaOH are added.

• 4) Draw what happens when 3 moles

NaOH are added.

HCl + NaOH Titration

• 1) 0 mL NaOH, pH is calculated from strong acid.

[H3O+] = 0.200 M

pH = -log (0.200) = 0.70

• 2) 5.00 mL NaOH, acid is still in excess; but by how

much?

mmol acid – mmol base

(0.200 M)(20.00 mL) – (0.100 M)(5.00 mL)

[H3O+] = mmol / total solution volume

[H3O+] = 3.50 mmol / 25.00 mL = 0.140 M

pH = -log (0.140) = 0.85

HCl + NaOH Titration

• 3) 40.00 mL NaOH added; at the equivalence point, neutral salt and water in solution. mmol acid = mmol base

pH = 7 (always 7 for strong acid-strong base!)

• 4) 50.00 mL NaOH added, base in excess. By how much? mmol base – mmol acid

(0.100 M)(50.00 mL) – (0.200 M)(20.00 mL)

1.00 mmol base excess / 45.00 mL = 0.01429 M NaOH

pOH = -log (0.01429) = 1.85, pH = 12.15

• Problems 15.13, 15.14

Weak Acid-Strong Base

• Ascorbic acid in flask, KOH is titrant in buret

• Find pH at 4 pts.

• Figure 15.8 shows strong

and weak acids.

• Titrate 50.00 mL of

0.100 M ascorbic acid w/

0.150 M KOH.

Find eq. pt., Ka, pKa,

and mmols of acid first

Weak Acid-Strong Base

• Draw 4 beakers.

• 1) Draw 2 moles weak acid.

• 2) Draw what happens when 1 mole KOH

is added.

• 3) Draw what happens when 2 moles KOH

are added.

• 4) Draw what happens when 3 moles KOH

are added.

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Weak Acid-Strong Base

• 4 regions in titration curve

• Before adding base: 0.00 mL base

• Before equivalence point: 10.00 mL base

• At equivalence point: ???? mL base

• After equivalence point: 50.00 mL base

Weak Acid-Strong Base

• Initial pH before adding base. This is a

weak acid. How do we find the pH of a

weak acid?

Ka = HA H2O H3O+ A-

Initial 0.100 M - 0 0

Change -x - +x +x

Equilibrium 0.100 - x - x x

Weak Acid-Strong Base

• Before equiv. pt.: this is the buffer zone (both weak

acid and its conjugate base are present).

Use change table to find mmoles excess acid and mmoles cong. base produced. All strong base is converted to conjugate acid (strong base is completely consumed).

[HA] = (mmoles acid – mmoles base) / total volume

[A-] = mmoles base / total volume

pH = pKa + log ([A-] / [HA])

Weak Acid-Strong Base

• Before equiv. pt.: 10.00 mL base Excess acid: 5.00 mmol acid – 1.50 mmol base =

3.50 mmol excess acid

All strong base is converted to conjugate base:

(0.150 M)(10.00 mL) = 1.50 mmol A-

divide by total volume = 60.00 mL to get

concentration

Or leave values in moles for Henderson-Hasselbach

pH = pKa + log (base/acid)

• Key Concept Problem 15.15; Problems 15.16, 15.17

Weak Acid-Strong Base

• At equivalence point: Find pH of salt (Ch. 14) We have seen that the product of a weak acid and a

strong base is a basic salt and water.

We can expect the pH to be greater than 7.

Since all the weak acid has been consumed and converted to its conjugate base at the equivalence point, the mmoles of A- are now known.

mmoles A- / total volume = [A-]

Conjugate base reacts with water (A- + H2O HA + OH-).

Set up ICE table (using Kb) and solve for [OH-] and pH.

Weak Acid-Strong Base

• At equivalence point:

5.00 mmol acid and 5.00 mmol base

So 5.00 mmol conj. base (A-) in flask with 83.33 mL total volume = 0.0600 M A-

ICE table: A- + H2O HA + OH-

Kb = Kw / Ka

Kb = (x2/0.0600-x)

x = [OH-]; then find pH

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Weak Acid-Strong Base

• After the equivalence point: Excess OH-

ions More than enough base is added to react with all

the acid in the flask. No HA remains, it is all converted to A-.

pH is determined primarily from excess [OH-].

[A-] is a minor contributor and doesn’t need to be calculated.

[OH-] = (mmoles base – mmoles acid)/ total volume

Weak Acid-Strong Base

• After the equivalence point:

50.00 mL of 0.100 M acid (5.00 mmol) and 50.00 mL

of 0.150 M base (7.50 mmol)

7.50 mmol OH- added – 5.00 mmol acid present =

2.50 mmol remaining OH-

divide by total volume = 0.0250 M OH-

pOH = -log (0.09091 M) = 1.60

pH = 14 – 1.60 = 12.39

Group Quiz #14

• Exactly 50.00 mL of 0.20 M hydrazoic acid (Ka = 1.9 x 10-5) are titrated with a 0.15 M KOH solution. Calculate the pH when 66.67 mL of base have been added:

•

Animations:http://www.chembio.uoguelph.ca/educmat/chm19104/chemtoons/chemtoons.htm

Half Equivalence Point

• 33.34 mL base added (half the volume

needed to get to equivalence point):

• [HA] = (10.00 mmol – 5.00 mmol)

• [A-] = 5.00 mmol

• [HA] = [A-]

• pH = pKa + log ([A-]/[HA]) = pKa

Weak Base-Strong Acid

• Figure 15.10

• Calculations are similar to weak acid/strong base; opposite values; extra steps to find pH values. See pages 613 - 615 for outline.

Acid-Base Indicators

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Polyprotic Acid Titrations

• One eq. pt.

for each

proton

• 2 eq. pts. and

2 half eq. pts.

• Figure 15.11 -

Alanine with

NaOH

Diprotic Acid Titration

• A: acid in water

• B: pKa1; 1st H removed;

50% H2A, 50% HA-

• C: 1st equiv. pt. (HA-)

• D: pKa2; 2nd H

removed; 50% HA-,

50% A2-

• E: 2nd equiv. pt. (A2-),

all acid reacted

• F: only excess base

Complex Ion Equilibria

Formation of complex ions can increase

solubility of an insoluble salt

Complex ion: ion containing a central metal

cation bonded to one or more molecules or

ions which are called ligands. The ligands

act as Lewis bases (e.g. NH3, H2O, OH-)

16.4 Complex Ion Equilibria

• Lewis acid-base reactions also reach a

state of equilibrium

• Metal ion + ligand complex ion

• Kf = [complex ion]/[metal ion][ligand]

(formation constant)

• Hg2+ + 4I- HgI42-

• Kf = [HgI42-]/[Hg2+][I-]4

Complex Ion Equilibria

• Complex ions are often formed stepwise:

• Hg2+ + I- HgI+

Kf1 = [HgI+]/[Hg2+][I-] = 7.9 x 1012

• HgI+ + I- HgI2

Kf2 = [HgI2]/[HgI+][I-] = 1.0 x 1011

• HgI2 + I- HgI3-

Kf3 = [HgI3-]/[HgI2][I

-] = 5.0 x 103

• HgI3- + I- HgI4

2-

Kf4 = [HgI42-]/[HgI3

-][I-] = 2.5 x 102

Demo: orange tornado

Complex Ion Equilibria

• Add all four equations together:

Hg2+ + 4I- HgI42-

Kf = [HgI42-]/[Hg2+][I-]4

Kf = Kf1 x Kf2 x Kf3 x Kf4 = 1.0x1030

• Values of Kf are listed in Table 15.4; they have a wide range of values and thus of stabilities.

• Unlike Bronsted-Lowrey polyprotic acids, successive Kf values may not differ by large factors, so there may be many species coexisting. See Figure 15.11.

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Solubility equilibria

Dissolution of slightly soluble salts in water

important biological examples:

tooth decay - tooth enamel dissolves in acidic soln

formation of kidney stones - salts precipitate in kidney

15.10 Solubility Equilibria

Many ions combine to form solid precipitates

in aqueous solutions. (Solubility rules)

These “insoluble” salts dissolve to a small

extent and form a saturated solution.

The undissolved solid and the dissociated

ions in solution establish an equilibrium

system that is characterized by the solubility

product constant, Ksp.

AgBr(s) Ag+(aq) + Br -(aq)

Ksp = [Ag+][Br -]

Ksp is the solubility product constant - the

equilibrium constant for insoluble salts

• It is a measure of how soluble a salt is in H2O

For salts with the same # of ions, the smaller the

Ksp, the less soluble the salt.

Table 15.2 shows some Ksp values

Example. The dissolution of AgBr Write the solubility equilibrium reactions and

Ksp expressions for a) MgF2 b) Ca3(PO4)2.

A) MgF2(s) Mg2+(aq) + 2F-(aq)

B) Ca3(PO4)2 (s) 3Ca2+ (aq) + 2PO43- (aq)

Ksp = [Ca2+]3[PO43-]2

Ksp = [Mg2+][F-]2

Solubility/Ksp Practice

• Ksp for silver bromide is 7.7 x 10-13. Calculate the molar and gram solubility (solve for x).

• The solubility of calcium sulfate is found experimentally to be 0.67 g/L. Calculate the value of Ksp for calcium sulfate.

• Ksp for copper (I) oxide is found to be 2.0 x 10-15. Calculate the molar and gram solubility.

• The solubility of calcium hydroxide is 0.233 g/L. Calculate Ksp.

• Worked example 15.8 – 15.10, Problems 15.21 –15.24

Solubility/Ksp Practice

• AgBr: x = 8.8 x 10-7 M; x = 1.6 x 10-4 g/L

• CaSO4: Ksp = 2.4 x 10-5

• Cu2O: x = 7.9 x 10-6 M; x = 1.1 x 10-3 g/L

• Ca(OH)2: Ksp = 1.24 x 10-7

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Solubility

• Ksp can be used to calculate the solubility, which

can be compared for any salts.

• Solubility (S) = molar concentration of dissolved

salt; ion concentrations are related to this by their

coefficients.

• Examples:

• AgCl: [Ag+] = S [Cl-] = S Ksp = (S)(S)

• Ag2S: [Ag+] = 2S [S2-] = S Ksp = (2S)2(S)

• Fe(OH)3: [Fe3+] = S [OH-] = 3S Ksp = (S)(3S)3

Common Ion Effect

• Solubility is decreased when a common ion is added

AgCl(s) Ag+(aq) + Cl-(aq)

• Common ion effect: add more Cl- to precipitate Ag+

from solution.

• Saturated solution of AgCl: Find (x)

Ksp = 1.70 x 10-10

• Add 0.100 M Cl-

0.100 >> 1.30 x 10-5, so [Cl-]= 0.100 M

• What is the new [Ag+]? Note this is x in ICE!

Common Ion Effect

• What will happen if I add solid NaF to a solution of saturated SrF2?

• SrF2(s) Sr2+(aq) + 2F-(aq)

• Problem 15.101: a) Calculate the molar solubility of strontium fluoride in pure water (Ksp

= 4.3 x 10-9).

• Calculate the molar solubility of strontium fluoride in 0.010 M sodium fluoride.

Common Ion Effect

• SrF2(s) Sr2+(aq) + 2F-(aq) (in water)

• Equil: x 2x

• Ksp = [Sr2+][F-]2 = 4.3 x 10-9

• x = 1.0 x 10-3 M

• SrF2(s) Sr2+(aq) + 2F-(aq) (in NaF)

• Initial: 0 0.010

• Equil: x 0.010 + 2x

• Ksp = [Sr2+][F-]2 = 4.3 x 10-9

• x = 4.3 x 10-5 M

• Worked ex 15.11, Problem 15.25

Effect of pH on Solubility

Addition of an acid can increase the

solubility of an insoluble basic salt.

E.g. CaF2(s) Ca2+(aq) + 2F-(aq)

Add strong acid (e.g. HCl) provides H3O+ ions:

H3O+ + F- HF + H2O

Adding H+ causes [F-] , equilibrium shifts

right to form more F- & solubility of CaF2 .

Group Quiz #15

• Calculate the solubility, both molar and

gram, of copper(II) hydroxide. Ksp = 1.6 x

10-19

• Calculate the molar solubility of copper(II)

hydroxide when 0.10 M copper(II) nitrate is

added.

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pH and solubility

• E.g. For the following salts, predict whether

the salt will dissolve in an acidic solution.

• A. AgBr _____________

• B. CdCO3 _____________

• C. PbCl2 _____________

• D. BaS _____________

Adding NH3 to AgCl solution

increases the solubility of AgCl:

1) AgCl(s) Ag+(aq) + Cl-(aq) K1 = 1.7 x10-10

2) Ag+(aq) + 2NH3(aq) Ag(NH3)2+(aq) K2 = 1.6 x 107

3) AgCl(s) + 2NH3(aq) Ag(NH3)2+(aq) + Cl-(aq)

Knet = K1 x K2 = 2.7 x 10-3

•Mixture of AgCl and AgBr can be separated: 5 M NH3

dissolves AgCl, but not AgBr.

Precipitation of Ionic Cmpds

• Note: book refers to IP, same idea as Q (value of concentration ratios NOT necessarily at equilibrium)

• Compare Q and K. System will shift until Qsp = Ksp

(a saturated solution)

• Example: We want to know if precipitate will form when 0.150 L of 0.10 M lead (II) nitrate and 0.100 L of 0.20 M sodium chloride are mixed?

• Find Qsp and relate it to Ksp.

Precipitation of Ionic Cmpds

• Worked Example 15.14: Will a precipitate

form when 0.150 L of 0.10 M lead (II) nitrate

and 0.100 L of 0.20 M sodium chloride are

mixed?

• What is the precipitate that will form? What

are Ksp and the equilibrium expression?

• Find total concentration of each ion once

mixed.

• Problem 15.29

Precipitation

• PbCl2(s) Pb2+(aq) + 2Cl-(aq)

• Calculate moles of each ion.

• Convert moles to concentration using total

volume.

• Plug concentrations into Qsp equation.

• If Qsp > Ksp, rxn shifts left (toward solid) and

precipitate will form.

• If Qsp < Ksp, rxn shifts right (toward ions) and

precipitate will not form.

Precipitation of Ionic Cmpds

• Q > Ksp Supersaturated; ppt forms

• Q = Ksp Saturated

• Q < Ksp Unsaturated; no ppt forms

• 2.45 mg of magnesium carbonate is placed

in 1.00 L of water. Will it all dissolve? Ksp =

4.0 x 10-5

• Find molarity of solid. Write equilibrium

expression for solubility. Calculate Qsp.

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Precipitation of Ionic Cmpds

• What are the silver and bromide ion concentrations if

0.0244 g of AgBr and 0.0111 g of NaBr are put into 1.00 L

of water? Will AgBr dissolve completely?

• Write solubility equilibrium expressions for AgBr and NaBr.

• Calculate Qsp. Qsp = [Ag+][Br -]

[Ag+] = 1.30 x 10-4 M, [Br-] = 1.30 x 10-4 + 1.08 x 10-4 M

• Ksp = 7.7 x 10-13

• Qsp > Ksp, what does this mean?

Not all of the AgBr can dissolve

• Worked example 15.14, Problem 15.29

Group quiz 16

Will a solution containing 4.0 x 10-5 M Cl-

and 2.0 x 10-4 M Ag+ form a precipitate

of AgCl? Ksp = 1.70 x 10-10

(Hint: think Q)

Qualitative Analysis

• Skipping section 15.14: Selective Precipitation

• 15.15 Qualitative analysis is used to identify

unknown ions in a solution.

152LL should read this section before qual lab!

• Each ion can be precipitated out by addition

of selective reagents.

• Purely qualitative research, like solving a

puzzle.