Chemistry Chapter 15

Acid-Base Titration and

pH

Self-Ionization of Water

H2O + H2O H3O+ + OH-

• In the self-ionization of water, two water molecules produce a hydronium ion and a hydroxide ion by transfer of a proton.

Ion Concentration in Water

A neutral aqueous solution

A. has a 7.0 M H3O+ concentration.

B. contains neither hydronium ions nor hydroxide ions.

C. has an equal number of hydronium ions and hydroxide ions.

D. None of the above

Test Yourself

Kw – Ionization Constant for Water

In pure water at 25 oC:

[H3O+] = 1 x 10-7 mol/L

[OH-] = 1 x 10-7 mol/L

Kw is a constant at 25 oC:

Kw = [H3O+][OH-]

Kw = (1 x 10-7)(1 x 10-7) = 1 x 10-14

The Value of Kw Changes With Temperature

Strong Acids Ionize Almost Completely in Solution!

Weak Acids Reach Equilibrium Points Early.HC2H3O2 + H2O H3O+ + CH3COO-

l + l aq + aq–3 2 3 3HNO ( ) H O( ) H O ( ) NO ( )

1 mol 1 mol 1 mol 1 mol

The strength of a base depends on the extent it dissociates.

1 mol 1 mol 1mols aq + aq2H O –NaOH( ) Na ( ) OH ( )

Hydronium Ions and Hydroxide IonsCalculating [H3O+] and [OH–]

• Strong acids and bases are considered completely ionized or dissociated in weak aqueous solutions.

s aq + aq2H O –NaOH( ) Na ( ) OH ( )

-14 -14

-123 – -2

1.0 10 1.0 10[H O ] 1.0 10 M

[OH ] 1.0 10

1 mol 1 mol 1 mol

• 1.0 × 10−2 M NaOH solution has an [OH−] of 1.0 × 10−2 M

• The [H3O+] of this solution is calculated using Kw.

Kw = [H3O+][OH−] = 1.0 × 10−14

Sample Problem

A 1.0 X 10–4 M solution of HNO3 has been prepared for a laboratory experiment.

a. Calculate the [H3O+] of this solution. (IONIZES COMPLETELY)

b. Calculate the [OH–].l + l aq + aq–3 2 3 3HNO ( ) H O( ) H O ( ) NO ( )

1 mol 1 mol 1 mol 1 mol

3 3 3

33

mol HNO 1 mol H O mol H Omolarity of H O

L solution 1 mol HNO L solution

[H3O+][OH−] = 1.0 × 10−14

-10

–14 –14–

-43

1.0 10 1.0 10[OH ]

[H O ] 1.0 101.0 10 M

Hydronium Ions and Hydroxide IonsCalculating [H3O+] and [OH–]

• If the [H3O+] of a solution is known, the [OH−] can be calculated using Kw.

[HCl] = 2.0 × 10−4 M

[H3O+] = 2.0 × 10−4 M

Kw = [H3O+][OH−] = 1.0 × 10−14

-14 -14

– -10-4

3

1.0 10 1.0 10[OH ] 5.0 10 M

[H O ] 2.0 10

Determine the hydronium and hydroxide ion concentration in

a solution that has 1.0 X 10 -4 M Ca(OH)2 .

1 mol 1 mol 2 mol

1.0 × 10−2 M NaOH solution has an [OH−] of (2) X 1.0 × 10−4 M– The [OH-] concentration is 2.0 X 10-4 M

• The [H3O+] of this solution is calculated using Kw.

• Kw = [H3O+][OH−] = 1.0 × 10−14

[H3O+][2.0 X 10-4 M] = 1.0 × 10−14

[H3O+] = 5.0 X 10-11 M

Pause for a CauseStudent Practice Pg. 522 Problem #8

Calculate the [H3O+] and [OH-] for each of the following:

a. 0.030 M HCl

b. 1.0 X 10-4 M NaOH

c. 5.0 X 10-3 M HNO3

d. 0.010M Ca(OH)2

Answers: a. [H3O+] = 3.0 X 10-2 M, [OH−] = 3.3 × 10−13 M; b. [H3O+] = 1.0 X 10-10 M, [OH−] = 1.0 × 10−4 M; c. [H3O+] = 5.0 X 10-3 M, [OH−] = 2.0 × 10−12 M; d. [H3O+] = 5.0 X 10-13 M, [OH−] = 2.0 × 10−2 M

pH

• pH comes from French words meaning “hydrogen power”. In chemistry, pH is a scale that indicates the concentration of hydronium ions [H3O+] in solutions.

pH pH ScaleScale

Calculating pH, pOHCalculating pH, pOHpH = -log10(H3O+)

pOH = -log10(OH-)

Relationship between pH and pOHRelationship between pH and pOH

pH + pOH = 14

Finding [HFinding [H33OO++], [OH], [OH--] from pH, pOH] from pH, pOH

[H3O+] = antilog -pH

[OH-] = antilog -pOH

pH +

pOH = 14

When is a solution an acid, a base, or a neutral solution?

• Solutions in which [H3O+] = [OH−] are neutral.

• Solutions in which the [H3O+] > [OH−] are acidic.

– [H3O+] > 1.0 × 10−7 M

• Solutions in which the [OH−] > [H3O+] are basic.

– [OH−] > 1.0 × 10−7 M

Calculating pH

• The pH of a solution is defined as the negative of the common logarithm of the hydronium ion concentration, [H3O+].

• pH = −log [H3O+]

– example: a neutral solution has a [H3O+] = 1×10−7– The logarithm of 1×10−7 is −7.0.

• pH = −log [H3O+] = −log(1 × 10−7) = −(−7.0) = 7.0

• What is the pH of 1.0 X 10-3 M HCl?

– pH = −log [H3O+] = −log(1.0 × 10−3) = −(−3.0) = 3.0

• What is the pH of a 1.0 X 10-2 M NaOH solution?

– pH = −log [H3O+] = −log(1.0 × 10−12) = −(−12) = 12

• What is the pH of 3.4 X 10-5 M HNO3?

– pH = −log [H3O+] = −log(3.4 × 10−5) = −(−4.47) = 4.47

-14 -14

-123 – -2

1.0 10 1.0 10[H O ] 1.0 10 M

[OH ] 1.0 10

Pause for a CauseStudent Practice Pg. 506 Practice Problems 1-4

1. What is the pH of a solution if the [H3O+] is 6.7 X 10-4?

2. What is the pH of a solution with a hydronium ion concentration of 2.5 X 10-2 M?

3. Determine the pH of a 2.5 X 10-6 M HNO3 solution.

4. Determine the pH of a 2.0 X 10-2 M Sr(OH)2 solution.

Answers: 1) pH = 3.17 2) pH =1.60 3) pH = 5.60 4) pH = 12.60

Determine the hydronium ion concentration of an aqueous solution

that has a pH of 4.0.

[H3O+] = antilog –pH[H3O+] = antilog – 4.0[H3O+] = 1.0 X 10-4

Determining Hydronium Ions from pH

The pH of a solution is measured and determined to be 7.52

• a. What is the hydronium ion concentration?• b. What is the hydroxide ion concentration?• c. Is the solution acidic or basic?

b. Kw = [H3O+][OH−] = 1.0 × 10−14

[3.0 X 10-8][OH-] = 1.0 × 10−14

[OH-] = 3.3 X 10-7 M

c. slightly basic

a. [H3O+] = antilog –pH [H3O+] = antilog – 7.52 [H3O+] = 3.0 X 10-8

Pause for a CausePractice Problems Pg. 508 # 1-4

1. The pH of a solution is determined to be 5.0. What is the hydronium ion concentration of this solution?

2. The pH of a solution is determined to be 12.0. What is the hydronium ion concentration of this solution?

3. The pH of an aqueous solution is measured as 1.50. Calculate the [H3O+] and [OH-] concentration.

4. The pH of an aqueous solution is 3.67. Determine the [H3O+].

1. [H3O+] = 1.0 X 10-5

2. [H3O+] = 1.0 X 10-12

3. [H3O+] = 3.2 X 10-2

[ OH-] = 3.2 X 10-12

4. [H3O+] = 2.1 X 10-4

The pH of a Substance Can be Found Using Indicators, pH Paper,

or pH Meters.

• pH meter – Determines the pH of a solution by measuring the voltage

between the two electrodes that a placed in the solution.• Acid-base indicators

– Compounds whose colors are sensitive to pH.• Transition interval

– The pH range over which an indicator changes color.

Measuring pH with Wide-Range Paper/ Narrow Range Paper

pH Indicators and Their Ranges

Problem: An unknown solution is colorless

when tested with phenolphthalein, but causes the indicator

phenol red to turn red. Use this information to determine the possible

pH of this solution.

1. Start with the balanced equation for the neutralization reaction, and determine the chemically equivalent amounts of the acid and base.

2. Determine the moles of acid (or base) from the known solution used during the titration.

3. Determine the moles of solute of the unknown solution used during the titration.

4. Determine the molarity of the unknown solution.

Steps in Determining the Molarity of a Solution.

Titration Calculations

Let’s Work this Sample Problem on the Board!

In a titration, 27.4 mL of 0.0154 M Ba(OH)2 is added to a 20.0 mL sample of HCl solution of unknown concentration until the equivalence point is reached. What is the molarity of the acid solution?

Answer: 4.22 X 10-2 M HCl

Let’s Work Another Sample Problem on the Board!

A 15.5 mL sample of 0.215 M KOH solution required21.2 mL of aqueous acetic acid solution in a titration experiment. Calculate the molarity of the acetic acid solution.

Answer: 0.157 M HC2H3O2

One Last Sample Problem on the Board!

By titration, 17.6 mL of aqueous H2SO4 neutralized 27.4 mL of 0.165 M LiOH solution. What is the molarity of the aqueous acid solution?

Answer: 0.0128 M H2SO4

Pause for a CauseStudent Practice Pg. 524 # 26, 26, 36

25. Suppose that 15.0 mL of 2.50 X 10-2 M aqueous H2SO4 is required to neutralize 10.0 mL of an aqueous solution of KOH. What is the molarity of the KOH solution?

26. In a titration experiment, a 12.5 mL sample of 1.75 M Ba(OH)2 just neutralized 14.5 mL of HNO3 solution. Calculate the molarity of the HNO3 solution.

36. Find the molarity of a Ca(OH)2 solution given that 428 mL of the solution is neutralized in a titration by 115 mL of 6.7 X 10-3 M HNO3

Answers: 25. 7.50 X 10-2 M KOH; 26. 3.02 X 10-2 M HNO3;

36. 9.0 X 10-4 M Ca(OH)2

Challenge ProblemPg. 902 # 359

• A chemist wants to produce 12.00 grams of barium sulfate by reacting a 0.600 M BaCl2 solution with excess H2SO4, as shown in the reaction below. What volume of BaCl2 solution should be used?– BaCl2 + H2SO4 BaSO4 + 2 HCl

Instructions for Titrations

Filling the Acid Buret

Adding the Indicator

Filling the Base Buret

The Experiment Begins

Titration Completed!

Titration CurvesTitration Curves

Test Yourself

1. Distilled water contains

A. H2O.

B. H3O+.

C. OH−.

D. All of the above

Test Yourself

2. What is the pH of a 0.0010 M HNO3?

A. 1.0

B. 3.0

C. 4.0

D. 5.0

Test Yourself

3. Which of the following solutions would have a pH value greater than 7?

A. [OH−] = 2.4 × 10−2 M

B. [H3O+] = 1.53 × 10−2 M

C. 0.0001 M HCl

D. [OH−] = 4.4 × 10−9 M

Test Yourself

4. If the pH of a solution of the strong base NaOH

is known, which property of the solution can be

calculated?

A. molar concentration

B. [OH−]

C. [H3O+]

D. All of the above

Test Yourself

5. A neutral aqueous solution

A. has a 7.0 M H3O+ concentration.

B. contains neither hydronium ions nor hydroxide ions.

C. has an equal number of hydronium ions and hydroxide ions.

D. None of the above

Test Yourself

6. Identify the salt that forms when a solution of H2SO4 is titrated with a solution of Ca(OH)2.

A. calcium sulfate

B. calcium hydroxide

C. calcium oxide

D. calcium phosphate

Test Yourself7. The pH of a solution is 6.32. What is

the pOH?

A. 6.32

B. 4.8 × 10−7

C. 7.68

D. 2.1 × 10−8

Test Yourself8. The Kw value for water can be affected

by:

A. dissolving a salt in the solution.B. changes in temperature.C. changes in the hydroxide ion

concentration.D. the presence of a strong acid

Test Yourself9. Which of the pH levels listed below

is the most acidic?

A. pH = 1

B. pH = 5

C. pH = 9

D. pH = 13

The End!The End!The End!The End!The End!The End!