Chem 321 Chapter 9

8/3/2019 Chem 321 Chapter 9

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Chapter 9:

Monoprotic Acid-Base Equilibria

Chapter 11:

Acid-Base Titrations


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Example: Determination ofExample: Determination ofHClHCl

concentration by titration withconcentration by titration withNaOHNaOH


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I. Solutions and Indicators for Neutralization Titrations

A. Standard Solutions:

The standards solutions used as titrants for unknown weakacids or bases are always strong bases or acids, respectively.

Standard titrant acids: dilute solutions of HCl, HClO4, or H2SO4.

Standard titrant bases: dilute solutions of NaOH, KOH.

The primary standards may not be strong acids or bases (e.g.,potassium acid phthalate, sodium oxalate, sodiumbicarbonate).


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B. The Theory of Indicator Behavior

1. pH-sensitive dyes have long been used as indicators.

Normally, the basic form(In) on the dye has a color different from the acidform, HIn:

HIn + H2O H3O+ + In-

In + H2O OH

-

+ HIn

+

][HIn

][In]OH[Ka

3

+

= [Eq.1]

][In

][HIn]OH[Kb

+

= [Eq. 2]

We can see that both equilibrium constant expressions above can be written:

][In

]Ka[HIn]OH[ 3

+

= [Eq. 1]

][In]Ka[HIn]OH[ 3

+

+

= {Note: Kw =KaKb = [OH-][H+]} [Eq. 2]

Therefore, the [H3O+] determines the ratio of the acid/conjugate base form of

the indicator.

To see the color of a particular form (acid or base) of the indicator, thatform must be present at tenfold higher concentration.


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For example,

To see the color of acid form, the ratio [HIn]/[In] must be equal to or greaterthan 10.

To see the color of base form, the ratio [HIn]/[In] must be equal to or lessthan 0.1.

This means that:

For acid color [H3O+] > Ka (10/1)For base color [H3O

+] < Ka (1/10)

Hence: indicator range = pKa 1, and the pH change in the area of theequivalence point must match this range or at least overlap it significantlyto use this indicator for endpoint detection. (note: how to select theindicator)


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9-1


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C. Titration Curves may be linear-segment curve or asigmoidal curve depending on what is plotted on the y-axis.

The X-axis units are always reagent or titrant volume.

The Y-axis may be in increments of analyte reacted orproduct formed (linear-segment curve) or a p-functionsuch as pH (s-curve).

The equivalence point is characterized by large changesin the relative concentrations of the reagent and analyte.(See Table 10-2)


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Titration Curves


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9-2


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D. The Titration of a Strong Acid with a Strong Base

Example: Determination ofExample: Determination ofHClHCl concentration by titration withconcentration by titration with NaOHNaOH

NaOH + HCl NaCl + H2O

moles = CNaOHVNaOH = CHClVHCl

1. H3O+ in the titration medium has two sources

a. From the H2O solvent

b. From the acid solute - usually this is in great excess relative contribution from

water because the Kw is so small

c. The mass balance equation describing this situation is:

[H 3 O + ] = C H C l + [O H -] = C H C l

d . T h e s a m e is t r u e f o r a s t r o n g b a s e a n d w e c a n w r ite :

[O H -] = C N a O H + [H 3 O+ ] = C N a O H


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2. Before the equivalence pointWe calculate the pH of the titration medium from theconcentration of unreacted strong acid:

baseacid

33

VV

]OH[ofMoles]OH[ofMoles]OH[

+

=

+

+

pH = - log [H3O+]

3. At the equivalence pointAll of the acid has reacted with the titrant base. For a strong acidtitrated with a strong base, the salt is a strong electrolyte andtherefore completely dissociated. It does not react with H2O. Theresulting solution is neutral (pH = 7.00) because:

HCl + NaOH H2O + Na+ + Cl-

2 H2O H3O+ + OH-

4. After the equivalence pointwe calculate the pH of the titration medium from the concentrationof unreacted strong base:

baseacid

3added

3

w

VV

]OH[ofMoles]OH[ofMoles

]OH[

K

]OH[ +

==

+

+


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9-1


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9-1


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9-2


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Any Questions?


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5. The Effect of Concentration on the shape of the curve:With a very dilute solution of strong acid which is titrated with

a very dilute solution of strong base, there will be a smallerrelative change in the pH immediately before and after theequivalence point


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6. The selection of an indicator

The indicator range (detectable color change) shouldoccur in the area of the equivalence point.

Concentration effect

i. titration of 0.0500 M HCl with 0.1000 M NaOH threeindicators (phenolphthalein, bromothymol blue,Bromocresol green)have color changes in thisrange.

ii. for the more dilute titration medium (0.000500 M HClwith 0.001000 M NaOH), only one of the indicators(bromothymol blue) is now suitable.

iii. This is because the relative pH change for thesecond curve is so small that two of the indicatorschange color before or after the equivalence point.


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Any Questions?


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E. Buffer Solutions:

A buffer solution resists changes in pH.

Buffers usually consist of a weak acid/conjugate base pairmixture in solution.

Since the titration of a weak acid (or base) with a strong base(or acid) will form a buffer solution, the curves constructedfor these titration systems will appear quite different fromthose where all the reactants are completely


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E1. The Calculation of the pH of Buffer Solutions:Example: We are preparing a buffer in which the acid, HA, and its

salt, NaA, are being added to the solution to give CHA and CNaA

For the species HA and A- we can write:a. Pertinent Equilibria

HA + H2O A- + H3O

+

A-+ H2O HA + OH-

2H2O H3O+ + OH-

b. Equilibrium Expressions

][HA

]A][OH[K

-3

a

+

= [Eq. 1]

][A

]HA][OH[K

-b

= [Eq. 2]

Kw =[H3O+] [OH-] [Eq. 3]

c. Mass balance equations:[HA] = CHA - [H3O

+] + [OH-] [Eq. 4]

[A-] = CNaA + [H3O+] - [OH-] [Eq. 5]


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d. Approximations:Since the concentrations of these species are likely to benegligible relative the CHA and CNaA, we can approximate:

[HA] = CHA[A-] = CNaA

This assumption is true only whenKa < 10-3 and the relative

concentrations of the acid or its conjugate base are relatively

high.

e. Solving equationsIf we rearrange Eq.1 and solve for [H3O

+] then

]A[][HAK]OH[

-

a3 =

+ [Eq.1]

Taking -log of both sides of Eq.1

HA

NaAa

-

a-aC

ClogpK

]HA[

][AlogpK

]A[

][HAlogpKpH +=+==

This equation implies that the pH of a buffer solution isindependent of the dilution of the solution since the relative

concentrations of conjugate base/acid do not change upondilution


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HA

NaA

a C

C

logpKpH +=

9-3

HCOO- + H2O < ==> HCOOH + H3O+


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9-4

+

+=

4

3

NH

NH

a C

C

logpKpH


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+

+=

4

3

NH

NH

aC

ClogpKpH


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Any Questions?


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F. Properties of Buffer Solutions1. Effect of Dilution:

Theoretically, pH does not change with dilution. However, ionic

strength changes with dilution (and therefore so will Ka). Forbuffers whose Ka values are strongly influenced by ionicstrength, we may see a pH change over large changes inconcentration.

2. Effect of Temperature:Since Ka changes as a function of temperature, we can expectbuffer pH to change with changes in temperature.

3. Effect of Added Acids or Bases:Buffer solutions tend to resist pH change, although the ratio of

base/acid changes depending on the amount of acid or baseadded

4. Buffer Capacity: The number of moles of strong acid or strong base that

causes the pH of 1.00 L of buffer to change by 1.00 pHunit.

The buffering capacity of the system for acid or basefalls off as the concentration ratio of weak acid to

conjugate base in the solution becomes larger orsmaller than 1.


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If ([A-]/[HA])1, the system will not buffer base effectively.

If ([A-]/[HA])= 1, buffering capacity to both acids and bases is

considered most effective and the pKa for the system is within 1

unit of the desired


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G. Titration Curves for Weak Acids:

There are 4 areas to consider

1) before the addition of base

2) before the equivalence point (buffer region 1)

3) at the equivalence point

4) after the equivalence point


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1. Before the addition of base:Calculated from the concentration and Ka of the weak acid.

2. After the addition of strong base but before the equivalencepoint:

]OH[ofMoles

]OH[ofMoles

logpK

V

]OH[ofMoles

V

]OH[ofMoles

logpKpH3

added

a

total

3

total

added

a +

+

+=+=

Note: The half-neutralized point pH = pKa and hence you canmeasure pKa from titration curve.

The half-neutralized point means pH at

eb V2

1V =

Note: Vb : volume of titrant

Ve: volume of titrant needed to reach the equivalence pointNote: You will need these questions and concepts for the

calculation in Chem 322 (potentiometric titration experiments).

3 At the equivalence point:


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3. At the equivalence point:The predominant equilibrium is the hydrolysis of H2O by the

salt of the weak acid:

A- + H2O HA + OH-

][A

]HA][OH[K

-b

=

Generally, you can solve the equilibrium constant equation for

[OH-] and assume that

total

3-

V

]OH[ofMoles][A

+

= Thus, bbCK]OH[ =

For weak acids that are titrated with strong bases, the pH at the

equivalence point will be basic.

4. Beyond the equivalence point:Both the anion of the weak acid and the excess base aresources of [OH-].

However, due to LeChatelier's Principle the addition of [OH-

] inthe form of a strong base will suppress the hydrolysis by theweak acid anion so that:

total

3added

V


+

=

9 49 5


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aa3 CK]OH[ =+

9-49-5

HOAC + H2O H3O+ + OAC-

]OH[ofMoles

]OH[ofMoles

logpKpH3

added

a +

+=


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total

3added

V

]OH[ofMoles]OH[ofMoles

]OH[

+

=

bbCK]OH[ =


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H. Titration Curves for Weak Bases:

There are 4 areas to consider

1) before the addition of acid

2) before the equivalence point (buffer region 1)

3) at the equivalence point

4) after the equivalence point

9-6


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bbCK]OH[=

9-6


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]OH[ofMoles

]OH[ofMoles

logpKpH3

a +

+=

aa3CK]OH[ =+


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total

added33

V


+

+

=

I. The Effect of Concentration:


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e ect o Co ce t at oAgain, as with the titration of strong acids with strong bases, as

the concentration of the weak acid or base becomes more dilute,

the relative change in pH at the equivalence point decreasesmaking the endpoint less sharp.

A: 0.1000 M acid with 0.1000 M base

B: 0.001000 M acid with 0.001000 M bas

I The Effect of Reaction Completeness:


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I. The Effect of Reaction Completeness:The smaller the Ka, the less sharp the endpoint when a weak acid

is titrated with a strong base (Figure 10-11). This depends also onconcentration, so that weaker acids can be titrated if concentratedsolutions are used.


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Any Questions?

Summary


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Summary How to select standard solutions and indicators for neutralization

titrations Theory of Indicator Behavior

Titration Curves

Theories: Plots and shapes of plots

Parameters: pH, Volume of titrants, equivalence point Calculations: Ka, pH, indicator choices, half-neutralized point

Effects: Concentration, reaction, composition, temperature,equilibrium constants

The titration of a strong acid with a strong base

The titration of a week acid with a strong base

The titration of a strong base with a strong acid

The titration of a week base with a strong acid

Buffer solutions: Definition and properties (e.g., buffer capacity)

Calculation of pH of the buffer solution

Applications


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Homework

9-B, D, E, 2, 5, 6, 22, 23, 27, 28, 33 11-A, B, F, 3, 6, 14

Before working on Homework,

Practice with all examples that we discussed in the class

and examples in the textbook!!

Chem 321 Chapter 9

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