Tài liệu Chapter 9: Monoprotic Acid-Base Equilibria pdf

To see the color of a particular form acid or base of the indicator, that form must be present at tenfold higher concentration... The Effect of Concentration on the shape of the curve:

Chapter 9:

Monoprotic Acid-Base Equilibria

Chapter 11:

Acid-Base Titrations

Example: Determination of HCl

I Solutions and Indicators for Neutralization Titrations

A Standard Solutions:

The standards solutions used as titrants for unknow n w eak acids or bases are alw ays strong bases or acids, respectively

Standard titrant bases: dilute solutions of NaOH, KOH

potassium acid phthalate, sodium oxalate, sodium

bicarbonate)

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 acid form, HIn:

HIn + H 2 O <====> H 3 O + + In

In + H 2 O <====> OH - + HIn +

] [HIn

] [In ] O H [

Ka 3

− +

= [Eq.1]

] [In

] [HIn ] OH [ Kb

] Ka[HIn ]

O H [ 3 + = − [Eq 1’]

] [In

] Ka[HIn ]

O H [ 3

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

Therefore, the [H 3 O + ] 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, that

form must be present at tenfold higher concentration

This means that:

For acid color [H 3 O + ] > K a (10/1)

For base color [H 3 O + ] < K a (1/10)

Hence: indicator range = pK a ± 1 , and the pH change in the area of the

equivalence point must match this range or at least overlap it significantly

indicator)

9-1

C Titration Curves – may be linear-segment curve or a

sigmoidal 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 or product formed (linear-segment curve) or a p-function such as pH (s-curve)

The equivalence point is characterized by large changes

in the relative concentrations of the reagent and analyte (See Table 10-2)

Titration Curves

9-2

D The Titration of a Strong Acid with a Strong Base

Example: Determination of HCl concentration by titration with NaOH

NaOH + HCl NaCl + H2O

moles = C NaOH V NaOH = C HCl V HCl

1 H 3 O + in the titration medium has two sources

a From the H 2 O solvent

b From the acid solute - usually this is in great excess relative contribution from water because the K w 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 i s 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 i t e :

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

2 Before the equivalence point

We calculate the pH of the titration medium from the

concentration of unreacted strong acid:

base acid

3 3

V V

] OH [ of Moles ]

O H [ of Moles ]

O H [

All of the acid has reacted with the titrant base For a strong acid titrated with a strong base, the salt is a strong electrolyte and

therefore completely dissociated It does not react with H 2 O The resulting solution is neutral (pH = 7.00) because:

HCl + NaOH <====> H 2 O + Na + + Cl

2 H 2 O <====> H 3 O + + OH

we calculate the pH of the titration medium from the concentration

of unreacted strong base:

base acid

3 added

3

w

V V

] O H [ of Moles ]

OH [ of Moles ]

O H [

K ]

OH [

9-1

9-1

9-2

Any Questions?

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 smaller

relative change in the pH immediately before and after the

equivalence point

6 The selection of an indicator

The indicator range (detectable color change) should occur in the area of the equivalence point

Concentration effect

i titration of 0.0500 M HCl with 0.1000 M NaOH three indicators ( phenolphthalein, bromothymol blue, Bromocresol green ) have color changes in this range

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

iii This is because the relative pH change for the

second curve is so small that two of the indicators change color before or after the equivalence point

Any Questions?

E Buffer Solutions:

A buffer solution resists changes in pH

Buffers usually consist of a weak acid / conjugate base pair

mixture in solution

Since the titration of a weak acid (or base) with a strong base (or acid) will form a buffer solution, the curves constructed for these titration systems will appear quite different from

those where all the reactants are completely

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 C HA and C NaA

a Pertinent Equilibria

HA + H 2 O <====> A - + H 3 O +

A - + H 2 O <====> HA + OH 2H 2 O <====> H 3 O + + OH -

-b Equilibrium Expressions

] [HA

] A ][

O H [ K

3

-a

+

= [Eq 1]

] [A

] HA ][

OH [

-−

= [Eq 2]

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

c Mass balance equations:

[HA] = C HA - [H 3 O + ] + [OH - ] [Eq 4]

[A - ] = C NaA + [H 3 O + ] - [OH - ] [Eq 5]

d Approximations:

Since the concentrations of these species are likely to be

negligible relative the C HA and C NaA , we can approximate:

[HA] = C HA

[A - ] = C NaA

This assumption is true only when K a < 10 -3 and the relative

concentrations of the acid or its conjugate base are relatively

high

e Solving equations

If we rearrange Eq.1 and solve for [H 3 O + ] then

] A [

] [HA K ] O H

-3 + = [Eq.1’]

Taking -log of both sides of Eq.1’

HA

NaA a

a

a

-C

C log pK

] HA [

] [A log pK

] A [

] [HA log pK

This equation implies that the pH of a buffer solution is

independent of the dilution of the solution since the relative

concentrations of conjugate base/acid do not change upon

dilution

NaA a

C

ClogpK

pH = +

9-3

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

ClogpK

pH

ClogpK

pH

Any Questions?

F Properties of Buffer Solutions

1 Effect of Dilution :

Theoretically, pH does not change with dilution However, ionic strength changes with dilution (and therefore so will K a ) For buffers whose K a values are strongly influenced by ionic

strength, we may see a pH change over large changes in

concentration

2 Effect of Temperature :

Since K a changes as a function of temperature, we can expect buffer 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 base added

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 pH unit

The buffering capacity of the system for acid or base falls off as the concentration ratio of weak acid to conjugate base in the solution becomes larger or smaller than 1

If ([A-]/[HA])<<1 , the system will not buffer acid effectively;

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

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

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 equivalence

point:

] O H [ of Moles

] OH [ of Moles log

pK V

] O H [ of Moles

V

] OH [ of Moles log

pK pH

3

added a

total 3 total

added

− +

−

+

= +

=

Note: The half-neutralized point pH = pKa and hence you can

measure pKa from titration curve

The half-neutralized point means pH at

e

b V 2

1

Note: Vb : volume of titrant

Ve: volume of titrant needed to reach the equivalence point

Note: You will need these questions and concepts for the

calculation in Chem 322 (potentiometric titration experiments)

3 At the equivalence point:

The predominant equilibrium is the hydrolysis of H 2 O by the salt of the weak acid:

A - + H 2 O <====> HA + OH -

] [A

] HA ][

OH [

V

] O H [ of Moles ]

4 Beyond the equivalence point:

Both the anion of the weak acid and the excess base are

sources of [OH - ]

However, due to LeChatelier's Principle the addition of [OH - ] in the form of a strong base will suppress the hydrolysis by the weak acid anion so that:

total

3 added

V

] O H [ of Moles ]

OH [ of Moles ]

OH [

+

−

a a

3O ] K C H

9-4

HOAC + H2O H3O+ + OAC

-] O H [ of Moles

] OH [

of

Moles log

pK pH

3 added

V

] O H [ of Moles ]

OH [ of Moles

] OH

H Titration Curves for Weak Bases :

There are 4 areas to consider

bC K

] OH

9-6

] O H [ of Moles

] OH [

of

Moles log

3O ] K C H

added

33

V

] OH [

of Moles ]

O H

[ of

Moles ]

O

H

[

−+

I The Effect of Concentration :

Again, 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 decreases

making the endpoint less sharp

A: 0.1000 M acid with 0.1000 M base

B: 0.001000 M acid with 0.001000 M base

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 on concentration, so that weaker acids can be titrated if concentrated solutions are used

Any Questions?

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

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!!