Acid-Base Titrations

1
Acid-Base Titrations

• Introduction
• 1.) Experimental Measurements of pKa
• pKa of amino acids in an active-site of a protein
  are related to its function
• Protein structure and environment significantly
  perturb pKa values
• In medicinal chemistry, pKa and lipophilicity of
  a candidate drug predict how easily it will cross
  a cell membrane
• Higher charge ? harder to cross membrane? not a
  good drug

2
Acid-Base Titrations

• Introduction
• 2.) Example
• impact of the Asp on the pKa of His in the
  His-Asp catalytic dyad.
• Glucose 6-phosphate dehydrogenase (G6PD)
  catalyzes the oxidation of glucose 6-phosphate
  using NAD or NADP
• His-240 is the general base that extracts a
  proton from the C1-OH of G6P

The pKa of His-240 in the G6PD apoenzyme is found
to be 6.4, which corresponds to an unidentified
pKa value of 6.3 that was previously derived from
the dependence of kcat on pH. These results
suggest that the pKa of His-240 is unperturbed by
Asp.
Biochemistry, Vol. 41, No. 22, 2002 6945
3
Acid-Base Titrations

• Introduction
• 3.) Overview
• Titrations are Important tools in providing
  quantitative and qualitative data for a sample.
• To best understand titrations and the information
  they provide, it is necessary to understand what
  gives rise to the shape of a typical titration
  curve.
• To do this, acid-base equilibria are used to
  predict titration curve shapes.

proton release from PAA decreases with increase
in the degree of dissociation for the highest
polymer concentration
conformational change of the PAA from rod-like
conformation to a random coil form,
J. Phys. Org. Chem. 2006 19 129135
4
Acid-Base Titrations

• Titration of Strong Base with Strong Acid
• 1.) Graph of How pH changes as Titrant is Added
• Assume strong acid and base completely dissociate
• Any amount of H added will consume a
  stoichiometric amount of OH-
• Reaction Assumed to go to completion
• Three regions of the titration curve
• Before the equivalence point, the pH is
  determined by excess OH- in the solution
• At the equivalence point, H is just sufficient
  to react with all OH- to make H2O
• After the equivalence point, pH is determined by
  excess H in the solution.

5
Acid-Base Titrations

• Titration of Strong Base with Strong Acid
• 1.) Graph of How pH changes as Titrant is Added
• Remember, equivalence point is the ideal goal
• Actually measure End Point
• Marked by a sudden physical change color,
  potential
• Different Regions require different kinds of
  calculations
• Illustrated examples
• The true titration reaction is

Titrant
Analyte
6
Acid-Base Titrations

• Titration of Strong Base with Strong Acid
• 2.) Volume Needed to Reach the Equivalence Point
• Titration curve for 50.00 mL of 0.02000 M KOH
  with 0.1000 M HBr
• At equivalence point, amount of H added will
  equal initial amount of OH-

mmol of OH- being titrated
mmol of HBr at equivalence point
When 10.00 mL of HBr has been added, the
titration is complete. Prior to this point,
there is excess OH- present. After this point
there is excess H present.
7
Acid-Base Titrations

• Titration of Strong Base with Strong Acid
• 3.) Before the Equivalence Point
• Titration curve for 50.00 mL of 0.02000 M KOH
  with 0.1000 M HBr
• Equivalence point (Ve) when 10.00 mL of HBr has
  been added
• When 3.00 mL of HBr has been added, reaction is
  3/10 complete

Initial volume of OH-
Calculate Remaining OH-
Total volume
Fraction of OH- Remaining
Initial concentration of OH-
Dilution Factor
Calculate H and pH
8
Acid-Base Titrations

• Titration of Strong Base with Strong Acid
• 4.) At the Equivalence Point
• Titration curve for 50.00 mL of 0.02000 M KOH
  with 0.1000 M HBr
• Just enough H has been added to consume OH-
• pH determined by dissociation of water
• pH at the equivalence point for any strong acid
  with strong base is 7.00
• Not true for weak acid-base titration

Kw
Kw 1x10-14
x x
9
Acid-Base Titrations

• Titration of Strong Base with Strong Acid
• 5.) After the Equivalence Point
• Titration curve for 50.00 mL of 0.02000 M KOH
  with 0.1000 M HBr
• Adding excess HBr solution
• When 10.50 mL of HBr is added

Calculate volume of excess H
Calculate excess H
Volume of excess H
Initial concentration of H
Dilution factor
Total volume
Calculate pH
10
Acid-Base Titrations

• Titration of Strong Base with Strong Acid
• 6.) Titration Curve
• Rapid Change in pH Near Equivalence Point
• Equivalence point is where slope is greatest
• Second derivative is 0
• pH at equivalence point is 7.00, only for strong
  acid-base
• Not True if a weak base-acid is used

11
Acid-Base Titrations

• Titration of Weak Acid with Strong Base
• 1.) Four Regions to Titration Curve
• Before any added base, just weak acid (HA) in
  water
• pH determined by Ka
• With addition of strong base ? buffer
• pH determined by Henderson Hasselbach equation
• At equivalence point, all HA is converted into A-

Ka
Kb
12
Acid-Base Titrations

• Titration of Weak Acid with Strong Base
• 1.) Four Regions to Titration Curve
• Beyond equivalence point, excess strong base is
  added to A- solution
• pH is determined by strong base
• Similar to titration of strong acid with strong
  base
• 2.) Illustrated Example
• Titration of 50.00 mL of 0.02000 M MES with
  0.1000 M NaOH
• MES is a weak acid with pKa 6.27
• Reaction goes to completion with addition of
  strong base

13
Acid-Base Titrations

• Titration of Weak Acid with Strong Base
• 3.) Volume Needed to Reach the Equivalence Point
• Titration of 50.00 mL of 0.02000 M MES with
  0.1000 M NaOH
• Reaction goes to completion with addition of
  strong base
• Strong plus weak react completely

mmol of HA
mmol of base
14
Acid-Base Titrations

• Titration of Weak Acid with Strong Base
• 4.) Region 1 Before Base is Added
• Titration of 50.00 mL of 0.02000 M MES with
  0.1000 M NaOH
• Simply a weak-acid problem

Ka
Ka 10-6.27
Calculate H
F - x x x
Calculate pH
15
Acid-Base Titrations

• Titration of Weak Acid with Strong Base
• 5.) Region 2 Before the Equivalence Point
• Titration of 50.00 mL of 0.02000 M MES with
  0.1000 M NaOH
• Adding OH- creates a mixture of HA and A- ?
  Buffer
• Calculate pH from A-/HA using
  Henderson-Hasselbach equation

Simply the difference of initial quantities
Calculate A-/HA
Simply ratio of volumes
Amount of added NaOH is 3 mL with equivalence
point is 10 mL
Relative Initial quantities (HA1) 1 - -
Relative Final quantities -
Calculate pH
16
Acid-Base Titrations

• Titration of Weak Acid with Strong Base
• 5.) Region 2 Before the Equivalence Point
• Titration of 50.00 mL of 0.02000 M MES with
  0.1000 M NaOH
• pH pKa when the volume of titrant equals ½Ve

Relative Initial quantities (HA1) 1 - -
Relative Final quantities -
17
Acid-Base Titrations

• Titration of Weak Acid with Strong Base
• 5.) Region 3 At the Equivalence Point
• Titration of 50.00 mL of 0.02000 M MES with
  0.1000 M NaOH
• Exactly enough NaOH to consume HA
• The solution only contains A- ? weak base

Relative Initial quantities (HA1) 1 1 - -
Relative Final quantities - - 1 1
Kb
F - x
x x
18
Acid-Base Titrations

• Titration of Weak Acid with Strong Base
• 5.) Region 3 At the Equivalence Point
• Titration of 50.00 mL of 0.02000 M MES with
  0.1000 M NaOH

Calculate Formal concentration of A-
A- is no longer 0.02000 M, diluted by the
addition of NaOH
Initial volume of HA
Initial concentration of HA
Dilution factor
Total volume
19
Acid-Base Titrations

• Titration of Weak Acid with Strong Base
• 5.) Region 3 At the Equivalence Point
• Titration of 50.00 mL of 0.02000 M MES with
  0.1000 M NaOH

Calculate OH-
Calculate pH
pH at equivalence point is not 7.00
pH will always be above 7.00 for titration of a
weak acid because acid is converted into
conjugate base at the equivalence point
20
Acid-Base Titrations

• Titration of Weak Acid with Strong Base
• 5.) Region 4 After the Equivalence Point
• Titration of 50.00 mL of 0.02000 M MES with
  0.1000 M NaOH
• Adding NaOH to a solution of A-
• NaOH is a much stronger base than A-
• pH determined by excess of OH-

Calculate volume of excess OH-
Amount of added NaOH is 10.10 mL with equivalence
point is 10 mL
Calculate excess OH-
Calculate pH
21
Acid-Base Titrations

• Titration of Weak Acid with Strong Base
• 5.) Titration Curve
• Titration of 50.00 mL of 0.02000 M MES with
  0.1000 M NaOH
• Two Important Features of the Titration Curve

Equivalence point OH- HA Steepest part of
curve Maximum slope
pHpKa Vb ½Ve Minimum slope
Maximum Buffer Capacity
22
Acid-Base Titrations

• Titration of Weak Acid with Strong Base
• 5.) Titration Curve
• Depends on pKa or acid strength
• Inflection point or maximum slope decreases with
  weaker acid
• Equivalence point becomes more difficult to
  identify

weak acid ? small slope change in
titration curve Difficult to detect equivalence
point
Strong acid ? large slope change in
titration curve Easy to detect equivalence point
23
Acid-Base Titrations

• Titration of Weak Acid with Strong Base
• 5.) Titration Curve
• Depends on acid concentration
• Inflection point or maximum slope decreases with
  lower acid concentration
• Equivalence point becomes more difficult to
  identify
• Eventually can not titrate acid at very low
  concentrations

High concentration ? large slope change in
titration curve Easy to detect
equivalence point
Low concentration ? small slope change in
titration curve Difficult to
detect equivalence point At low enough
concentration, can not detect change
24
Acid-Base Titrations

• Titration of Weak Base with Strong Acid
• 1.) Simply the Reverse of the Titration of a
  Weak Acid with a Strong Acid
• Again, Titration Reaction Goes to Completion
• Again, Four Distinct Regions to Titration Curve
• Before acid is added ? just weak base reaction
• pH determined from Kb
• Before equivalence point, ? buffer
• pH determined from Henderson Hasselbach equation

Kb
F - x x
x
25
Acid-Base Titrations

• Titration in Diprotic Systems
• 1.) Principals for Monoprotic Systems Apply to
  Diprotic Systems
• Multiple equivalence points and buffer regions
• Multiple Inflection Points in Titration Curve

Two equivalence points
Kb1
Kb2
26
Acid-Base Titrations

• Titration in Diprotic Systems
• 2.) A Typical Case
• Titration of 10.0 mL of 0.100 M base (B) with
  0.100 M HCl
• pKb1 4.00 and pKb2 9.00
• Volume at First Equivalence Point (Ve)
• Volume at Second Equivalence Point Must Be 2Ve
• Second reaction requires the same number of moles
  of HCl

mmol of B
mmol of HCl
27
Acid-Base Titrations

• Titration in Diprotic Systems
• 2.) A Typical Case
• Point A
• Before Acid Added
• Weak base problem

Kb1
0.100 - x x x
28
Acid-Base Titrations

• Titration in Diprotic Systems
• 2.) A Typical Case
• Point between A B
• Before First Equivalence Point
• Buffer problem

Point (1.5 mL) is before first equivalence point
(10 mL)
29
Acid-Base Titrations

• Titration in Diprotic Systems
• 2.) A Typical Case
• Point B
• Before First Equivalence Point
• Buffer problem

Point B (5 mL) is halfway to first equivalence
point (10 mL)
pH pKa210.00
30
Acid-Base Titrations

• Titration in Diprotic Systems
• 2.) A Typical Case
• Point C
• First Equivalence Point
• Intermediate form of the Diprotic acid

Account for dilution for formal concentration (F)
of BH
Solve for pH using intermediate form equation
Initial volume of B
Initial concentration of B
Dilution factor
Total volume
31
Acid-Base Titrations

• Titration in Diprotic Systems
• 2.) A Typical Case
• Point D
• Before Second Equivalence Point
• Buffer Problem

Point D (15 mL) is halfway to second equivalence
point (2x10 mL). First, subtract Ve (10 mL)
pH pKa15.00
32
Acid-Base Titrations

• Titration in Diprotic Systems
• 2.) A Typical Case
• Point E
• Second Equivalence Point
• Weak acid problem

Account for dilution for formal concentration (F)
of BH22
Initial volume of B
Initial concentration of B
Total volume
Dilution factor
pH determined by acid dissociation of BH22
Kb2
33
Acid-Base Titrations

• Titration in Diprotic Systems
• 2.) A Typical Case
• Point E
• Second Equivalence Point
• Weak acid problem

Ka1
0.0333 - x x x
34
Acid-Base Titrations

• Titration in Diprotic Systems
• 2.) A Typical Case
• Beyond Point E
• Past Second Equivalence Point
• Strong acid problem

pH from volume of strong acid added. Addition of
25.00 mL
Excess acid
Concentration of H
pH
35
Acid-Base Titrations

• Titration in Diprotic Systems
• 3.) Blurred End Points
• Two or More Distinct Equivalence Points May Not
  be Observed in Practice
• Depends on relative difference in Kas or Kbs
• Depends on Relative strength of Kas or Kbs

Only one Equivalence point is clearly evident
Second Ka is too strong and is not a weak acid
relative to titrant
36
Acid-Base Titrations

• Titration in Diprotic Systems
• 4.) Using Derivatives to Find End Point
• Useful when End points overlap
• End Point of titration curve is where slope is
  greatest
• dpH/dV is large
• DpH change in pH between consecutive points
• DV average of pair of volumes
• Second derivative is similar difference using
  first derivative values

End point 2nd derivative is zero
End point 1st derivative is maximum
Dph 4.400-4.2450.155
37
Acid-Base Titrations

• Titration in Diprotic Systems
• 5.) Using Gran Plot to Find End Point
• Method of Plotting Titration Data to Give a
  Linear Relationship
• A graph of Vb10-pH versus Vb is called a Gran
  plot

where Vb volume of strong base added Ve
volume of base needed to reach equivalence
point gA-, gHA activity coefficients 1
38
Acid-Base Titrations

• Titration in Diprotic Systems
• 5.) Using Gran Plot to Find End Point
• Plot is a straight line
• If ratio of activity coefficients is constant
• Slope -KagHA/ga-
• X-intercept Ve (must be extrapolated)
• Measure End Point with data Before Reach End
  Point
• Only use linear region of Gran Plot
• Changing ionic strength changes activity
  coefficients
• added salt to maintain constant ionic strength

Slope Gives Ka
x-intercept gives Ve
Never Goes to Zero, approximation that every mole
of OH- generates one mole of A- is not true as
Vb approaches Ve
39
Acid-Base Titrations

• End Point Determination
• 1.) Indicators compound added in an acid-base
  titration to allow end point detection
• Common indicators are weak acids or bases
• Different protonated species have different colors

40
Acid-Base Titrations

• End Point Determination
• 1.) Indicators compound added in an acid-base
  titration to allow end point detection
• Color Change of Thymol Blue between pH 1 and 11

pK 8.9
pK 1.7
41
Acid-Base Titrations

• End Point Determination
• 2.) Choosing an Indicator
• Want Indicator that changes color in the vicinity
  of the equivalence point and corresponding pH
• The closer the two match, the more accurate
  determining the end point will be

Bromocresol purple color change brackets the
equivalence point and is a good indicator choice
Bromocresol green will change color Significantly
past the equivalence point resulting in an error.
42
Acid-Base Titrations

• End Point Determination
• 2.) Choosing an Indicator

The difference between the end point (point of
detected color change) and the true equivalence
point is the indicator error Amount of indicator
added should be negligible
Indicators cover a range of pHs
43
Acid-Base Titrations

• End Point Determination
• 3.) Example

a) What is the pH at the equivalence point when
0.100 M hydroxyacetic acid is titrated with
0.0500 M KOH? b) What indicator would be a good
choice to monitor the endpoint?