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Acid-Base Titrations

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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

- pKa of amino acids in an active-site of a protein are related to its function

- 1.)Experimental Measurements of pKa

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

- impact of the Asp on the pKa of His in the His-Asp catalytic dyad.

- 2.)Example:

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

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.

- 3.)Overview

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: 129–135

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.

- 1.)Graph of How pH changes as Titrant is Added

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:

- 1.)Graph of How pH changes as Titrant is Added

Titrant

Analyte

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-

- 2.)Volume Needed to Reach the Equivalence Point

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.

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

- Titration curve for 50.00 mL of 0.02000 M KOH with 0.1000 M HBr

- 3.)Before the Equivalence Point

Initial volume of OH-

Calculate Remaining [OH-]:

Total volume

Fraction of OH-

Remaining

Initial concentration

of OH-

Dilution Factor

Calculate [H+] and pH:

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

- Titration curve for 50.00 mL of 0.02000 M KOH with 0.1000 M HBr

- 4.)At the Equivalence Point

Kw

Kw= 1x10-14

x x

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

- Titration curve for 50.00 mL of 0.02000 M KOH with 0.1000 M HBr

- 5.)After the Equivalence Point

Calculate volume of excess H+:

Calculate excess [H+]:

Volume of excess H+

Initial

concentration

of H+

Dilution factor

Total volume

Calculate pH:

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

- Rapid Change in pH Near Equivalence Point

- 6.)Titration Curve

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-
- Weak base with pH determined by Kb

- Before any added base, just weak acid (HA) in water

- 1.)Four Regions to Titration Curve

Ka

Kb

K

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

- Beyond equivalence point,excess strong base is added to A- solution

- 1.)Four Regions to Titration Curve

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

- Titration of 50.00 mL of 0.02000 M MES with 0.1000 M NaOH

mmol of HA

mmol of base

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:

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

Calculate pH:

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

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

Kb

F - x x x

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

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

Volume of excess OH-

Initial

concentration

of OH-

Total volume

Dilution factor

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:

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

pH=pKa

Vb = ½Ve

Minimum slope

Maximum Buffer Capacity

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

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

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
- Va=½Ve then pH = pKa (for BH+)
- pKa and pKb can be determined from titration curve

Kb

F - x x x

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

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 Be2Ve
- Second reaction requires the same number of moles of HCl

- Titration of 10.0 mL of 0.100 M base (B) with 0.100 M HCl

mmol of B

mmol of HCl

Acid-Base Titrations

- Titration in Diprotic Systems
2.) A Typical Case

- Point A
- Before Acid Added
- Weak base problem

- Point A

Kb1

0.100 - x x x

Acid-Base Titrations

- Titration in Diprotic Systems
2.) A Typical Case

- Point between A &B
- Before First Equivalence Point
- Buffer problem

- Point between A &B

Point (1.5 mL) is before first equivalence point (10 mL)

Acid-Base Titrations

- Titration in Diprotic Systems
2.) A Typical Case

- Point B
- Before First Equivalence Point
- Buffer problem

- Point B

Point B (5 mL) is halfway to first equivalence point (10 mL)

pH = pKa2=10.00

Acid-Base Titrations

- Titration in Diprotic Systems
2.) A Typical Case

- Point C
- First Equivalence Point
- Intermediate form of the Diprotic acid

- Point C

Account for dilution for formal concentration (F) of BH+

Solve for pH using intermediate form equation

Initial volume of B

Initial

concentration

of B

Total volume

Dilution factor

Acid-Base Titrations

- Titration in Diprotic Systems
2.) A Typical Case

- Point D
- Before Second Equivalence Point
- Buffer Problem

- Point D

Point D (15 mL) is halfway to second equivalence point (2x10 mL). First, subtract Ve (10 mL)

pH = pKa1=5.00

Acid-Base Titrations

- Titration in Diprotic Systems
2.) A Typical Case

- Point E
- Second Equivalence Point
- Weak acid problem

- Point E

Account for dilution for formal concentration (F) of BH2+2

Initial volume of B

Initial

concentration

of B

Total volume

Dilution factor

pH determined by acid dissociation of BH2+2

Kb2

Acid-Base Titrations

- Titration in Diprotic Systems
2.) A Typical Case

- Point E
- Second Equivalence Point
- Weak acid problem

- Point E

Ka1

0.0333 - x x x

Acid-Base Titrations

- Titration in Diprotic Systems
2.) A Typical Case

- Beyond Point E
- Past Second Equivalence Point
- Strong acid problem

- Beyond Point E

pH from volume of strong acid added. Addition of 25.00 mL:

Excess acid:

Concentration of H+:

pH:

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

- Two or More Distinct Equivalence Points May Not be Observed in Practice

Only one Equivalence point is clearly evident

Second Ka is too strong and is not a weak acid relative to titrant

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 = 4.400-4.245=0.155

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

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

- Plot is a straight line

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

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

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

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.

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

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?