Lecture 8 Buffers and Titration Curves

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Schedule8:10-9:00 Questions9:00-9:45 Test on Acids and Bases9:45-12:00 Buffers and titration curves

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Chapter 15 - Buffers

What do you know about buffers?• What are they used for?• Why are they important?• Anything else?

A buffer is made of a weak acid/weak base conjugate pair in solution

• HF/KF• HNO2/NaNO2

• NH4Cl/NH3

• H2CO3/NaHCO3

• KHCO3/K2CO3

NOT HCl/KCl or HNO3/NaNO3

A buffer resists change in pH when acid or base is added to the solution

WHY?

Major species in a buffer

HA, A¯, H2O

When H3O+ is added to the solution, what happens?

Equilibrium Linking Major Species

HA + H2O ⇄ A¯ + H3O+

Le Chatelier’s principle says the reaction will shift left, but how effective is this mechanism to

absorb added acid?

HA + H2O ⇄ A¯ + H3O+

To answer that question we need to look at the size of K for the reaction:

H3O+ + A¯ H2O + HA

Consider an acetate buffer equilibrium:

HAc + H2O Ac¯ + H⇄ 3O+

When a strong acid is added to a HAc/Ac¯ buffer solution,

H3O+ + Ac¯ H2O + HAc

The reaction goes effectively to completion due to the large K!

Virtually all the added acid is absorbed as long as there is some acetate ion around to react with the added acid.

45

105.5108.1

11

aKK

HAc + H2O Ac¯ + H⇄ 3O+

Similarly for added OH¯ to an acetate buffer

OH¯ + HAc H2O + Ac¯

It is a general result to say:

Strong acid added to weak base goes to completionStrong base added to weak acid goes to completion

So if you have a buffer equilibrium: HA + H2O A¯ + H⇄ 3O+

Added H3O+ or OH¯ will be absorbed by the reaction, buffering the pH.

914

5

108.1101

108.11

xK

K

KK

w

a

b

SUMMARIZE

HAc + H2O Ac¯ + H⇄ 3O+

H3O+ + Ac¯ H2O + HAc

OH¯ + HAc H2O + Ac¯

Added H3O+ or OH¯ will be absorbed by the reaction, buffering the pH.

So a buffer needs: 1) an acid/base equilibrium and

2) 2) reasonble amounts of both components of the acid/base pair

9108.1 K

4105.5 K

Which of the following could be used to make a buffer?

1. HF and KF2. CH3NH2 and CH3NH3Cl3. NaOH and HCl4. NaOH and HNO2

5. HCl and NH3

6. K2HPO4 and NaOH7. K2HPO4 and HNO3

Calculation of buffer pH

What is the pH of a buffer made by mixing 0.10mol HF and 0.2mol NaF to 1000ml of water?

HF + H2O F¯ + H⇄ 3O+

I 0.1 0.2 0 (ignoring auto-ionization of water)C -x +x +xE 0.1-x 0.2-x x Ka = 7.2x10-4

Make the usual approximations to get:

4102.71.0

)2.0( x

Ka Solving, x = [H3O+] = 3.6x10-4

pH = -log(3.6x10-4) = 3.4

Note that the pH depended on the ratio of base to acid and on the value of the Ka.

Consider a hypochlorous buffer made by adding HOCl and NaOCl to the same solution.

The governing equilibrium is HOCl + H2O OCl¯ + H⇄ 3O+

][

]][[ 3

HOCl

OHOClKa

As before, the hydrogen ion concentration depends on the ratio of base and acid:

][

][][ 3

OCl

HOClKOH a

][

][][ 3

OCl

HOClKOH a

This can be rearranged by taking the negative log of both sides:

][

][loglog]log[ 3

OCl

HOClKOH a

][

][log

HOCl

OClpKpH a

Generalizing,

][

][log

acid

basepKpH a

aka the Henderson-Hasselbalch equation

][

][log

acid

basepKpH a

Two important observations to be made here:1. When the concentrations of weak acid and conjugate base

are equal, pH = pKa 2. This equation is based on assumed approximations.

][

]][[

][

]][[ 33

acid

OHbase

xacid

OHxbaseKa

When the approximations are not valid, the Henderson-Hasselbalch equation is not valid.

Over what pH range will a buffer control the pH?

][

][log

acid

basepKpH a

There must be some weak base present to absorb added H+

andThere must be some weak acid present to absorb added OH¯

In practical terms, this means should be kept between 0.1 and 10. ][

][

acid

base

pH = pKa ± 1

A buffer’s pKa defines its buffering range.

Table 17-1, p.822

What acid/base pair would you choose to buffer at pH 6.5?

What acid/base pair would you choose to buffer at pH 5.0?

1. Ammonia/conj acid2. Methylamine/conj acid 3. Ethylamine/conj acid4. Aniline/conj acid 5. Pyridine/conj acid6. I’m lost

When given a Kb or pKb, you must convert it to the pKa to determine the pH range for the buffer.

What acid/base pair would you choose to buffer at pH 7.4?

You can use this equation to calculate approximate buffer pH

][

][log

acid

basepKpH a

What is the pH of a buffer containing 0.15M NH3 and 0.40M NH4ClO3? Ka (NH4

+) = 5.55x10-10

pKa = -log(5.55x10-10) = 9.26

83.840.0

15.0log26.9 pH

Note: This suggests way too much precision – you will be lucky to be at pH = 8.8±0.5

What is the approximate pH of a buffer that contains 0.2M KHCO3 and 0.3M K2CO3?

K+ is a spectator ion: active species areHCO3¯ and CO3

-2

Ka of the weak acid HCO3¯ is 5.6x10-11, pKa =10.3

5.102.0

3.0log3.10log

acid

basepKapH

What is the approximate pH of a buffer that contains 0.1M KH2PO4 and 0.3M K2HPO4?

1.2.62.7.73.12.84.1.75.6.76.11.8

A small note about nomenclature.

When we say we have a 0.20M fluoride buffer, we mean that [HF]+[F¯] = 0.20

So a buffer that contains 0.20M H2CO3 and 0.10M KHCO3 is called a 0.30M carbonate buffer.

Just to review where we are:

A buffer consists of a weak acid/weak base conjugate pair

A buffer works through Le Chatelier’s Principle

Because the reaction of a strong acid/base with a weak base/acid goes to completion, virtually all added H+ or OH¯ is absorbed

The pH range of a given buffer pair is pKa ± 1

The pH of a buffer can be calculated using pH = pKa + log(b/a)

What molar ratio of NaH2PO4 to Na2HPO4 is required to make a pH 7.5 phosphate buffer?

For phosphate, the three Ka values are: 7.5x10-3, 6.2x10-8, and 4.8x10-13.

1. 0.52. 23. 0.34. I am lost

][

][log

acid

basepKpH a

pKa of H2PO4¯ is 7.2

A pH 7.5 phosphate buffer is made using 0.1 moles NaH2PO4 and 0.2 moles Na2HPO4 dissolved in 1.0 liter of water. Remembering that the reaction of a strong acid with a weak base goes to completion, what is the pH after 0.1 moles of HNO3 is added?For phosphate, the three Ka values are: 7.5x10-3, 6.2x10-8, and 4.8x10-13

1. 0.52. 6.73. 7.74. 6.95. I am lost

Hint: first determine what is in solution after the strong acid/weak base reaction, and then use that to determine the pH

Moles HPO4¯2

before

Moles H2PO4¯ before

Moles H+ added

Moles HPO4¯2

after

Moles H2PO4¯ after

pH

0.2 0.1 0 0.2 0.1 7.5

0.2 0.1 0.05

0.2 0.1 0.1 0.1 0.2 6.9

0.2 0.1 0.15

0.2 0.1 0.2

Effect of adding various amounts of strong acid to a 0.3M, pH 7.5 phosphate buffer.

Ignore any possible effects of dilution.

How do you determine the capacity of a buffer – how many

moles of strong acid or base it will protect against?

Buffer Capacity

A buffer works through Le Chatelier’s Principle

HA + H2O ⇄ A¯ + H3O+

The number of moles of acid a buffer can absorb is limited by the #moles of A¯

The number of moles of base a buffer can absorb is limited by the #moles of HA

Could a 500ml solution of 0.2M KH2PO4/0.1M K2HPO4 buffer against addition of 30ml of added 2M KOH?1. Yes2. No3. Lost I am

The number of moles of acid a buffer can absorb is limited by the #moles of A¯

The number of moles of base a buffer can absorb is limited by the #moles of HA

What is the maximum volume of added strong acid that a 500ml solution of 0.2M KH2PO4/0.1M K2HPO4 could buffer against?

1. 10 ml of 1 M HCl2. 25 ml of 1 M HCl3. 40 ml of 1 M HCl4. Lost I am

The number of moles of acid a buffer can absorb is limited by the #moles of A¯

The number of moles of base a buffer can absorb is limited by the #moles of HA

Bottom line on buffer capacity:

to determine capacity vs. acid, look at #moles of weak base present

to determine capacity vs. base, look at #moles of acid present

Titration

• Strong acid/strong base• Strong acid/weak base• Strong base/weak acid

Setup to Do pH Titration of an Acid or Base

Photo © Brooks/Cole, Cengage Learning Company. All rights reserved.

Titration of 50ml of 0.20M HNO3 with 0.100M NaOH: No NaOH Added

Of solution in the beaker (called analyte)

From the burette, called the titrant

Titration of 50ml of 0.20M HNO3: 10.0 mL of 0.100 M NaOH Added

Titration of 50ml of 0.20M HNO3: 50.0 mL (total) of 0.100 M NaOH Added

Titration of 50ml of 0.20M HNO3: 100.0 mL (total) of 0.100 M NaOH Added

Titration of 50ml of 0.20M HNO3: 150.0 mL (total) of 0.100 M NaOH Added

Titration of 50ml of 0.20M HNO3: 200 mL (total) of 0.100 M NaOH Added

Titration of 50ml of 0.20M HNO3 with 0.100 M NaOH

Note: at the equivalence point the number of moles of OH¯ added = the number of moles of H3O+ titrated

The terms equivalence point and end point mean the same thing.

Strong base/weak acid titration

Unlike the titration of a strong acid, the pH of a weak base is buffered at pH valued of pKa ± 1.

][

][log

acid

basepKpH a

][

][log

acid

basepKpH a

The endpoint of the titration is at 50 mL of added OH¯. The midpoint is halfway, at 25 ml of added OH¯.

At the midpoint, pH = pKa.

In other words, the pKa can be read directly from the titration curve.

Below is shown the titration of a weak base with HClO4.

For this buffer it shows how the pH changes with added strong acid.

It can be thought of as a buffer profile.

Each point in this titration is the result of a separate experiment.

Point by point is shown buffer pH for a given buffer composition. In sum, it shows how the pH changes with added strong acid.

It gives you the pKa of the weak acid/base buffer pair.

What percent of the NH3 has been converted to NH4+ after

25ml of HClO4 have been added?

Titration of 100 ml of 0.05M NH3

NH3 + H3O+ NH4+ + H2O

What is the pKa of the conjugate weak acid? a. 11 b. 3 c. 9.3 d. 4.7 e. lost

][

][log

acid

basepKpH a

Titration of 100 ml of 0.05M NH3

What percent of the NH3 has been converted to NH4+ after

20ml of HClO4 has been added?

After 40ml of HClO4 has been added?After 50 ml?

What are the major species in solution at the end of the

titration?

a. ClO4¯, NH3, H3O+ b. HClO4, NH3 c. ClO4¯, NH4

+, H3O+ d. HClO4, NH4

+

If the volume of the analyte NH3 is 100 mL, what was its

concentration at the start of the titration?

a. 0.10M b. 0.20M c. 0.05M d. Lost!

Titration of 100 ml of 0.05M NH3

What is buffering region here, in terms of mL HClO4 added?

Does a buffering range of pH = pKa ± 1 seem about right?

How would you calculate the pH at the endpoint of this titration of 100 ml of 0.05M NH3?

Hint: first you need to know what will react with water, and its concentration!

What is the pH at the midpoint of a HOCl titration (Ka = 3.5x10-8)1. 7.52. 6.53. Lost

What is the pH at the midpoint of a OCl¯ titration (Kb = 2.9x10-7)4. 7.55. 6.56. lost

Consider the titration of 0.20M HOCl. What is the concentration of OCl¯ at the midpoint of the titration (ignoring dilution)?1. 0.20M2. 0.10M3. Not possible to determine without more information4. lost

Titration of a polyprotic acid: H3PO4

• pKa values• Species at 5ml

intervals• pH of

amphoteric salts

How to prepare a buffer

How to prepare a bufferSuppose you wanted to make a pH 7.4 phosphate buffer

Given that pKa1 = 2.12, pKa2 = 7.21, and pKa3 =12.3, what chemicals would you use from this list:H3PO4, KH2PO4, K2HPO4, K3PO4

What would be the ratio of Base/Acid that you would use?

Suppose you wanted a 0.20M, pH 7.4 phosphate buffer. How much base and how much acid would you use to make 1 liter of buffer?

The steps for a buffer preparation calculation:

1. Determine the weak acid/weak base couple using the pH of the buffer as a guide

2. Determine the ratio of base to acid in the buffer using pH = pka + log(B/A)

3. Determine the actual concentrations of B and A to be used based on the desired buffer concentration and the B/A ratio.

Example: Make a 0.15M pH 6.7 carbonate buffer.

1. Determine the weak acid/weak base couple using the pH of the buffer as a guide

For H2CO3, pKa1 = 6.4, pKa2 = 10.3

Choose the weak acid with pKa1 = 6.4, and its conjugate base: H2CO3/HCO3¯

Example: Make a 0.15M pH 6.7 carbonate buffer.

2. Determine the ratio of base to acid in the buffer using pH = pka + log(B/A)

6.7 = 6.4 + log([HCO3¯]/[H2CO3])

[HCO3¯]/[H2CO3] = 2.0

Example: Make a 0.15M pH 6.7 carbonate buffer.

3. Determine the actual concentrations of B and A to be used based on the desired buffer concentration and the B/A ratio.

[HCO3¯]/[H2CO3] = 2.0

[HCO3¯] + [H2CO3] = 0.15

Solve these two equations for the two unknowns:

[HCO3¯] = 0.10M [H2CO3] = 0.05M

Try a problem: What would you need in solution to have a 0.30M, pH 7.1, hypochlorous buffer?HClO: pKa= 7.41. Determine the weak acid/weak base couple

using the pH of the buffer as a guide2. Determine the ratio of base to acid in the buffer

using pH = pka + log(B/A)3. Determine the actual concentrations of B and A

to be used based on the desired buffer concentration and the B/A ratio.

Could you prepare this buffer using only HClO and KOH?

How many moles of HClO would you use to prepare 1.0L of 0.30M, pH 7 buffer?1. 0.12. 0.23. 0.34. lost

About how many moles KOH would you expect to need to make 1.0L the buffer?5. 0.16. 0.27. 0.38. lost