Acid-Base Equilibria: A Comprehensive Guide with Exercises, Slides of Chemistry

Acids that break up completely in water; these are strong acids. Acids that do not dissociate completely in water are call weak acids.

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INTRODUCTION
ACID-BASE EQUILIBRIA
ACID-BASE EQUILIBRIA
What are acids and bases? Svante Arrhenius noticed that acids release hy-
drogen ions in solution. He classifi ed acids and bases in this way: acids are
compounds that dissociate, or break up, in water to give a proton; bases are
compounds that dissociate in water to accept a proton.
Acids that break up completely in water; these are strong acids. Acids that
do not dissociate completely in water are call weak acids. Can you guess
what bases that dissociate completely are called? Do you think weak bases
Things that don’t dissociate completely are most interesting - and often
overlooked when it comes to safey! Take vinegar, for example. Did you
know that this common kitchen item is actually a weak acid called acetic
acid? While it’s not dangerous in the form you buy at the grocery store be-
cause it’s very dilute (about 4-5% acetic acid), more concentrated solutions
of acetic acid can be quite dangerous even though it’s a weak acid.
Take a look at the dissociation of acetic acid in water.
Consider an acetic acid burn on your skin. Because acetic acid is neutral,
it can be absorbed into the skin readily. Now you’ve got acetic acid in your
hypodermis - the lower layer of your skin! If it were to remain neutral and
not dissociate, this wouldn’t be a problem, but it does dissociate. The ions
then attack the layers of skin and burn it. All the while, more weak acid can
enter the hypodermis causing further damage, and a very severe burn.
CH
3
COOH
H
+
+
CH
3
COO
-
How about the chemical workers -
are they unionized or ionized?
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INTRODUCTION

What are acids and bases? Svante Arrhenius noticed that acids release hy-

drogen ions in solution. He classified acids and bases in this way: acids are

compounds that dissociate, or break up, in water to give a proton; bases are

compounds that dissociate in water to accept a proton.

Acids that break up completely in water; these are strong acids. Acids that

do not dissociate completely in water are call weak acids. Can you guess

what bases that dissociate completely are called? Do you think weak bases

dissociate completely?

Things that don’t dissociate completely are most interesting - and often

overlooked when it comes to safey! Take vinegar, for example. Did you

know that this common kitchen item is actually a weak acid called acetic

acid? While it’s not dangerous in the form you buy at the grocery store be-

cause it’s very dilute (about 4-5% acetic acid), more concentrated solutions

of acetic acid can be quite dangerous even though it’s a weak acid.

Take a look at the dissociation of acetic acid in water.

Consider an acetic acid burn on your skin. Because acetic acid is neutral,

it can be absorbed into the skin readily. Now you’ve got acetic acid in your

hypodermis - the lower layer of your skin! If it were to remain neutral and

not dissociate, this wouldn’t be a problem, but it does dissociate. The ions

then attack the layers of skin and burn it. All the while, more weak acid can

enter the hypodermis causing further damage, and a very severe burn.

CH

3

COOH H

+ CH

3

COO

How about the chemical workers -

are they unionized or ionized?

H

2

O

Alternating Current

Switch

Bulb

Filament

Electrodes

Sample

Sample

ELECTROLYTES

Solution

We can do the same type of experiment with

solutions. Solutions are homogeneous mixtures

of a solute dissolved in a solvent (module #).

When substances are dissolved in water, the

solutions can be tested by seeing if the solu-

tion conducts electricity, just as the metal of the

screwdriver does. An electrolyte is a substance

whose aqueous solutions conduct electricity.

Electrolytes are often identified by experiments

testing the conductivity of solutions.

A simple conductivity experiment is the following:

A plastic screwdriver handle is placed against the

electrodes - no light! When the metal part is used

  • bulb lights brightly! The handle is an insulator,

whereas the metal is a conductor!

In the following pictures, you will be asked to

determine if the solutions are conductors or non-

conductors. These pictures will help you realize

the defi nitions of some key chemical terms, and

hopefully some chemical concepts!

►The diagram below represents the apparatus

with electrodes dipped into liquid water. Is liquid

water a conductor? Look at the top left-hand

corner of the conductivity experiment (the light

bulb) to answer the question.

Be aware of the potential danger of alter-

nating current electricity. Do not attempt

any of these experiments without appropri-

ate supervision.

0.7 M Acetic Acid Solution.

Solute:

H

CO

2

CH

3

CO

2

H

(aq)

NH

4

Cl

-

OH

-

_______

HCO

3

-

►Name the ions in solution. Which species

is the anion? Which species is the cation?

Is the solute an electroyte?

►Name the ions in solution.

Name the molecules in solution.

Is the solute an electrolyte?

►Write the formula for the anion.

Write the formula for the cation.

Write the formula for the solute.

Write the formula for the solvent.

►Is the solute completely dissociated?

Complete the list above of the chemical spe-

cies in solution.

ELECTROLYTES

NaOH Na

+ OH

  • CH

3

COOH H

+ CH

3

COO

Let’s do some ChemLogs in order to further

understand strong electrolytes.

►Why is the equilibrium arrow used for this

weak electrolyte dissociation?

Let’s do some ChemLogs in order to further

understand weak electrolytes.

Na

NaOH

Na

OH

CH

333

COOH

HH

CHCHCH

33

COOCOOCOO

CH

333

COOH

►List the weak electrolytes. List the strong

electrolytes.

Notice the solutes which dissociate completely

cause the light to shine brightly. The dim light

is caused by partial dissociation. Solutes that

dissociate completely are called STRONG

ELECTROLYTES. Solutes that dissociate only par-

tially are called WEAK ELECTROLYTES.tially are called WEAK ELECTROLYTES.

0 1 2 3 4 5 6 7 89 10

10 9 8 7 6 5 4 3 21

0 1 2 3 4 5 6 7 89 10

10 9 8 7 6 5 4 3 21

H

NH

44

Cl

(aq)(aq)

An Ammonium Cloride Solution.

Solute:

CO

2 (aq)2 (aq)

A Carbon Dioxide Solution.

Solute:

(x

mol L

mol L

mol L )

(x

mol L

mol L

mol L )

NaOH

(aq)(aq)

0.7 M Sodium Hydroxide Solution.

Solute:

CH

3

CO

2

H

Dissociation is the separation of ions that occurs

when an ionic compound dissolves.

An ACID is a proton (H

ion) donor. A BASE is

a proton acceptor. This is called the Bronsted-

Lowry system.Lowry system.

SO

4

2-

H

2

SO

4 (aq)

KCl

(aq)

HNO

3 (aq)3 (aq)

KOH

(aq)(aq)(aq)(aq)

K

pH is a measure of the concentration of H

ELECTROLYTES

►Fill in the “empty” ChemLogs for each of the

following experiments:

H

OH

-

NO

3

-

H

K

0.8 M Nitric Acid Solution.

0.8 M Potassium Hydroxide Solution.

0.8 M Potassium Chloride Solution.

0.8 M Sulfuric Acid Solution.

H

2

SO

4

KCl

HNO

33

KOH

H

2

SO

4

KCl

HNO

3

KOH

SO

4

2-

K

Cl

2H

►Strong electrolytes that dissociate completely

to give H

ions are called strong acids. Name

the strong acids on this page.

►Strong electrolytes that completely dissociate

to give a H

acceptor are called strong bases.

Name the strong bases on this page.

►There are other solutes that are strong elec-

trolytes. These are called salts. Name the salts

on this page.

►For each of the solution on this page, state

whether the ph is less than 7, greater than 7, or

equal to 7.

► Complete the chemical reaction and the

chemLog where necessary.

(x

mol L

mol L

mol L )

Solute:

Solute:

Solute:

Solute:

Cl

10 9 8 7 6 5 4 3 21 0 1 2 3 4 5 6 7 89 10

10 9 8 7 6 5 4 3 210 1 2 3 4 5 6 7 89 10

0 1 2 3 4 5 6 7 89 10 10 9 8 7 6 5 4 3 21 0 1 2 3 4 5 6 7 8910 10 9 8 7 6 5 4 3 21

(x

mol L

mol L

(x10 mol L )

mol L

mol L

mol L )

(x

mol L

mol L

mol L )

When pH is between 1 and 7, the solution is

acidic. When the pH is between 7 and 14, the

solution is basic. The pH of pure water is 7 (neu-

tral pH).

pH = –log [H

]

CONJUGATE ACIDS AND BASES

HNO

2

H

NO

2

-

We’ve already seen the following reaction earlier,

but let’s study it more.

We know that HNO

2

is an acid because it gives a

H

ion;

HNO

2

H

NO

2

-

However, at equilibrium, NO

2

-

accepts a proton to

become HNO

2

. That makes NO

2

-

a base;

HNO

2

H

NO

2

-

So, HNO

2

is an acid, and NO

2

-

is its conjugate

base. On the other hand, NO

2

-

is a base, and

HNO

2

is its conjugate acid.

The species formed when an acid loses a proton is

called a CONJUGATE BASE. The species formed

when a base gains a proton is called a CONJU-

GATE ACID.

A simple way to remember how to identify acids

and their conjugate bases, and bases and their

conjugate acids, is the following table:

from the acid,

substract H

conjugate base + H

to the base,

add H

conjugate acid

►What do you notice about the arrangement of

the water molecules around the H

ion in picture

The oxygen atoms in the water molecules have a

slightly negative charge (negative dipole). The H

ion is actually bonded to several water molecules.

As you can see from the picture, a more complete

way of writing the reaction of the dissociation of

nitrous acid is

NO

2

-

H

Nitrous Acid Solution.

HNO

2

HNO

2

H

3

O

NO

2

-

+ H

2

O

We call the H

3

O

ion the hydronium ion.

Note: Water must be acting as a base in this reac-

tion (see next section).

HNO

2

H

11

O

5

NO

2

-

+ 5 H

2

O

Obviously, this could get complicated (and long!)

very fast. A more common way to

►Identify the acid and conjugate base in the fol-

lowing reaction:

We chemists usually just write the most simpli-

fi ed version using H

. You may notice that some

books do use the hydronium ion. As a student, it

is important to recognize that these two versions

indicate the same thing - a proton surrounded by

water molecules.

CH

3

COOH H

+ CH

3

COO

ACIDS

BASES

When NH

3 (g)

is dissolved in water, it acts as a

base. Bases accept protons.

NH

3

NH

4

OH

-

+ H

2

O

Notice that H

2

O is acting as an acid. We cannot

exclude H

2

O as a reactant because we need to

have a balanced chemical reaction.

The dissociation of water gives both an acid

(substance that provides a proton) and a base

(substance that accepts a proton). We call water

AMPHIPROTIC.

K

w

) = 1 x 10

H

2

O

H

+ OH

In the general equilibrium module, we learned to write

equilibrium constants. For water,

K

c

[H

][OH

]

[H

2

O]

Since the concentration of H

2

O in water is 55.6 M,

it can be regarded as a constant. A simplified

version of K

c

is called the ion-product constant

of water.

K

w

= [H

][OH

]

K

w

is a constant. At 25°, the concentrations of

both H

and OH

are 1 x 10

mol L

►Will the value of K

w

change at varying tem-

peratures? Explain.

Remember the definition of pH from earlier in this

module.

CONJUGATE ACIDS AND BASES

Other examples include:

pH = – log [H

]

pOH = – log [OH

]

pK

w

= - log K

w

►Determine the pH, pOH, and pK

w

for the

dissociation of water. Check your answers by

using the fact that pH + pOH = pK

w

►What is the pH of a solution in which the pOH = 4?

Which is greater for this solution - the value of

[H

] or the value of [OH

]?

OH

H

H

2

O + H

2

O

H

3

O

+ OH

which can be simplified to

For most purposes, we can simplify pictures of

solvent molecules. The neutral water molecules

in the following picture are simplified to a blue

background. The ions in the water are thus shown

more clearly.

Now that we’ve seen that acids in water give hy-

drogen ions, let’s look at pure water. We’ve stud-

ied the following picture earlier and determined

that water is a non-electrolyte because the light

bulb didn’t light. While all of this is true, there’s

more to this story.

H

2

O

Pure Distilled Water

►For a review, state the defi nition of a non-

electrolyte.

When a very sensitive light is used in the conduc-

tivity experiment, the light lights. How can this

be? Well, pure water does form ions in solution;

it forms protons and hydroxide ions. But, the con-

centration of these ions is so low that a sensitive

light is needed in the conductivity experiment to

see evidence of the ions. To show this in the form

of a reaction, we write

This calculation can be used for more than just the

concentration of H

. The pX of X (where X is any

number) is equal to the –log of X.

►Water is an example of a molecule which gives

2 conjugate acid/base pairs. What are they?

Note that there are no units associated with equi-

librium constant values, K. This is standard, and

you are not expected to show units.

º C K

w

pK

w

0 0.12 x 10

10 0.29 x 10

25 1.01 x 10

Ion Product of Water.

INDICATORS

Water molecules

HIn

In

-

HIn H

  • In

C

15

H

15

N

3

O

2

H

+ C

15

H

14

N

3

O

2

-

H

One way to determine the pH of a solution is to use an indicator. An indicator exists in different colored forms

depending on whether the compound is protonated or unprotonated. The indicator shown is purple cabbage extract.epending on whether the compound is protonated or unprotonated. The indicator shown is purple cabbage extract.

►The 1 x 12 array shown below shows the pH where the color changes.

Mark which pH values show [HIn] > [In

-

].

Mark which pH values show [HIn] < [In

-

].

Mark which pH values show [HIn] = [In

-

].

K

a

[In

-

]

[HIn]

=

[H

]

Therefore, when [HIn] = [In

-

],

K

a

[In

-

]

[HIn]

=

[H

]

= 1, so, K

a

= [H

].

►Which part of the solution causes the color, the solute or the solvent?

H

pH =pH = 4 5 6 7 8 9

►Is purple cabbage indicator an acid or a

base?

►Write the K

a

expression for HIn H

  • In

Rearranging the K

a

expression gives

To see “pure” color,

[In

-

]

[HIn]

=

for blue. For “pure” purple,

[In

-

]

[HIn]

=

K

a

=

[H

]

K

a

=

[H

]

K

a

=

[H

]

10 K

a

=

[H

]

Therefore, the pH range of an indicator is pK

a

Malachite green

Cresol red

Metacresol purple

Orange IV

Thymol blue

Methyl yellow

Bromophenol blue

Congo red

Methyl orange

Methyl red

Chlorophenol red

Litmus

para-Nitrophenol

Bromocresol purple

Bromocresol green

Neutral red

Phenol red

Cresol red

Curcumin α

meta-Cresol purple

Thymol blue

Phenolphthalein

Malachite green

Thymolphthalein

Alizarin yellow R

Curcumin ß

Clayton yellow

Various indicators

Bromothymol blue

Thompson-Markow

Universal Indicator

pH Ranges of Indicators

pH

[H

]

10

Here is a list of several acid/base indicators and

the pH range in which they are useful:

A universal indicator, shown at the bottom, is a

mixture of several indicators. Universal indica-

tors have a wider range of usefullness because

they mix indicators.

INDICATORS

►What is the pH range of the Thompson-Mar-

kow universal indicator?

What is [H

] at pH 0?

►The Thompson-Markow Universal Indica-

tor is a mixture of six indicators. Metacresol purple

is one of them; name the 5 others.

INDICATOR WELL TRAYS

pH

pH

pH

pOH

pOH

pOH

1 2 3 4 5 6 7 8 9 10 11 12 13 14

14 13 12 11 10 9 8 7 6 5 4 3 2 1

1 2 3 4 5 6 7 8 9 10 11 12 13 14

1 2 3 4 5 6 7 8 9 10 11 1213 14

14 13 12 11 10 9 8 7 6 5 4 3 2 1

14 13 12 11 10 9 8 7 6 5 4 3 2 1

pH

pOH

1 2 3 4 5 6 7 8 9 10 11 12 13 14

14 13 12 11 10 9 8 7 6 5 4 3 2 1

pH

pH

pH

pOH

pOH

pOH

1 2 3 4 5 6 7 8 9 10 11 12 13 14

14 13 12 11 10 9 8 7 6 5 4 3 2 1

1 2 3 4 5 6 7 8 9 10 11 12 13 14

1 2 3 4 5 6 7 8 9 10 11 1213 14

14 13 12 11 10 9 8 7 6 5 4 3 2 1

14 13 12 11 10 9 8 7 6 5 4 3 2 1

pH

pOH

1 2 3 4 5 6 7 8 9 10 11 12 13 14

14 13 12 11 10 9 8 7 6 5 4 3 2 1

pH

1 2 3 4 5 6 7 8 9 10 11 12 13 14

pH

pH

pOH

pOH

pOH

1 2 3 4 5 6 7 8 9 10 11 12 13 14

14 13 12 11 10 9 8 7 6 5 4 3 2 1

1 2 3 4 5 6 7 8 9 10 11 1213 14

14 13 12 11 10 9 8 7 6 5 4 3 2 1

14 13 12 11 10 9 8 7 6 5 4 3 2 1

pH

pOH

1 2 3 4 5 6 7 8 9 10 11 12 13 14

14 13 12 11 10 9 8 7 6 5 4 3 2 1

Below are several chemLogs showing the pH and pOH for each

well. Each well contains a solution of methyl orange at the differ-

ent pH values listed..

►What can you determine

about the relationship between

pH and pOH?

►Complete the following

equation:

pH + pOH = ______

►What is the pK

a

of methyl

orange?

►The approximate pH

range of any indicator is the

range between the pK

a

and the pK

a

    1. What is the

pH range of methyl orange?

►Remember that K

a

x K

b

K

w

for any conjugate acid/

base pair. What is the pK

b

for

methyl orange? Using pK

b

determine the pOH range for

methyl orange.

pH

TITRATION

ACID BASE EQUILIBRIAACID BASE EQUILIBRIA

HCl

Five drops of 0.01 M HCl were added to each of

the wells in the 1 x 12 tray.

►Is the solution in each of these

wells acidic, neutral, or basic?

Are the solutions at equilibrium?

To each well above, drops of 0.01 M NaOH were

added. The numbers above the wells represents

the drops of NaOH added.the drops of NaOH added.

►Which solution is acidic?

Which solution is neutral?

Which solution is basic?

Where are the water molecules that are shown

coming from?

Write the net ionic equation for this titration

reaction.

Is [H

] higher in the well with 1 drop of base

added, or 5 drops added? What about pH?

Is [H

] higher in the well with 5 drop of base

added, or 10 drops added? What about pH?

►So, as [H

] increases, pH decreases, and

vice versa. What happens to pH as [OH

-

]

increases?

►What is the pH of the 0.01 M HCl that we

started with?

H

2

O

DEFINITION:

pH = - log [H

]

NaOH NaCl

HCl H

2

NaOH NaCl O

A solution of strong base, NaOH, can be titrated

with a solution of strong acid, HCl. The overall

chemical reaction for the titration is the following:chemical reaction for the titration is the following:

pH

Drops of 0.01 M NaOH Added

A B C D E B

��

��

���

►Experiment B is a strong acid titrated with

a strong base. Try to produce the titration

curve for this experiment. The chemLog is

shown at the right to help you with this.

TITRATION

ACID BASE EQUILIBRIAACID BASE EQUILIBRIA

Thompson-Markow

Universal Indicator

Titration of Strong Acid

with Strong Base

Titration of Weak Acid

with Strong Base

Titration of Strong Acid

with Weak Base

Titration of Weak Acid

with Weak Base

HCl

H

2

O

NaOH

NaCl

A solution of HCl is shown in each of the drawings.

TITRATION

ACID BASE EQUILIBRIAACID BASE EQUILIBRIA

���� ����

���� ����

►What is the limiting reagent for each of the

sketches that you drew?

►Which of the sketches that you drew is at

equilibrium?

►Are the drawings of HCl in solution (before

NaOH is added) at equilibrium?

►Draw a sketch for each sample after the

NaOH shown has been added. The water mol-

ecules are shown for you by the pink background.

A LIMITING REAGENT is a reactant that governs

the maximum yield of product that is possible.

For example, when 1 NaOH is added to a solu-

tion with 10 HCl, the NaOH is the limiting reagent

because it governs how many NaCl and water

molecules can be formed in the reaction.

►Is the pH of each of the solutions that you

have drawn acidic, neutral, or basic?

HCl H

2

NaOH NaCl O

BUFFERS

In experiments, we often need to control the [H

]

of the solution. This is done with buffers. A buff-

ered solution resists changes in [H

]. Buffers can

have a predetermined pH, with acidic buffers at

any chosen value between pH 0-7, and basic buf-

fers at any chosen value between pH 7-14.

Two dilute

solutions of

acetic acid

at the same

concentration.

Add acid.

Add base.

When acid is added, the buffer

accepts protons.

When base is added, the buffer

donates protons.

Add more

acid.

Add more

base.

The buffer capacity is an indication of the amount

of acid or base that can be added before the buffer

loses its ability to resist the pH change.

►At which point in each of the additions above

was the buffer capacity exceeded?

acetic acid

acetate ion

proton

sodium

Acidic buffers are solutions containing weak acids

and the salts of weak acids, eg. CH

3

COOH and

CH

3

COONa. Basic buffers are solutions contain-

ing weak bases and the salts of weak bases, eg.

NH

3

and NH

4

Cl.

CH

3

COOH H

+ CH

3

COO

CH

3

COONa Na

+ CH

3

COO

CH

3

COOH H

+ CH

3

COO

CH

3

COONa Na

+ CH

3

COO

HCl

NaOH

HCl

NaOH

HENDERSON-HASSELBALCH EQUATION

How can we design a buffer with a specifi ed pH?

Let’s examine the chemical reaction for solution

containing a general weak acid and its salt - a

buffer.

K

a

x

[A

[A

[A ]

[HA]

HA H

+ A

+ A

+ A

►Write the K

a

expression for this reaction.

After rearranging the K

a

expresstion to determine

what [H

] is equal to, we determine that

[H

] =

We can now determine the pH. Write the pH expres-

sion by taking the negative log of each side of the

[H

] expression.

pH = – log [H

] =

K

a

x

[A

[A

[A ]

[HA]

  • log

[A

[A

[A ]

[HA]

= – log K

a

  • log

[HA]

[A

[A

[A ]

= pK

a

  • log

Since acidic buffers are solutions of weak acids

and their salt, HA loses only a tiny fraction of its

protons. What are the dominant species (the most

concentrated) in solution? They HA, becasue HA

is a weak acid, and A

is a weak acid, and A

is a weak acid, and A , because it comes from the

complete dissociation of the salt NaA. Because

they are so dominant in solution, we can approxi-

mate [HA] and [A

mate [HA] and [A

mate [HA] and [A ] of a buffer by their initial con-

centrations. The Henderson-Hasselbalch equation

states that:

pH ≈

[HA]

[A

[A

[A ]

pK

a

  • log

initial

Let’s calculate the pH of a buffer solution in which

0.040 M CH

3

COONa

(aq)

and 0.080 M CH

3

COOH

(aq)

are mixed at 25 °C.

►Identify the acid and its conjugate base in this

mixture. Identify the ions from the salt in this

mixture.

►Write the equilibrium equation for acetic acid,

and rearrange the K

a

for this equation to give

[H

].

►Use the Henderson-Hasselbalch equation to

find the pH.

NaA Na

+ A

A

A