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Acids and Bases - the Three Definitions

1. The Arrhenius Definition of an Acid

2. Acid strength and pKa

3. Ka, pKa, pKb

4. polyprotic acids, pKa1, pKa2, pKa3

5. Kb and pKb

6. Base strength and pKb

7. The pH scale and the

8. Autoionization of water, Kw

9. pH, pOH, and pKa

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Acids and Bases - Simple Definitions

Arrhenius Definition:

Acids: increases [H+] in aqueous solution

Bases: increases [OH-] in aqueous solution

Bronsted-Lowry Definition: (based on proton transfer reactions)

Acids: proton (H+) donor

Bases: proton (H+) acceptor

Lewis Definition:

Acids: electron pair acceptor

Bases: electron pair donor

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Ka and pKa

Acetic Acid is a weak Arrhenius acid, which liberates H+ in solutions

CH3COOH (aq) = CH3COO- (aq) + H+ (aq)

Ka =

[CH3COO-] [H+][CH3COOH]

= 1.76 x 10-5

The pKa is by definition the negative of log10 Ka:

pKa = - log10 (1.76 x 10-

5) = 4.75

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Ionization Constants (1)

5

Ionization Constants (2)

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Kb and pKb

Arrhenius bases liberate OH- in solution.

Kb is the equilibrium constant for this reaction.NH4OH (aq) = NH4

+ (aq) + OH- (aq)

Kb =

[NH4+] [OH-]

[NH4OH]

= 1.76 x 10-5

pKb = - log10 Kb (definition)

pKb = - log10 (1.8 x 10-

5) = 4.74

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Ka and Acid Strength

The stronger the acid, the larger the Ka and the smaller the pKa:

CH3COOH (aq) = CH3COO- (aq) + H+ (aq) Ka = 1.76 x 10-5

HCN (aq) = CN- (aq) + H+ (aq) Ka = 6.17 x 10-10

pKa = 4.75

HNO2 (aq) = NO2- (aq) + H+ (aq)

Ka = 4.6 x 10-4 pKa = 3.34

pKa = 9.21

stronger

weaker

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Polyprotic Acids

pKa1, pKa2, pKa3 describe the dissociation of the first, second, and third ionizable protons.H2CO3 (aq) = HCO3

- (aq) + H+ (aq) Ka1 = 4.3 x 10-7HCO3

- (aq) = CO32- (aq) + H+ (aq)

Ka2 = 5.6 x 10-11

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Kb and Base Strength

The stronger the base, the larger the Kb and the smaller the pKb:

NH4OH (aq) = NH4+ (aq) + OH- (aq)

Kb = 1.8 x 10-5 pKb = 4.74

stronger

weaker

PO43- (aq) + H2O (l) = HPO4

2- (aq) + OH- (aq) Kb = 4.5 x 10-2 pKb =

1.34

Conclusion: phosphate anion is a stronger base than NH4OH.

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Acidity/Basicity of a Solution and the pH ScaleThe degree of acidity or basicity of a solution is measured on the pH scale:

pH = -log10 [H+]

[H+] pH

1 M 0

10-2 M 2

10-4 M 4

10-6 M 6

10-8 M 8

10-10 M 10

10-12 M 12

10-14 M 14

low pH (≈0-1) is strongly acid

high pH (≈13-14) is strongly basic

pH 7 is a neutral solution

pOH = -log10 [OH-]

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Self-Ionization of WaterThe concentrations of H+ and OH- are related by the self- ionization of water -

H2O = H+ + OH- Kw = [H+] [OH-] = 10-14 (at 25°C)

What is the [H+] in pure water? If x = the molarity of [H+] , H2O = H+ + OH- Kw = [H+] [OH-] = 10-14

x x x2 = 10-14

Therefore, x = [H+] = [OH-] = 10-7 M

in pure water at 25°CPure water is pH 7.0. pH 7 a neutral solution,

[H+] = [OH-]

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pH and pOH: Measures of Acidic and Basicity

Because of the self-ionization of water, [H+] and [OH-] are not

independent quantities but are related byKw = [H+] [OH-] = 10-14

pOH is a logarithmic measure of the [OH-] concentration

pH + pOH = 14

pOH = -log10 [OH-]

From the expression for Kw:

-Log10 Kw = - log10 [H+] - log10[OH-] = +14

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Acidity, Basicity, pH, and pOH

pH or pOH can be used to measure acidity

[H+] pH pOH

1 M 0 14

10-2 M 2 12

10-4 M 4 10

10-6 M 6 8

10-8 M 8 6

10-10 M 10 4

10-12 M 12 2

10-14 M 14 0

low pH or high pOH is strongly acid

pH 7 is a neutral solution

high pH or low pOH is strongly acid

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Measurement of pH: the pH Meter

pH varies linearly with output voltage and can be

measured over the range pH 0 to

pH 14

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Acids and Bases – Simple Definitions

Arrhenius Definition:

Acids: increases [H+] in aqueous solution

Bases: increases [OH-] in aqueous solution

Bronsted-Lowry Definition: (based on proton transfer reactions)

Acids: proton (H+) donor

Bases: proton (H+) acceptor

Lewis Definition:

Acids: electron pair acceptor

Bases: electron pair donor

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Bronsted-Lowry Definition

Many proton transfer reactions occur in aqueous solution. These are also acid-base neutralizations according to the Bronsted-Lowry definition (but not according to the Arrhenius definition).

For example, weak acids can neutralize weak bases by a proton transfer reaction. In such reactions there are always two acids and two bases.

HNO2(aq) + NH3(aq) = NO2-(aq) +

NH4+(aq)

acid base base acid

The acids are the proton donors, the bases are proton acceptors.

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Bronsted-Lowry Acid/Base Pairs

Each species participating in a proton transfer reaction can exist in a protonated form and a de-protonated form. The protonated form is the Bronsted acid, and the de-protonated form is the Bronsted base. Thus one speaks of “conjugate acid/base pairs”.

In any Bronsted acid/base neutralization, there are

1. Two Bronsted conjugate acids

2. Two Bronsted conjugate bases

3. Two Bronsted conjugate acid/base pairs

HNO2(aq) + NH3(aq) = NO2-(aq) + NH4

+(aq)Bronsted acid Bronsted base conjugate acid/base pair

Bronsted base Bronsted acid conjugate acid/base pair

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Bronsted-Lowry Acid-Base Neutralizations

H2PO4-(aq) + HCO3

-(aq) = HPO42-(aq) +

H2CO3(aq)

HCl(g) + NH3(g) = NH4Cl (s)

2 NH3(g) + CO2(g) NH2CONH2(aq) + H2O(l)

Which of the following reactions are acid/base neutralizations in the Bronsted-Lowry picture?

Pick out the conjugate acid/base pairs.

H3O+(aq) + OH-(aq) = 2 H2O (l)

Note: any Arrhenius acid (or base) is also a Bronsted acid (or base)

Acid BaseBase Acid

Acid AcidBase Base

not Bronsted-Lowry

Bronsted-Lowry

Bronsted-Lowry

Acid Base

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In the Bronsted-Lowry Definition, many species can function either as Acids OR Bases

H2PO4-(aq) + HCO3

-(aq) = HPO42-(aq) +

H2CO3(aq)

H2PO4-(aq) + HCO3

-(aq) = H3PO4(aq) + CO3

2-(aq)

In this reaction, H2PO4- functions as a

Bronsted acid (why?)

In this reaction, H2PO4- functions as a

Bronsted base (why?)

Whether a chemical species is a Bronsted-Lowry acid or base can depend on the reaction it is in.

Is H2PO4- an acid or a base?

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Relationship of Ka and Kb for a Bronsted Acid/Base Pair

A- + H2O = HA + OH-

[HA] [OH-]

[A-] Kb =

HA + H2O = A- + H3O+

[A-] [H3O+]

Ka =

conj acid

conj base

H3O+H2O

conj acid

conj base

OH-H2O

A Ka can be defined for any conjugate acid, and a Kb for its conjugate base.

Note that Ka . Kb

= Kw

[HA]

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