Acids and Bases

•  Brønsted Acids and Bases •  The Acid-Base Properties of Water •  The pH Scale •  Strong and Weak Acids and Bases •  Conjugate Acid-Base Pairs

Brønsted Acids and Bases When a Brønsted acid donates a proton, what remains of the acid is known as a conjugate base. The two species HCl and Cl– are known as a conjugate acid-base pair or simply a conjugate pair.

HCl(aq) + H2O(l) ⇌       H3O+(aq) + Cl–(aq)

Gains a proton

Loses a proton

acid base conjugate acid

conjugate base

Brønsted Acids and Bases When a Brønsted base accepts a proton, the newly formed protonated species is known as a conjugate acid.

NH3(aq) + H2O(l) ⇌       NH4+(aq) + OH–(aq)

acid base conjugate acid

conjugate base

Gains a proton

Loses a proton

The Acid-Base Properties of Water A species that can behave either as a Brønsted acid or a Brønsted base is called amphoteric.

H2O(l) + H2O(l) ⇌       H3O+(aq) + OH–(aq)

Kw = [H3O+][OH–] = 1.0 x 10–14 (at 25°C)

The Acid-Base Properties of Water The relative amounts of H3O+ and OH– determine whether a solution is neutral, acidic, or basic.

§ When [H3O+] = [OH–], the solution is neutral

§ When [H3O+] > [OH–], the solution is acidic

§ When [H3O+] < [OH–], the solution is basic

Kw = [H3O+][OH–] = 1.0 x 10–14 (at 25°C)

Practice Problem The concentration of hydroxide ions in the antacid milk of magnesia is 5.0 x 10–4 M. Calculate the concentration of hydronium ions at 25°C.

The pH Scale The acidity of an aqueous solution depends on the concentration of hydronium ions, [H3O+]. The pH of a solution is defined as the negative base-10 logarithm of the hydronium ion concentration (in mol/L) In pure water at 25°C, [H3O+] = log1.0 x 10–7

pH = –log(1.0 x 10–7) = 7.00 pH is a dimensionless quantity.

pH = –log[H3O+] [H3O+] = 10–pH

The pH Scale

The pH Scale A pOH scale analogous to the pH scale can be defined as the negative base-10 logarithm of the hydroxide ion concentration. From the definition of pH and pOH:

pOH = –log[OH–] [OH–] = 10–pOH

pH + pOH = 14.00

The pH Scale

Practice Problem Determine the pH of a solution at 25°C in which the hydronium ion concentration is 3.2 x 10–9 M.

Practice Problem Calculate the hydronium ion concentration at 25°C in which the pOH is 2.74.

Strong Acids and Bases Strong acid dissociations are not treated as equilibria, rather as processes that go to completion.

Hydrochloric acid HCl(aq) + H2O(l) H3O+(aq) + Cl–(aq)

HBr(aq) + H2O(l) H3O+(aq) + Br–(aq) Hydrobromic acid

HI(aq) + H2O(l) H3O+(aq) + I–(aq) Hydroiodic acid

HNO3(aq) + H2O(l) H3O+(aq) + NO3–(aq) Nitric acid

HClO3(aq) + H2O(l) H3O+(aq) + ClO3–(aq) Chloric acid

HClO4(aq) + H2O(l) H3O+(aq) + ClO4–(aq) Perchloric acid

H2SO4(aq) + H2O(l) H3O+(aq) + HSO4–(aq) Sulfuric acid

Strong Acids and Bases The list of strong bases consists of the hydroxides of alkali metals and the heaviest alkaline earth metals.

LiOH(aq) Li+(aq) + OH–(aq)

NaOH(aq) Na+(aq) + OH–(aq)

KOH(aq) K+(aq) + OH–(aq)

RbOH(aq) Rb+(aq) + OH–(aq)

CsOH(aq) Cs+(aq) + OH–(aq)

Ca(OH)2(aq) Ca2+(aq) + 2OH–(aq)

Sr(OH)2(aq) Sr2+(aq) + 2OH–(aq)

Ba(OH)2(aq) Ba2+(aq) + 2OH–(aq)

Group 1A hydroxides

Group 2A hydroxides

Practice Problems 1. Calculate the concentration of HNO3 in a solution at 25°C that has a pH of 2.06. 2. Calculate the pH of a 6.1 x 10–2 M Ba(OH)2 solution at 25°C.

Weak Acids The ionization of a weak monoprotic acid HA in water is represented by:

Ka is called the acid ionization constant.

The larger the value of Ka, the stronger the acid.

HA(aq) + H2O(l) ⇌       H3O+(aq) + A–(aq)

[ ]

+3

a

H O AHA

K−⎡ ⎤ ⎡ ⎤⎣ ⎦ ⎣ ⎦=

Solution (at 25 °C) Ka pH

0.10 M HF 7.1 x 10–4 2.09

0.10 M CH3COOH 1.8 x 10–5 2.87

Practice Problem-Weak Acids Calculate the pH of a 0.50 M HF solution at 25°C.

HF(aq) + H2O(l) ⇌       H3O+(aq) + F–(aq)

[ ]

+3 4

a

H O F7.1 10

HFK

−

−⎡ ⎤ ⎡ ⎤⎣ ⎦ ⎣ ⎦= = ×

Percent Ionization

A quantitative measure of the degree of ionization is percent ionization.

[ ]3 eq

0

H Opercent ionization 100%

HA

+⎡ ⎤⎣ ⎦= ×

Solution (at 25 °C) pH % ionization

0.5 M HF 1.72 3.8

1.0 M HF 1.57 2.7

Percent Ionization

HF(aq) + H2O(l) ⇌     H3O+(aq) + F–(aq)

Solution (at 25 °C) pH % ionization

0.5 M HF 1.72 3.8

1.0 M HF 1.57 2.7

Practice Problems Determine the Ka of a weak acid that has a concentration of 0.065 M and a pH of 2.96 at 25°C.

Weak Bases The ionization of a weak base is incomplete and is treated in the same way as the ionization of a weak acid.

Kb is called the base ionization constant.

The larger the value of Kb, the stronger the base.

B(aq) + H2O(l) ⇌       HB+(aq) + OH–(aq)

[ ]

+

b

HB OHB

K−⎡ ⎤ ⎡ ⎤⎣ ⎦ ⎣ ⎦=

Practice Problems-Weak Base Calculate the pH of a 0.040 M ammonia solution at 25°C.

NH3(aq) + H2O(l) ⇌       NH4+(aq) + OH–(aq)

+4 5

b3

NH OH1.8 10

NHK

−

−⎡ ⎤ ⎡ ⎤⎣ ⎦ ⎣ ⎦= = ×

⎡ ⎤⎣ ⎦

Conjugate Acid-Base Pairs A strong acid ionizes completely in water:

HCl(aq)                           H+(aq) + Cl–(aq) No affinity for

the H+ ion

Cl–(aq) + H2O(l)                           HCl(aq) + OH–(aq) X

The chloride ion is a weak conjugate base.

Conjugate Acid-Base Pairs A strong acid ionizes completely in water:

HF(aq) ⇌               H+(aq) + F–(aq) Strong affinity for the H+ ion

F–(aq) + H2O(l) ⇌       HF(aq) + OH–(aq)

The fluoride ion is a strong conjugate base.

Conjugate Acid-Base Pairs A strong acid has a weak conjugate base.

A weak acid has a strong conjugate base.

A strong base has a weak conjugate acid.

A weak base has a strong conjugate base.

Conjugate Acid-Base Pairs A simple relationship between the ionization constant of a weak acid (Ka) and the ionization constant of a weak base (Kb) can be derived:

CH3COOH(aq) ⇌             H+(aq) + CH3COO–(aq)

CH3COO– (aq) + H2O(l) ⇌           CH3COOH(aq) + OH–(aq)

H2O(l) ⇌           H+(aq) + OH–(aq)

[ ]

+3

a3

H CH COOCH COOH

K−⎡ ⎤ ⎡ ⎤⎣ ⎦ ⎣ ⎦=

[ ]3b

3

CH COOH OH

CH COOK

−

−

⎡ ⎤⎣ ⎦=⎡ ⎤⎣ ⎦

[ ][ ]+

3 3

3 3

H CH COO CH COOH OHH OH

CH COOH CH COO

− −

+ −

−

⎡ ⎤ ⎡ ⎤ ⎡ ⎤⎣ ⎦ ⎣ ⎦ ⎣ ⎦ ⎡ ⎤ ⎡ ⎤× = ⎣ ⎦ ⎣ ⎦⎡ ⎤⎣ ⎦

Ka x Kb = Kw

Practice Problems Determine the Kb of the benzoate ion (C6H5COO–).

Diprotic and Polyprotic Acids Diprotic and polyprotic acids undergo successive ionizations, losing one proton at a time, and each has a Ka associate with it.

Ka1 > Ka2 For a given acid, the first ionization constant is much larger than the second, and so on.

H2CO3(aq) ⇌         H+(aq) + HCO3–(aq)

HCO3– (aq) ⇌          H+(aq) + CO3

2– (aq) + 2

3a2

3

H CO

HCOK

−

−

⎡ ⎤ ⎡ ⎤⎣ ⎦ ⎣ ⎦=⎡ ⎤⎣ ⎦

[ ]

+3

a12 3

H HCOH CO

K−⎡ ⎤ ⎡ ⎤⎣ ⎦ ⎣ ⎦=

Practice Problem

Calculate the concentrations of all species present at equilibrium in a 0.10 M solution of oxalic acid (H2C2O4) at 25°C.

H2C2O4(aq) ⇌         H+(aq) + HC2O4–(aq) Ka1 = 6.5 x 10–2

HC2O4– (aq) ⇌          H+(aq) + C2O4

2– (aq) Ka2 = 6.1 x 10–5

Acid-Base Properties of Salt Solutions Salt hydrolysis occurs when ions produced by the dissociation of a salt react with water to produce either hydroxide ions or hydronium ions. Basic salts (conjugates of weak acids): Acidic salts (conjugates of weak bases)

F–(aq) + H2O(l) ⇌       HF(aq) + OH–(aq)

NH4+(aq) + H2O(l) ⇌       NH3(aq) + H3O+(aq)

Acid-Base Properties of Salt Solutions Calculate the pH of a 0.10 M solution of sodium fluoride (NaF) at 25°C.

Acid-Base Properties of Salt Solutions The pH of salt solutions can be qualitatively predicted by determining which ions facilitate hydrolysis. Examples

A cation that will make a solution acidic is

§ The conjugate acid of a weak base

§ A small, highly charged metal ion (other than Group 1A or 2A)

NH4+ , CH3NH3

+ , C2H5NH3+

Al3+ , Cr3+ , Fe3+ , Bi3+

An anion that will make a solution basic is

§ The conjugate base of a weak acid

CN– , NO2– , CH3COO–

A cation that will not affect the pH of a solution is

§ A Group 1A or heavy Group 2A cation (except Be2+)

Li+ , Na+ , Ba2+

An anion that will not affect the pH of a solution is

§ The conjugate base of a strong acid

Cl– , NO3– , ClO4

–

Acid-Base Properties of Salt Solutions The pH of a solution that contains a salt in which both the cation and the anion hydrolyze depends on the relative strengths of the weak acid and base. Qualitative predictions can be made using the Kb (of the salts anion) and the Ka (of the salts cation).

§ When Kb > Ka, the solution is basic

§ When Kb < Ka, the solution is acidic

§ When Kb ≈ Ka, the solution is neutral or nearly neutral

Lewis Acids and Bases A Lewis base is a substance that can donate a pair of electrons.

A Lewis acid is a substance that can accept a pair of electrons.

Ammonia, a Lewis base

Boron trifluoride a Lewis acid

empty unhybridized 2pz

orbital

A coordinate covalent bond

Acids and Bases

Brønsted Acids and Bases The Acid-Base Properties of Water The pH Scale Strong Acids and Bases The Ionization Constant, Ka Calculating pH from Ka Using pH to Determine Ka The Ionization Constant, Kb Calculating pH from Kb Using pH to Determine Kb The Strength of a Conjugate Acid or Base The Relationship Between Ka and Kb of a Conjugate Acid-Base Pair Diprotic and Polyprotic Acids Basic Salt Solutions Acidic Salt Solutions Neutral Salt Solutions Lewis Acids and Bases