Chem 1310: Introduction to physical chemistry

Part 4: Acids and bases in water

Peter H.M. Budzelaar

About acids and bases

Acids and bases play a key role in chemistry, in particular in water (including in living things).

Acid-base reactions are fairly simple examples of chemical equilibria. Because they are so important, they still merit special attention.

Also, you will see a relation between chemical structure and reactivity for the first time here.

What is an acid?•Brønsted-Lowry:

– An acid is an H+ donor

– A base is an H+ acceptor

•Lewis:– An acid is an electron-pair acceptor

– A base is an electron-pair donor

The Lewis definition is the more general one. In water, the two are nearly equivalent, and talking about H+ is easier than figuring out where the electrons go, so we mostly use Brønsted-Lowry.

What is an acid? (2)

In water, we never have free H+ but rather H3O+. This is what you will see in all equations. However, acid-base reactions still involve transfer of a proton.

A "free proton" is so electron-poor and reactive it will attach itself to anything it encounters.

Acids and bases in water

An acid donates a proton to water, forming H3O+.

H2S + H2O HS⇋ - + H3O+

The acid can donate a proton.

Its conjugate base can accept a proton.

acidconjugate base

acid conjugate base

H2S is a neutral acidH2O is a neutral base.HS- is an anionic base.H3O+ is a cationic acid.

Acids and bases in water (2)

NH4+ + H2O NH⇋ 3 + H3O+

HSO4- + H2O SO⇋ 4

2- + H3O+

acidconjugate base

acid conjugate baseNH4

+ a cationic acidHSO4

- is an anionic acid.

acidconjugate base

acid conjugate base

Acids and bases in water (3)

The reaction doesn't have to be with water:

HSO4- + NH3 SO⇋ 4

2- + NH4+

But this is just a combination of the equations on the previous slide.

acidconjugate base

acid conjugate base

Acids, bases and equilibria

For acid-base reactions (in water), we don't worry about kinetics.

Equilibria are established instantly.

What about bases?

A base abstracts a proton from water, forming OH-.

H2O + NH3 OH⇋ - + NH4+

It doesn't matter whether you are talking about an acid and its conjugated base, or a base and its conjugated acid...

conjugate acidbase

conjugate acid base

What about bases?

H2O + H2O OH⇋ - + H3O+

Water is an acid and a base!

conjugate acidbase

conjugate acid base

Acid and base strength

In water, you cannot have acids stronger than H3O+

They simply protonate water, forming H3O+ quantitatively.

We call them "strong acids".

Nor can you have bases stronger than OH-.They simply deprotonate water, forming OH-

quantitatively.

We call them "strong bases".

Water is a convenient reference

There will be a scale for acids:

and a similar one for bases:

strong weak very weakH3O+ H2O

strongweakvery weakH2O OH-

Water as a reference(H3O+/H2O/OH-)

H2SO4 + H2O HSO4- + H3O+

H2SO4 is a very strong acid (>H3O+)

HSO4- is a very weak base, weaker than H2O

H2CO3 + H2O HCO3- + H3O+

H2CO3 + OH- HCO3- + H2O

H2CO3 is a weaker acid than H3O+

HCO3- is a weaker base than OH-

CH4 + OH- CH3- + H2O

CH4 is a very weak acid, CH3- a very strong base.

Water as a reference(H3O+/H2O/OH-)

H2O + H2O OH⇋ - + H3O+

KW depends on temperature(factor of 10 over 30°).

Always valid, also in presenceof added acids and bases.

If we know [H3O+], we also know [OH-] = KW/[H3O+].No need to calculate separately.

142

2

3 10O][H

]][OHO[H

wK

H2O is the"almost pure"

solvent

Water as a reference(H3O+/H2O/OH-)

In pure water, [H3O+] = [OH-], so:

x = [H3O+] = [OH-], x2 = 10-14, x = 10-7 mol/L.

We call a solution:

• neutral if [H3O+] = [OH-] = 10-7 mol/L.

• acidic if [H3O+] > [OH-] ([H3O+] > 10-7, [OH-] < 10-7)

• basic if [H3O+] < [OH-] ([H3O+] < 10-7, [OH-] > 10-7)

pH and acidity

pH is defined as

pH = - log [H3O+] ( [H3O+] = 10-pH )

base 10 logarithm, don't confuse with "natural logarithm" ln!

Defined in this way to have a convenient range,normally 0-14:

pH = 7: [H3O+] = [OH-] = 10-7 mol/L, neutral

pH = 0: [H3O+] = 100 = 1 mol/L, very acidic (1M acid!)

pH = 14: [H3O+] = 10-14 mol/L, [OH-]= 1 mol/L,very basic (1M base!)

pH and acidity

Since [H3O+][OH-] = 10-14,log [H3O+] + log [OH-] = -14 = -pH + log [OH-]pH = 14 + log [OH-] = 14 - pOH

this isnearly always

negative!

Measuring pH

• Electronic ("pH meter")Just put electrode in solution, read out the pH. Needs to be calibrated, but is fairly accurate.

• Indicator (solution or paper)Contains an organic base that changes colour on protonation (or acid that changes colour on deprotonation).Convenient, easy to carry, limited accuracy(ca 1 pH unit).

A scale for acid strength

We characterize the strength of an acidby its Ka value:

HA + H2O A⇋ - + H3O+

The strength of its conjugate baseis given by its Kb value:

A- + H2O HA + OH⇋ -

[HA]

]O][H[A 3

aK

][A

][HA][OH-

bK

143

3 10]][OHO[H][A

][HA][OH

[HA]

]O][H[A

wba KKK

A scale for acid strength

You do not need separate values for Ka and Kb!(for the same acid/base pair)

Whether a Ka for an acid is tabulated, or a Kb for its conjugated base, is a matter of convention and convenience.

Often, you will find tables of pKa (= - log Ka) and pKb (= - log Kb).

pH calculationsfor strong acids and bases

Strong acids and bases are always fully dissociated, so we know immediately how much H3O+ or OH- is generated.0.02 M CsOH solution.

OH- is a strong base. [OH-] = 2·10-2 mol/L,[H3O+] = 5·10-13 mol/L, pH = 12.3

0.13 M HClO4 solution.

HClO4 is a strong acid. [H3O+] = 0.13 mol/L,pH = 0.9

pH calculationsfor strong acids and bases

Take care! We were neglecting the contribution of water itself, assuming all H3O+/OH- came from the added acid/base.

For very low concentrations this is no longer true, and we need to use the "x method".

Low concentrations ofstrong acids and bases

6·10-7 mol/L HNO3. Originally, we had[H3O+] = [OH-] = 10-7 mol/L. We add 6·10-7 mol/L [H3O+], but some will be consumed by reactionwith [OH-].

H3O+ OH-

initial 10-7+6·10-7 10-7

change -x -x

equilibrium 7·10-7-x 10-7-x

Low concentrations ofstrong acids and bases

Calculation:

Final [H3O+] = 6.2·10-7, pH = 6.2.

777

14277

1472

141472

773

108.02

103.6108

2

106*4)108(108

0106108

10107108

)10)(107(]][OHO[H

x

xx

xx

xxKW

pH calculationsfor weak acids and bases

Cannot assume all acid has dissociated.Need to use the equilibrium expression for Ka.

0.022 M acetic acid (Ka = 1.8·10-5).

HOAc OAc- H3O+

initial 0.022 0 (10-7)

change -x +x +x

equilibrium 0.022-x x x

pH calculationsfor weak acids and bases

Calculation:

Simplified version, according to book (MSJ p791),

assuming x « 0.022:

Final pH: 3.2

Check your answer: 0.022-6.3·10-4 0.021,reasonable (but not ideal) approximation.

52

3 108.1022.0[HOAc]

]][OAcO[H

x

xKa

472522

103.6100.4108.1022.0022.0

xxx

x

x

pH calculationsfor weak acids and bases

Full calculation:

Final pH: 3.2

435

7255

752

572

52

102.62

1027.1108.1

2

100.4*4)108.1(108.1

0100.4108.1

108.1100.4

108.1022.0

x

xx

xx

x

x

pH calculationsfor weak acids and bases

For very weak acids (Ka < 10-10) or very small concentrations of weak acids ([HA] < 10-5)we would need to take explicitly into account:

• partial dissociation of the acid• auto-ionization of water

This gets too complicated for solving without a computer.

Types of acids

Acids have a proton that is easily lost (transferred).

It will be attached to an electronegative atom X (typically, at least as electronegative as nitrogen).

Examples:

H-F is acidic

H-OH is somewhat acidic

H-OClO3 is very acidic

Why are some acids weak, others strong?

There are trends, but there is not a simple, single rule.

H-X acids (X not oxygen)

CH4 NH3 H2O HF

SiH4 PH3 H2S HCl

GeH4 AsH3 H2Se HBr

SnH4 SbH3 H2Te HI

very weak acidsweak acidsstrong acids

decreasingX-H bond strength

(MSJ p352)easier loss of H+

increasingX electronegativity

(MSJ p355)more stable X-

H-X acids (X not oxygen)

Second (and third) dissociation is always much more difficult than first.

It is harder to remove H+ from an anion than from a neutral molecule!

So HS- is a much weaker acid than H2S.

H-O-X acidsStronger if:• X more

electronegative• More oxygen atoms

attached to X

Both stabilize negative charge on anion

H2CO3 HNO3

HNO2

H2OH2O2

H4SiO4 H3PO4

H3PO3

H2SO4

H2SO3

HOClHClO2

HClO3

HClO4

H3AsO4

H3AsO3

H2SeO4

H2SeO3

HOBrHBrO2

HBrO3

Also transition-metal acids: H2CrO4, HMnO4, etc

So what about HNO2, HClO2, H2SO3 ?

Very strong oxo-acids:

Hydrated metal ions

Cr(OH2)63+ + H2O Cr(OH⇋ 2)5(OH)2+ + H3O+

Cr3+ is a Lewis acid, complexeswith Lewis base H2O.

The complexation makes water more acidic.

Higher charge, smaller radius of metal ion stronger Brønsted-acidity of hydrated ion.

Organic acids:carboxylic acids

The C=O groupis electron-withdrawingand allows resonancestabilization. Without it,the OH group is hardly acidic.

C

O

OH

+ H2O

C

O

O

C

O

O+ H3O+

Common organic acids

H C

O

OH

CH3 C

O

OH

CH3CH2CH2 C

O

OH

CH3(CH2)16 C

O

OH

C

O

OHC

O

OH

O

CCH3

O

Formic acid(the stuff that hurtswhen an ant bites)

Acetic acid(vinegar,wine gone bad)

Butyric acid("unwashed" smell)

Stearic acid(the Na salt ishousehold soap)

Benzoic acid(common foodpreservative)

Acetylsalicylic acid(Aspirin)

The strength of an organic acid(see MSJ p782)

Formic (our reference)

Acetic: weaker(CH3 donating)

Fluoroacetic: stronger(F withdrawing)

Trifluoroacetic: strong!

H C

O

OH

CH3 C

O

OH

CH2F C

O

OH

CF3 C

O

OH

C

O

OH

C C

O

OHCH3

O

Benzoic: stronger (resonance)

Pyruvic: stronger(withdrawing)

Curiosities

HCN: Hydrocyanic acid, Prussic acid.Negative charge stabilized by N atom.Toxic! (not because of acidity)

HN3: Hydrazoic acid. Nitrogens areless effective than oxygens at stabilizing negative charge, but hey can do so.Toxic (like HCN).Salts used in explosives and airbags.

C N

N N N

Curiosities (2)

Ascorbic acid (vitamin C).

Essential food componentand preservative.

The anion has adelocalized negativecharge and severalelectron-withdrawingoxygens.

O OH

HO OH

HCOH

H2COH

O OH

O OH

HCOH

H2COH

O OH

O OH

HCOH

H2COH

Types of bases• Anions of weak acids.

Weaker acid stronger conjugate base (Ka*Kb = Kw!).

• Hydroxides• Ammonia, amines

Phosphines are much weaker bases

Bases are often used for cleaning purposes. They break down many organic compounds ("liquid plummr"). Don't get strong base on your skin.

Amines cause the "fishy" smell of fish.

A special case:amino-acids, zwitterions

Amino-acids combine an acidic and a basic group in the same molecule. In the solid state and in neutral polar solvents, they exist as zwitterions:

This is not resonance but tautomerism!

H2NCH2

COOH H3NCH2

COO

Amino acids

• In acidic solution, they exist in the protonated cationic form:

• In basic solution, they exist in the deprotonated anionic form:

H3NCH2

COOH

H2NCH2

COO

Peptides and proteins

Peptides (including proteins) are formed by coupling amino acids head-to-tail, via peptide linkages.

These linkages are neither acidic nor basic.

Only the head, tail and some side groups (see MSJ p592) are acidic or basic.

H2NCH2

COOH+

H2NCH

COOH

CH3

H2NCH2

O

NHCH

CH3

COOHH3N

CH2

C

O

NHCH

CH3

COO

- H2O

Strength of bases

Bases must be able to accept a proton, so they must have an available electron pair:

HO

H HO

H

H+ H3O+ + H2O

HN

H

H

HN

H

HH+ H3O+ + H2O

H2O is a weak base.

NH3 is a stronger base.N less electronegative electron pair more available

HO

HO

H+ H3O+ + H2O

HO+ H2O + OH-O

OH- is a strong base,O2- is even stronger(negative charge!).

Strength of bases

In general, provided an atom has an available electron pair, basicity goes up:

• going up in the periodic table (NH3>PH3)

• going left in the periodic table (NH3>H2O)

• with increasing negative charge(PO4

3->HPO42->H2PO4

-)

• with more electron-donating substituents (CH3OH>H2O)

Solutions of salts

• A salt consists of an anion (conjugate base of an acid) and a cation (often an acid itself, or conjugate acid of a base). It is formed by neutralization of the acid with the base (or vice versa).

• If both the original acid and the original base are strong, the solution will be neutral (the conjugate base and acid are very weak).NaCl = salt of HCl (strong) and NaOH (strong): neutral.

Solutions of salts

• If the original acid is strong but the base is weak, the solution is acidic.NH4Cl: from HCl + NH3. NH4

+ is (weakly) acidic.

• If the original acid is weak but the base is strong, the solution is basic.NaOAc: from HOAc + NaOH. OAc- is (weakly) basic.

• If both acid and base were weak:– If Ka(acid) > Kb(base), solution is acidic.

– If Ka(acid) < Kb(base), solution is basic.

pH calculations for salts

• For a salt of strong acid and weak base: need only consider conjugate acid of weak base. See calculations for weak acids.

• For a salt of weak acid and strong base: need only consider conjugate base of weak acid. See calculations for weak bases.

• For salts of weak acid and weak base: need to include both, calculation can be complicated.

Lewis acidity that is notBrønsted-Lowry acidity

Metal ions are strong Lewis acids. They bind H2O, but also other Lewis bases like NH3 or anions of various acids.

Cu(H2O)62+ + 4 NH3 Cu(NH3)4

2+ + 6 H2O

HgI2 + 2 I- HgI42-

AgCl + 2 S2O32- Ag(S2O3)2

3- + Cl-

light blue deep dark blue

red,insoluble

colourless solution

white,insoluble

Lewis acidity that is notBrønsted-Lowry acidity

Other elements can act like Lewis acids(but generally the electron pairs move around then)

O C O + OH O C

O

O

H

+ OHO S

O

O

O S

O

OHO