Ch 16: Acid-Base Equilibria

Brown, LeMay Ch 16AP Chemistry

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16.1: Acids and Bases

* Defined by Svante Arrhenius in 1880’s Arrhenius acids: produce protons;

increase [H+]HCl (aq) → H+ (aq) + Cl- (aq)

Arrhenius bases: produce hydroxides; increase [OH-]

NaOH (aq) → Na+ (aq) + OH- (aq)or

NH3 (aq) + H2O (l) ↔ NH4+ (aq) + OH- (aq)

3

16.2: Dissociation of Water

Autoionization of water:H2O (l) ↔ H+ (aq) + OH- (aq)

][

]][[

2OH

OHHKc

M 55.6 g 18.0

mol 1

wKOHH -1410 x 0.1]][[

KW = ion-product constant for water

H3O+ (aq) or H+ (aq) = hydronium

L 1

g 1000 (l)] O[H2

4

16.3: The pH Scale

pH = -log [H+] = -log [H3O+]

or [H+] = 10-pH

[H+][OH-] = KW = 1.0x10-14

-log ([H+][OH-]) = -log KW

-log [H+] + -log[OH-] = -log (1.0x10-14)

pH + pOH = 14.00

pOH = -log [OH-] or [OH-] = 10-pOH

pX = -log [X]

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16.3: The pH Scale

If [H+]<[OH-], then [H+]<1.0x10-7

Ex: pH = -log[1.0x10-10] = 10.00 (basic)

If [H+] = [OH-]Since [H+][OH-] = 1.0x10-14

[H+] = [OH-] = 1.0x10-7

pH = -log[1.0x10-7] = 7.00 (neutral)

If [H+]>[OH-], then [H+]>1.0x10-7

Ex: pH = -log [1.0x10-3] = 3.00 (acidic)

pH

14

7

0

pOH

0

7

14

6

Johannes Brønsted (Denmark)Thomas Lowry (England),

1923

Brønsted-Lowry acids: H+ donor Brønsted-Lowry bases: H+ acceptor

NH3 (aq) + H2O (l) ↔ NH4+ (aq) + OH- (aq)

Base Acid

16.4: Brønsted-Lowry Acids & Bases

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Amphoterism Amphoteric: capable of acting as either

an acid or baseH2O (l) ↔

Acting as an acid

Acting as a base

Al(OH)3 (aq) ↔

Al(OH)4- (aq) + H+(aq)

Al(OH)2+ (aq) + OH-(aq)

Al(OH)3 (aq) + H2O(l) ↔

OH- (aq) + H+(aq)

* Amphiprotic: can accept or donate a p+

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Conjugated Acid-Base Pairs

For acid “HA”:HA (aq) + H2O (l) ↔ A- (aq) + H3O+ (aq)

acid base conjugate base

For base “B”:

B (aq) + H2O (l) ↔ HB+ (aq) + OH- (aq)

base acid

conjugate acid

conjugate base

conjugate acid

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Relative Acid-Base Strengths The stronger an acid (the greater its

ability to donate p+), the weaker its conjugate base (the lesser its ability to accept p+).

The stronger a base, the weaker its conjugate acid.

In an acid-base equilibrium, the p+ is transferred from the strongest acid to the strongest base.HSO4

- + CO32- ↔ SO4

2- + HCO3-

Stronger acidStronger base

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16.5: Strong Acids and Bases

Strong acids and bases fully ionize in water (equilibrium is shifted “entirely” toward ions).

Strong acids:HI, HBr, HCl, HClO4, HClO3, H2SO4, HNO3

Ex: In 6M HCl solution, 0.004% exist as molecules

Strong bases:LiOH, NaOH, KOH, RbOH, CsOH, Ca(OH)2, Sr(OH)2, and Ba(OH)2

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16.6: Weak Acids

Weak acids partially ionize in water (equilibrium is somewhere between ions and molecules).

HA (aq) ↔ A- (aq) + H+ (aq)

eqa HA

AHK

][

]][[

Ka = acid-dissociation constant in water

Weak acids generally have Ka < 10-3

See Appendix D for full listing of Ka values

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Ex: Calculate the pH of 2.0 M HCl solution (Ka≈106) Strong acid, completely dissociated HCl (aq) → H+ (aq) + Cl- (aq)

  HCl (aq) H+ (aq) Cl- (aq)

Initial

Change

Final

2.0 M

- 2.0 M

0 M

0 M 0 M

+ 2.0 M + 2.0 M

2.0 M 2.0 M

So:

[HCl]initial = [H+]final = [Cl-]final = 2.0 M

pH = - log [H+] = - log [2.0] = -0.30

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Ex: Calculate pH of 2.0 M HF solution (Ka=7.2x10-4) Weak acid, partially dissociated HF (aq) ↔ H+ (aq) + F- (aq)

  HF (aq) H+ (aq) F- (aq)Initial

Change

Equilibrium

2.0 M- x M

(2.0 – x) M

0 M 0 M+ x M + x Mx M x M

eq

aHF

FHK

][

]][[102.7 4-

x

x

0.2

2

xHF

xx

initial

][

))((

Using quadratic eq’n, 0 = x2 + 7.2 x 10-4x – 1.44 x 10-3

x = 3.7229 x 10-2 or – 3.8669 x 10-2 = [H+]

pH = - log [H+] = - log [3.7 x 10-2] = 1.43

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Or, since weak acids partially dissociate, assume that [HF]init >> [H+]eq

Then, [HF]init – [H+] ≈ [HF]init

0.20.2102.7

224 x

x

x

pH = - log [H+] = - log [3.8 x 10-2] = 1.42 General rule: if [H+] 5% of [HA], it is better to

use quadratic formula.

23104.1 x

][108.3104.1 23 Hx

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Percent Ionization of an Acid

100%[HA]

][HIonization %

init

eq

Ex: Calculate the % ionization of:

•2.0 M solution of HCl

•2.0 M solution of HF

0%01100%[2.0]

.0]2[Ionization %

1.9%100%[2.0]

].8x103[Ionization %

-2

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Polyprotic acids: have more than one H+ to “donate”Ex: H2SO3 (aq) ↔ HSO3

- (aq) + H+ (aq)

Ka1 = 1st acid-dissociation constant = 1.7 x 10-2

HSO3- (aq) ↔ SO3

2- (aq) + H+ (aq)

Ka2 = 2nd acid-dissociation constant = 6.4 x 10-8

Ka1>Ka2; 1st H+ dissociates more easily than

the 2nd.

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* Polyprotic Acids

Ascorbic acid (Vitamin C):

Citric acid:

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16.7: Weak Bases

Partially ionize in water.B (aq) + H2O (l) ↔ BH+ (aq) + OH- (aq)

eqb B

OHBHK

][

]][[

Kb = base-dissociation constant in water

In practice,

eqb B

OHBHK

][

]][[

initialB

x

][

2

xB

xx

initial

][

))((

where x = [OH-]

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16.8: Relationship between Ka and Kb

Weak base: NH3(aq) + H2O(l) ↔ NH4+(aq)+OH-

(aq)

Conjugate acid: NH4+(aq) ↔ NH3(aq) + H+

(aq)

][

]][[

4

3

NH

NHHKa

][

]][[

3

4

NH

OHNHKb

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NH3 (aq) + H2O (l) ↔ NH4+ (aq) + OH- (aq)

+ NH4+ (aq) ↔ NH3 (aq) + H+ (aq)

][

]][[

][

]][[

4

3

3

4

NH

HNH

NH

OHNHKK ab

H2O (l) ↔ H+ (aq) + OH-

(aq)And:

]][[ HOHTherefore: 14100.1 wab KKK

For a conjugate acid-base pair

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In general, when two reactions are added to give a 3rd, the equilibrium constant for the 3rd reaction equals the product of the equilibrium constants of the two added reactions.

Furthermore:

)100.1log(log)log( 14 wab KKK

00.14logloglog wab KKK

00.14 wab pKpKpK

14100.1 wab KKK

For a conjugate acid-base pair

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16.9: Salt Solutions as Acids & Bases

Hydrolysis: acid/base reaction of ion with water to produce H+ or OH-

Anion (A-) = a conjugate baseA- (aq) + H2O (l) ↔ HA (aq) + OH- (aq)

Cation (B+) = a conjugate acidB+ (aq) + H2O (l) ↔ BOH (aq) + H+ (aq)

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Predicting pH of Salt Solutions

Salt type Cation AnionHydrolyze

s to produce

pH

Consider the relative strengths of the acid and base from which the salt is derived:

Strong electrolyte

Ex: Ca(NO3)2

Ca2+

conjugate acid of strong base

Ca(OH)2

NO3-

conjugate base of strong

acid HNO3

Neither H+ nor OH- 7

Salt type Cation AnionHydrolyze

s to produce

pH

ClO- (aq) + H2O (l) ↔ HClO (aq) + OH- (aq)

eqb ClO

OHHClOK

][

]][[

xClO

xx

initial ][

))((

initiala

wb ClO

x

K

KK

][

2

Weak electrolyte

Ex: NaClO

Na+

conjugate acid of strong base, NaOH

ClO-

conjugate base of weak acid, HClO

OH-

> 7

where x = [OH-]

Salt type Cation AnionHydrolyze

s to produce

pH

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

eq

aNH

HNHK

][

]][[

4

3

xNH

xx

initial ][

))((

4

initialb

wa

NH

x

K

KK

][ 4

2

Weak electrolyte

Ex: NH4Cl

NH4+

conjugate acid of weak

base, NH3

Cl-

conjugate base of strong

acid, HCl

H+ < 7

where x = [H+]

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16.10: Acid-Base Behavior & Chemical Structure Stronger acids, HA, have:

1. H with a higher +

2. Weaker H-A covalent bond (smaller bond enthalphy)

3. More stable conjugate bases A-

Stronger oxyacids, HxOz-Y, have:

1. Central nonmetal “Y” with higher electronegativity

2. More O atoms

Ex: Rank these in order from strongest to weakest: HClO, HClO2, HCl, HBr

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16.11: Lewis Acids & Bases Lewis acid: “e- pair acceptor”

Brønsted-Lowry acid = H+ donor Arrhenius acid = produces H+

Lewis base: “e- pair donor” B-L base = H+ acceptor Arrhenius base = produces OH-

Ex:NH3 + BF3 → NH3BF3

Lewis base Lewis acid Lewis salt

6 CN- + Fe3+ → Fe(CN)63-

Lewis base Lewis acid Coordination compound

Gilbert N. Lewis

(1875 – 1946)