Percent dissociation of weak acidsPercent dissociation of weak acids

Percent dissociation = Percent dissociation =

[HA][HA]dissociateddissociated x 100% x 100%

[HA][HA]initialinitial

Increases as KIncreases as Kaa increases increases

For given acid, increases with dilutionFor given acid, increases with dilution

Dissociation increases with dilutionDissociation increases with dilution

Percent dissociation of acetic acid

0

1

2

3

4

5

0.00 0.20 0.40 0.60 0.80 1.00 1.20

Concentration/ M

% d

isso

ciat

ion

Polyprotic acidsPolyprotic acids

Dissociations are stepwiseDissociations are stepwise

HH22COCO33 + H + H22O = HO = H33OO++(aq) + HCO(aq) + HCO33--(aq)(aq)

HCOHCO33--(aq) + H(aq) + H22O = HO = H33OO++(aq) + CO(aq) + CO33

2-2-(aq)(aq)

7

32

331 103.4

][

]][[

xCOH

HCOOHKa

11

3

233

2 106.5][

]][[

xHCO

COOHKa

KKaa decreases with each step decreases with each step

It is harder to remove a proton from a It is harder to remove a proton from a negative ion than from a neutral moleculenegative ion than from a neutral molecule

Solution contains mixture of all speciesSolution contains mixture of all species

Strongest acid is the unionized molecule Strongest acid is the unionized molecule HHnnXX

Use the same strategy described Use the same strategy described earlierearlier

What are concentrations of species present in What are concentrations of species present in 0.020 M solution of carbonic acid?0.020 M solution of carbonic acid?

Step 1: initial species are HStep 1: initial species are H22COCO33 and H and H22OO

Step 2:Step 2: K Ka1a1 » K» Kww principal process is ionization of principal process is ionization of

HH22COCO33

ICE Age TwoICE Age Two

Principal Principal processprocess

Cod(aq) + HCod(aq) + H22O = CodHO = CodH++(aq) + OH(aq) + OH--(aq)(aq)

Initial concInitial conc 0.00120.0012 00 00

ChangeChange -x-x xx xx

Equilibrium Equilibrium concconc

0.0012 - x0.0012 - x xx xx

Step 5: Obtain x from KStep 5: Obtain x from Kaa

x

xxx

COH

HCOOHKa

020.0103.4

][

]][[ 7

32

331

5

72

7

103.9

020.0103.4

020.0103.4

xx

xx

x

xxx

X <<0.02

Step 6: Big concentrationsStep 6: Big concentrations

[[HH33OO++] = [HCO] = [HCO33--] = x = 9.3 x 10] = x = 9.3 x 10-5-5 M M

[[HH22COCO33] = 0.020 – x = 0.020 M] = 0.020 – x = 0.020 M

Step 7: small concentrationsStep 7: small concentrations

Obtained from subsidiary equilibria:Obtained from subsidiary equilibria:HCOHCO33

--(aq) + H(aq) + H22O = HO = H33OO++(aq) + (aq) + COCO332-2-(aq)(aq)

[CO[CO332-2-]] = K = Ka2a2 = 5.6 x 10 = 5.6 x 10-11-11 M M

In general, [AIn general, [A2-2-] = K] = Ka2a2

5

23

5

11

3

233

2

103.9

103.9

106.5][

]][[

x

COx

xHCO

COOHKa

Ignore H3O+ generated in

second ionization

Step 7 contd.Step 7 contd.

[OH[OH--] from dissociation of water:] from dissociation of water:

Mxx

x

OH

KOH w 10

5

14

3

101.1103.9

100.1

Step 8: Calculate pHStep 8: Calculate pH

pH = -logpH = -log1010[H[H33OO++]]

= -log(9.3x10= -log(9.3x10-5-5))

= 4.03= 4.03

Weak base equilibriaWeak base equilibria

Treated in an analogous way to weak acidsTreated in an analogous way to weak acids

Worked exampleWorked example

Calculate pH and concentrations of Calculate pH and concentrations of species in 0.0012 M solution of codeinespecies in 0.0012 M solution of codeine

Cod + HCod + H22O = CodHO = CodH++(aq) + OH(aq) + OH--(aq)(aq)

KKbb = 1.6x10 = 1.6x10-6-6

HH22O + HO + H22O = HO = H33OO++(aq) + OH(aq) + OH--(aq)(aq)

KKww = 1.0 x 10 = 1.0 x 10-14-14

Principal reaction is protonation of Principal reaction is protonation of codeinecodeine

Principal Principal processprocess

Cod(aq) + HCod(aq) + H22O = CodHO = CodH++(aq) + OH(aq) + OH--(aq)(aq)

Initial concInitial conc 0.00120.0012 00 00

ChangeChange -x-x xx xx

Equilibrium Equilibrium concconc

0.0012 - x0.0012 - x xx xx

Step 5: dissociationStep 5: dissociation

5

62

6

104.4

0012.0106.1

106.10012.0][

]][[

xx

xx

xx

xx

COD

OHCODHKb

X <<0.0012

Step 6: Big concentrationsStep 6: Big concentrations

[CodH[CodH++] = [OH] = [OH--] = x = 4.4x10] = x = 4.4x10-5-5 M M

[Cod] = 0.0012 – x = 0.0012 M (x[Cod] = 0.0012 – x = 0.0012 M (x«0.0012)«0.0012)

Step 7: small concentrationsStep 7: small concentrations

[H[H33OO++] from dissociation of water] from dissociation of water

Mx

x

x

OH

KOH w 10

5

14

3 103.2104.4

100.1

Step 8: Calculate pHStep 8: Calculate pH

pH = -logpH = -log1010[H[H33OO++]]

= -log(2.3x10= -log(2.3x10-10-10))

= 9.64= 9.64

Relationship between KRelationship between Kaa and K and Kbb for for

conjugate acid-base pairconjugate acid-base pairAcidAcid

HA + HHA + H22O = HO = H33OO++(aq) + A(aq) + A--(aq)(aq)

BaseBase

AA-- + H + H22O = HA(aq) + OHO = HA(aq) + OH--(aq)(aq)

][

]][[ 3

HA

AOHKa

][

]][[

A

OHHAKb

w

ba

KOHOH

A

OHHAx

HA

AOHxKK

]][[

][

]][[

][

]][[

3

3

K for the overall reaction is product K for the overall reaction is product of K’s for individual reactionsof K’s for individual reactions

In generalIn general

KKnetnet = K = K1 1 x Kx K22 x K x K33 x… x…

For conjugate acid-base pairsFor conjugate acid-base pairs

KKaa x K x Kbb = K = Kww

SaltsSalts

Products of acid-base neutralizationProducts of acid-base neutralization

HHClCl + + NaNaOH = OH = NaClNaCl + H + H22OO

HHClCl + + KKOH = OH = KClKCl + H + H22OO

HHNONO33 + + KKOH = OH = KNOKNO33 + H + H22OO

2H2HClCl + + CaCa(OH)(OH)22 = = CaClCaCl22 + 2H + 2H22OO

HHCNCN + + NaNaOH = OH = NaCNNaCN + H + H22OO

Unequally yokedUnequally yoked

Consequences for “neutralized” solutions of the Consequences for “neutralized” solutions of the following combinationsfollowing combinations

Strong acidStrong acid + + strong basestrong baseNEUTRALNEUTRAL

Strong acidStrong acid + + weak baseweak baseACIDICACIDIC

Weak acidWeak acid + + strong basestrong baseBASICBASIC

Salts that yield neutral solutionsSalts that yield neutral solutions

Group 1A cationsGroup 1A cations

Group 2A cations (except BeGroup 2A cations (except Be2+2+))

Anions from strong monoprotic acidsAnions from strong monoprotic acids

(Cl(Cl--, Br, Br--, I, I--, NO, NO33--, ClO, ClO44

--))

Salts that yield acid solutionsSalts that yield acid solutions

Salts of weak basesSalts of weak bases

NHNH44++(aq) + H(aq) + H22O = NHO = NH33 + H + H33OO++(aq) (aq)

Hydrated small polarizing metal cationsHydrated small polarizing metal cations

What is pH of a 0.10 M solution of AlClWhat is pH of a 0.10 M solution of AlCl33

KKaa = 1.4 x 10 = 1.4 x 10-5-5

Using prior strategy:Using prior strategy:– Al(HAl(H22O)O)66

3+3+, Cl, Cl-- and H and H22O are initial speciesO are initial species

– Al(HAl(H22O)O)663+3+ is stronger acid than H is stronger acid than H22O O

Principal Principal processprocess

Al(HAl(H22O)O)66++(aq) + H(aq) + H22O(l) = HO(l) = H33OO++(aq) + (aq) +

Al(HAl(H22O)O)55OHOH2+2+(aq)(aq)

Initial concInitial conc 0.100.10 00 00

ChangeChange -x-x xx xx

Equilibrium Equilibrium concconc

0.10 – x0.10 – x xx xx

pH = -log(1.2 x 10pH = -log(1.2 x 10-3-3) = 2.92) = 2.92

Mxx

xx

x

xxx

OHAl

OHOHAlOHKa

3

52

5362

2523

102.1

104.110.0

10.0104.1

])([

])()(][[

X << 1

Salts that yield basic solutionsSalts that yield basic solutions

Salts of weak acid and strong baseSalts of weak acid and strong base

CNCN--(aq) + H(aq) + H22O = HCN(aq) + OHO = HCN(aq) + OH--(aq)(aq)

Calculation of pH follows same strategy as Calculation of pH follows same strategy as for the salt of strong acid and weak base for the salt of strong acid and weak base except use expression for Kexcept use expression for Kbb

Weak acid and base: what then?Weak acid and base: what then?

Competition between relative acid strength Competition between relative acid strength of cation and base strength of anionof cation and base strength of anion

Consider (NHConsider (NH44))22COCO33

NHNH44++(aq) + H(aq) + H22O = HO = H33OO++(aq) + NH(aq) + NH33(aq) K(aq) Kaa

COCO332-2-(aq)(aq) + + HH22O = HCOO = HCO33

--(aq) + OH(aq) + OH--(aq) K(aq) Kbb

If KIf Kaa > K > Kbb then pH < 7 then pH < 7

If KIf Kaa < K < Kbb then pH > 7 then pH > 7

If KIf Kaa ≈≈ K Kbb then pH then pH ≈ 7≈ 7

Summing upSumming upTypes of saltTypes of salt ExamplesExamples Ions that react

with waterpH of solution

Cation from strong base, anion from strong acid

NaCl, Ba(NO3)2, None 77

Cation from weak base, anion from strong acid

NH4Cl, (CH3)4CCl Cation <7

Small highly charged cation, anion from strong acid

AlCl3, Cr(NO3)3

Hydrated cation < 7< 7

Cation from strong base, anion from weak acid

NaCN, KF, Na2CO3

Anion 7

Cation from weak base, anion from weak acid

NH4CN, NH4F

Both

<7 if Ka > Kb

>7 if Ka < Kb

≈7 if Ka ≈ Kb

Factors affecting acid strengthFactors affecting acid strength

How easily is the H – X bond broken?How easily is the H – X bond broken?– the less easily dissociated, the weaker the the less easily dissociated, the weaker the

acid.acid.

Bond strengthBond strength– Bond strength increases, acid strength Bond strength increases, acid strength

decreasesdecreases

PolarityPolarity– For a given bond strength, the more polar the For a given bond strength, the more polar the

more easily dissociated – closer to Hmore easily dissociated – closer to H++

In a group, bond strength is the In a group, bond strength is the more important factormore important factor

Polarity is not a good predictor: H-X polarity Polarity is not a good predictor: H-X polarity decreases down the group as acid strength decreases down the group as acid strength increasesincreasesBond strength decreases more strongly down Bond strength decreases more strongly down the groupthe group– Bond length increases sharplyBond length increases sharply

FF ClCl BrBr IIBond strength/kJmolBond strength/kJmol-1-1 567567 431431 366366 299299H – X bond length/H – X bond length/ÅÅ 0.9170.917 1.2741.274 1.4081.408 1.6081.608

ElectronegativityElectronegativity 4.04.0 3.03.0 2.82.8 2.52.5

Electronegativity more reliable Electronegativity more reliable indicator in a periodindicator in a period

H-X polarity increases across periodH-X polarity increases across period

Acid strength increases across periodAcid strength increases across period

Bond strength shows weaker trendBond strength shows weaker trend– Bond lengths vary littleBond lengths vary little

CC NN OO FFBond strength/kJmolBond strength/kJmol-1-1 410410 390390 460460 570570H – X bond length/H – X bond length/ÅÅ 1.0911.091 1.0081.008 0.9580.958 0.9170.917

ElectronegativityElectronegativity 2.52.5 3.03.0 3.53.5 4.04.0

Summing upSumming upElectronegativity increasesAcid strength increases

Bond strength decreases

Acid strength increases

NH3 H2O HF

PH3 H2S HCl

AsH3 H2Se HBr

Oxoacids and strength – where are Oxoacids and strength – where are the electrons goingthe electrons going

How to weaken the OH bond and increase How to weaken the OH bond and increase its polarity?its polarity?– Increase electronegativity of YIncrease electronegativity of Y– Increase oxidation number of Y (number of O Increase oxidation number of Y (number of O

atoms around Yatoms around Y

Both serve to withdraw electrons from the Both serve to withdraw electrons from the H making it more positive – closer to HH making it more positive – closer to H++

Increasing electronegativity of YIncreasing electronegativity of Y

In a homologous series, increasing electronegativity of Y In a homologous series, increasing electronegativity of Y increases strengthincreases strength– Y draws charge away from the H atom, more easily ionizedY draws charge away from the H atom, more easily ionized

NOTE: Opposite dependence to series HA, where A = F, NOTE: Opposite dependence to series HA, where A = F, Cl, Br, ICl, Br, I

Acid strengthAcid strength

AcidAcid HOIHOI HOBr HOCl

KKaa2.3 x 10-11 2.0 x 10-9 3.5 x 10-8

ElectronegativityElectronegativity 2.52.5 2.82.8 3.0

Increasing oxidation number (O atoms)Increasing oxidation number (O atoms)

More O atoms around Y, more acidicMore O atoms around Y, more acidic– The O atoms draw charge away from the H atom, The O atoms draw charge away from the H atom,

more easily ionizedmore easily ionized

Also think in terms of relative stabilities of the Also think in terms of relative stabilities of the oxoanions formed in the processoxoanions formed in the process

Acid strengthAcid strength

AcidAcidHOClHOCl HOClO HOClO2 HOClO3

Hypochlorous Chlorous Chloric Perchloric

KKaa3.5 x 10-8 1.2 x 10-2 -1 Large

Oxidation Oxidation number of Clnumber of Cl 1 3 5 7

Lewis acids – no protons requiredLewis acids – no protons required

Lewis acid: an electron pair acceptor (BFLewis acid: an electron pair acceptor (BF33))

Lewis base: an electron pair donor (NHLewis base: an electron pair donor (NH33))

ACCEPTORDONOR

BF3 NH3

Lewis definition casts the net Lewis definition casts the net furtherfurther

All Arrhenius acids are BrAll Arrhenius acids are Brønsted acidsønsted acids

All All BrBrønsted acids are Lewis acidsønsted acids are Lewis acids

The converses are not trueThe converses are not true

ExamplesExamples– AlAl3+3+(acid) H(acid) H22O (base)O (base)

– CuCu2+2+(acid) NH(acid) NH33 (base) (base)

– SOSO33 (acid) H (acid) H22O (base)O (base)