Zumdahl’sZumdahl’sChapter 14Chapter 14Zumdahl’sZumdahl’sChapter 14Chapter 14

AcidsAcids

BasesBasesAcidsAcids

BasesBases

Chapter ContentsChapter ContentsChapter ContentsChapter Contents

Acid-Base ModelsAcid-Base Models Acidity and KAcidity and Kaa

pH, pOH, and pKpH, pOH, and pKaa

Calculating pHCalculating pH Dominant SourcesDominant Sources

Polyprotic AcidsPolyprotic Acids % dissociation% dissociation

Bases and KBases and Kbb

Conjugate Acids Conjugate Acids and Basesand Bases

Structure and Structure and StrengthStrength

OxoacidsOxoacids Lewis AcidsLewis Acids Acid-Base Solution Acid-Base Solution

Al Gore RhythmsAl Gore Rhythms

Acid-Base ModelsAcid-Base ModelsAcid-Base ModelsAcid-Base Models

DefinitioDefinition of Acidn of Acid

Example Example of Acidof Acid

DefinitioDefinition of n of BaseBase

Example Example of Baseof Base

SvanteSvante

ArrheniuArrheniuss

Donates Donates HH++ HClHCl Donates Donates

OHOH–– NaOHNaOH

BrBrøsted-østed-LowryLowry

Donates Donates HH++ HClHCl Accepts Accepts

HH++

NHNH33 or or HH22OO

G.N.G.N.

LewisLewisAccepts Accepts electronelectron

BFBF33Donates Donates electronelectron

:: NH NH33

CausticCaustic Characteristics CharacteristicsCausticCaustic Characteristics Characteristics

Greek: Greek: kaustikoskaustikos kaieinkaiein “to burn” “to burn” Acids & bases corrode nearly Acids & bases corrode nearly

everythingeverything HA(HA(aqaq) + H) + H22O(O(ll) ) H H33OO++((aqaq) + A) + A––((aqaq))

HA “acid” and AHA “acid” and A–– “conjugate base”“conjugate base” HH22O “base” and HO “base” and H33OO++ “conjugate acid”“conjugate acid”

HH33OO++ “hydronium ion”“hydronium ion” no free protons!no free protons!

KKaa = [H = [H++] [A] [A––] / [HA] ] / [HA] “acid dissociation contant”“acid dissociation contant”

Acidity and KAcidity and KaaAcidity and KAcidity and Kaa

Strong acid: KStrong acid: Kaa meansmeans [HA] [HA]eqeq = 0 = 0

Weak acid: KWeak acid: Kaa 0 0 oror [HA] [HA]eqeq [HA] [HA]00

AA––((aqaq) + H) + H33OO++((aqaq) ) HA( HA(aqaq) + H) + H22O(O(ll)) K=KK=Kaa

––11 or weak acid is associated with a or weak acid is associated with a strong conjugate base and vice versa.strong conjugate base and vice versa.

AcidsAcids HHSOSO44–– HHCC22HH33OO22 HHCNCN

KKaa 1.21.21010––22 1.81.81010––55 6.26.21010––1010

pH, pOH, and pKpH, pOH, and pKaapH, pOH, and pKpH, pOH, and pKaa

pX pX –– log log1010(X)(X) Reduces KReduces Kww = 1.01 = 1.01221010––1414 to pK to pKww = 13.995 = 13.995

to a manageable entity for comparisonto a manageable entity for comparison Actually pKActually pKww = 14 is usually memorized. = 14 is usually memorized.

2 H2 H22O(O(ll) ) H H33OO++((aqaq) + OH) + OH––((aqaq) K = K) K = Kww

pH+pOH=pKpH+pOH=pKww because K because Kww = [H = [H++][OH][OH––]] AcidAcid (pH<7), Neutral (pH=7), (pH<7), Neutral (pH=7), BaseBase (pH>7) (pH>7) E.g., pH(0.1 E.g., pH(0.1 MM acetic acid) = acetic acid) = 2.872.87

Calculating pHCalculating pHCalculating pHCalculating pH

Strong acidsStrong acids [H[H++]]eqeq = [HA] = [HA]00

pH = p[HA]pH = p[HA]00

Strong basesStrong bases [OH[OH––]]eqeq = [BOH] = [BOH]00

pOH = p[BOH]pOH = p[BOH]00

pH = 14 – pOHpH = 14 – pOH Don’t be fooled Don’t be fooled

by [HA]by [HA]00 << 10 10––77

Weak AcidsWeak Acids KKaa = [H = [H++][A][A––] / [HA]] / [HA] KKaa = x = x22 / ( [HA] / ( [HA]00 – x) – x) KKaa x x22 / [HA] / [HA]00

x x ( K ( Kaa [HA] [HA]00 ) )½½

pH = – logpH = – log1010(x)(x) Weak BasesWeak Bases

x x ( K ( Kbb [MOH] [MOH]00 ) )½½

pH = 14 - pxpH = 14 - px

Dominant SourcesDominant SourcesDominant SourcesDominant Sources

If more than one HIf more than one H++ source source (multiple (multiple

acids acids oror a polyprotic acid), a polyprotic acid), pK pKaa will usually will usually differ by a few units, and the differ by a few units, and the largestlargest will will determinedetermine [H [H++]]eqeq. . E.g., 0.01E.g., 0.01MM H H33POPO44

pKpKaa: 2.12, 7.21, and 12.32, respectively: 2.12, 7.21, and 12.32, respectively Use KUse Kaa for 1 for 1stst H H only:only: pH = 2.24 pH = 2.24 (quadratic formula)(quadratic formula)

DeterminesDetermines H H33POPO44, H, H22POPO44––, , andand H H++

Use other two pKUse other two pKaa to find HPO to find HPO4422–– and PO and PO44

33––

% Dissociation% Dissociation% Dissociation% Dissociation

Weak electrolyte present in molecular Weak electrolyte present in molecular form mostly with few ions & will have form mostly with few ions & will have a small % dissociation a small % dissociation unlessunless diluted. diluted.

100% 100% [ionic form] / [initial amount] [ionic form] / [initial amount] E.g., 0.1 E.g., 0.1 MM acetic acid = [initial amount] acetic acid = [initial amount]

[acetate ion] [acetate ion] (0.10 K (0.10 Kaa))½½ = 0.0013 = 0.0013 MM % dissoc. % dissoc. 100% 100% (K (Kaa/0.1)/0.1)½½ = 1.3% = 1.3%

0.01 M gives 4.2% shows 0.01 M gives 4.2% shows moremore ionization ionization upon dilution upon dilution (but pushes the “5% approx.”)(but pushes the “5% approx.”)

Bases and KBases and KbbBases and KBases and Kbb

Strong base: [OHStrong base: [OH––]]eqeq = [MOH] = [MOH]00 where M=metal and pH = 14 - pOHwhere M=metal and pH = 14 - pOH

Weak bases often Weak bases often aminesamines, , ::NRNR33

where R = H and/or organic groupswhere R = H and/or organic groups Amine steals HAmine steals H++ from H from H22O to leave OHO to leave OH––

KKbb = [NR = [NR33HH++] [OH] [OH––] / [] / [::NRNR33]]

For NHFor NH33 ((ammoniaammonia, , notnot an an amineamine),), K Kbb = 1.8 = 1.81010––55

Same pH rules & approximations apply.Same pH rules & approximations apply.

Conjugate Acids and Conjugate Acids and BasesBasesConjugate Acids and Conjugate Acids and BasesBases

““Salt of a weak (Salt of a weak (acidacid/base) is itself a /base) is itself a weak (weak (basebase/acid).”/acid).” Example of a weak base, NHExample of a weak base, NH33

NHNH44++ + OH + OH–– NH NH33 + H + H22O K = KO K = Kbb

––11

HH22O O H H++ + OH + OH–– K = K K = Kww ((addadd eqns) eqns)

NHNH44++ NH NH33 + H + H++ K Kconjugateconjugate = K = Kww / K / Kbb

KKacidacid(NH(NH44++) = 10) = 10––1414/1.8/1.81010––55 = 5.5 = 5.51010––1010

Weaker parent yields Weaker parent yields strongerstronger conjugate!conjugate!

Conjugate pH CalculationsConjugate pH CalculationsConjugate pH CalculationsConjugate pH Calculations

Salts of Salts of strongstrong parents are parents are neutral;neutral; those of very weak bases, very acidic:those of very weak bases, very acidic: Fe(HFe(H22O)O)66

3+3+ Fe(H Fe(H22O)O)55OHOH2+2+ + H + H++

pKpKa1a1 = 2.2 = 2.2 oror K Ka1a1 = 6.3 = 6.31010–3–3 (pK (pKbb = 11.8) = 11.8)

pH of 3 pH of 3 MM Fe(NO Fe(NO33))33 ? ? (HNO(HNO33 strong; ignore!) strong; ignore!)

KKa1a1 = [FeOH = [FeOH2+2+] [H] [H++] / [Fe] / [Fe3+3+] = x] = x22 / (3-x) / (3-x)

x x [3K [3Ka1a1]]½½ = 0.14 = 0.14 (5% OK)(5% OK) pH = 0.86 pH = 0.86 pKpKa2a2 = 3.5, pK = 3.5, pKa3a3 = 6, pK = 6, pKa4a4 = 10 = 10

NON-Dominant SituationsNON-Dominant SituationsNON-Dominant SituationsNON-Dominant Situations

In that Fe complex, pKIn that Fe complex, pKa1a1 and pK and pKa2a2 are are very close (2.2 and 3.5), so the very close (2.2 and 3.5), so the second conjugate may be important:second conjugate may be important: Fe(HFe(H22O)O)55OHOH2+2+ Fe(H Fe(H22O)O)44(OH)(OH)22

++ + H + H++

This will certainly be the case at This will certainly be the case at lower formal iron concentrations, F, lower formal iron concentrations, F, since % dissociation is greater there. since % dissociation is greater there. Try F=0.01Try F=0.01

Simplifing ApproximationsSimplifing ApproximationsSimplifing ApproximationsSimplifing Approximations

Even at F=0.01, we can safely Even at F=0.01, we can safely ignore pKignore pKa3a3, pK, pKa4a4, and pK, and pKww, since , since theythey are dominated by pKare dominated by pKa1a1 and pK and pKa2a2..

Abbreviate those equilibria asAbbreviate those equilibria as AA3+3+ B B2+2+ + H + H++ KK11 = B H / A = B H / A

BB2+2+ C C++ + H + H++ KK22 = C H / A = C H / A

But those are 2 eqns in 4 unknowns!But those are 2 eqns in 4 unknowns!

2 Additional Conditions!2 Additional Conditions!2 Additional Conditions!2 Additional Conditions!

Conservation of iron requires thatConservation of iron requires that F = A + B + CF = A + B + C

Conservation of charge must include Conservation of charge must include a spectator anion for Aa spectator anion for A3+3+ such as 3 Cl such as 3 Cl––

3 A3 A3+3+ + 2 B + 2 B2+2+ + C + C++ + H + H++ = 3 F = 3 F (conc. Cl(conc. Cl––))

Notice that higher charges get scaled Notice that higher charges get scaled byby their charge for proper balance. their charge for proper balance.

Solve 4 Solve 4 NonlinearNonlinear EquationsEquationsSolve 4 Solve 4 NonlinearNonlinear EquationsEquations

Original equations:Original equations: F = A + B + CF = A + B + C 3F = 3A + 2B + C + H3F = 3A + 2B + C + H B H = KB H = K11 A A

C H = KC H = K22 B B

Remove A by substituting from 1Remove A by substituting from 1stst eqneqn A = F – B – C A = F – B – C

Solve 3 Nonlinear Solve 3 Nonlinear EquationsEquationsSolve 3 Nonlinear Solve 3 Nonlinear EquationsEquations

Remaining after substitutionRemaining after substitution 3F = 3F – 3B – 3C + 2B + C + H3F = 3F – 3B – 3C + 2B + C + H B H = KB H = K11 ( F – B – C ) ( F – B – C )

C H = KC H = K22 B B

SimplifySimplify H = B + 2CH = B + 2C B H = KB H = K11 F – K F – K11 B – K B – K11 C C

C H = KC H = K22 B B substitutesubstitute C = K C = K22 B / B / HH

Solve 2 Nonlinear Solve 2 Nonlinear EquationsEquations

H = B + 2 KH = B + 2 K22 B / H B / H

B H = KB H = K11 F – K F – K11 B – K B – K11 K K22 B / H B / H

SimplifySimplify HH22 = B H + 2 K = B H + 2 K22 B B B = H B = H22 / (H + 2K / (H + 2K22))

B HB H22 = K = K11 F H – K F H – K11 B H – K B H – K11 K K22 B B

Substitute for BSubstitute for B HH33 + K + K11 H H22 – K – K11 (F – K (F – K22)H – 2 K)H – 2 K11 K K22 F = 0 F = 0

Only H remains as an unknown!Only H remains as an unknown!

Solve 1 Cubic EquationSolve 1 Cubic EquationSolve 1 Cubic EquationSolve 1 Cubic Equation

Use the Use the dominantdominant solution as first guess solution as first guess in an iteration to the in an iteration to the non-dominantnon-dominant one. one. AA3+3+ B B2+2+ + H + H++ KK11 = B H / A = B H / A

KK11 = x = x22 / (F – x) / (F – x)

xx22 + K + K11 x – F K x – F K11 = 0 = 0

x = ( – Kx = ( – K11 + [K + [K1122 + 4F K + 4F K11]]½½) / 2) / 2

x = 5.3x = 5.31010–3–3 H H F = 0.01, KF = 0.01, K11 = 6 = 61010–3–3, and K, and K22 = 3 = 31010– 4– 4

HH33 + 6 + 61010–3–3 H H22 – 5.8 – 5.81010–3–3 H – 3.6 H – 3.61010–8 –8 = 0= 0

HHoutout = (3.6 = (3.6 1010–8 –8 + + 5.85.81010–3–3 H Hinin – – 661010–3–3 HHinin

22))1/31/3

HHinin (the guess) (the guess) HHoutout (the refinement) (the refinement)

5.35.31010–3–3 5.65.61010–3–3

5.65.61010–3–3 5.585.581010–3–3

5.585.581010–3–3 5.585.581010–3–3

[H[H++] = 5.58] = 5.581010– 3– 3 MM and by B = H and by B = H22 / (H + / (H + 2K2K22),),

[B[B2+2+] = 5.04] = 5.041010– 3– 3 MM and by C = K and by C = K22 B / H, B / H,

[C[C++] = 2.7 ] = 2.7 1010– 3– 3 MM which makes [A which makes [A3+3+] = ] = 4.74.71010– 3– 3 MM

More Conjugate More Conjugate CalculationsCalculationsMore Conjugate More Conjugate CalculationsCalculations

HCOHCO33–– H H++ + CO + CO33

22–– pK pKa2a2 = 10.25 = 10.25 pH of 0.10 pH of 0.10 MM Na Na22COCO33 ? ? (NaOH strong; ignore)(NaOH strong; ignore)

COCO3322–– + H + H22O O HCO HCO33

–– + OH + OH–– K = K K = Kww/K/Ka2a2

K = [HCOK = [HCO33––] [OH] [OH––] / [CO] / [CO33

2–2–] = x] = x22 / (0.10-x) / (0.10-x) x x [0.10 [0.10 1.8 1.81010–4–4 ] ]½½ = 4.2 = 4.21010–3–3 (5% OK)(5% OK)

pOH = 2.37 pOH = 2.37 pH = 14.00 – 2.37 = 11.63 pH = 14.00 – 2.37 = 11.63 Sodium carbonate is in laundry soap.Sodium carbonate is in laundry soap.

Acid Structure and Acid Structure and StrengthStrengthAcid Structure and Acid Structure and StrengthStrength

Higher polarity liberates protons.Higher polarity liberates protons. While all hydrogen halides are strong While all hydrogen halides are strong

acids (save HF), acidity lessens with acids (save HF), acidity lessens with halide size.halide size.

Even non-adjacent electronegativity Even non-adjacent electronegativity drains edrains e–– density, liberating protons. density, liberating protons. HClO is weak but HClOHClO is weak but HClO44 is strong. is strong.

(the H is attached to only 1 of the oxygens)(the H is attached to only 1 of the oxygens)

ClCl33CCOCCO22H is much stronger than CHH is much stronger than CH33COCO22HH

OxoacidsOxoacidsOxoacidsOxoacids

German: OGerman: O22 = = sauerstoffsauerstoff or the or the stuffstuff that makes that makes soursour oxoacids, oxoacids, ––XX––OO––HH

True when X is a fairly electronegative True when X is a fairly electronegative non-metal non-metal (halogen, N, P, S)(halogen, N, P, S) or a metal in a or a metal in a high oxidation state high oxidation state (e.g., H(e.g., H22CrOCrO44))

True as nonadjacent electronegativity True as nonadjacent electronegativity aids polarity (e.g., CHaids polarity (e.g., CH33COCO22H)H)

Oxygen-containing BasesOxygen-containing BasesOxygen-containing BasesOxygen-containing Bases

M – O – HM – O – H Metals in lower oxidation states tend Metals in lower oxidation states tend

to give up the OHto give up the OH–– and not the H and not the H++

Sr(OH)Sr(OH)22 Sr Sr2+2+ + 2 OH + 2 OH––

Al(OH)Al(OH)33 is basic; Al is basic; Al3+3+ is acidic. is acidic.

Water is amphoteric too, acting as a Water is amphoteric too, acting as a base by becoming Hbase by becoming H33OO++, for example., for example.

– BrBrønsted definition: water ønsted definition: water acceptsaccepts the proton. the proton.

Lewis Acids and BasesLewis Acids and BasesLewis Acids and BasesLewis Acids and Bases

Water is both acid & base by Lewis too.Water is both acid & base by Lewis too. Base via HBase via H22OO:: + H + H++ H H33OO++

donates lone pair edonates lone pair e–– to proton to proton

Acid via HAcid via H22O + SO + S2–2– OH OH–– + HS + HS–– accepts the one of sulfide’s electronsaccepts the one of sulfide’s electrons

Lewis’ is the most general definitionLewis’ is the most general definition E.g., CuE.g., Cu2+2+ + 6 + 6 ::NHNH33 Cu(NH Cu(NH33))66

2+2+ Cu’s the acid and Cu’s the acid and ::NHNH33’s the base.’s the base.

Acid-Base AlgorithmAcid-Base AlgorithmAcid-Base AlgorithmAcid-Base Algorithm

Know the Know the significant species significant species for the conditions.for the conditions.

Ignore the rest.Ignore the rest. For quantitative For quantitative

reactions, keep reactions, keep only the products.only the products.

Find acids & Find acids & bases.bases.

Solve controlling KSolve controlling K Write K expression.Write K expression. Set initial conditions Set initial conditions

for smallest change.for smallest change. Define all species in Define all species in

terms of x (change).terms of x (change). Find x solving K Find x solving K

exp.exp. Check any approx.Check any approx. Find pH & [species]Find pH & [species]