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Zumdahls Chapter 15

Applications of

Aqueous Equilibria

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Chapter Contents

Acid-Base Equilibria Common Ion Effect

Buffers

Titration Curve

Indicators

Solubility Solubility Product

Common Ion Effect

pH and Solubility

Complex Equilibria

Complexes andSolubilities

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Acid-Base Titrations

Le Chtlier: restoration of equilibriumreplaces species lost. QK

E.g., H2O is a weaker electrolyte thanvirtually any other weak acid, so

Titrating weak acid with strong basebinds

proton in water, removing product! such titrations are quantitative.

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Common Ion in Acid-Base

Le Chtlier: restoration of equilibriumconsumes addends. QK

Addition of an ion already in equilibrium(Common Ion Effect)restores K byconsuming the common ion.

NH3 + H2O NH4+ + OH Kb=1.8105 0.1 M NH3 [OH

] [1.81050.1] = 4103

Make it 0.1 M NH4+ and [OH] 1.8105 !

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Buffer Solutions

Kb = [BH+][OH]/[B]

If [B]=[BH+], then [OH] = Kb

Ka = [H+][A]/[HA]

If [HA]=[A], then [H+] = Ka

Furthermore, in eithercase, excess H+

or OH finds abundanceof its reactant!

Associated robust pH, a bufferhallmark.

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Buffer Calculation

0.1 M ea. [NH4+] & [NH3]; pOH = 4.74

100 mL of this buffer contains 10 mmolof each of those species.

Reactfully 5 mmol OH(in same 100 mL)

Kb = (0.1

0.05+x) (0+x) / (0.1+0.05x) x = [OH]new (3 Kb)

or pOHnew = 4.27 5% rule OK due to starting point of full reaction!

pOH = 0.47 trivialgiven even a 50%addend!

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Titration Curves (0.1 M acetic)

Titration: Weak Acid by Strong Base

0

2

4

6

8

10

12

14

0 0.05 0.1 0.15 0.2 0.25

Volume of Base

pH

While [HA]/[A] or [B]/[BH+]notnear zero, buffering makes

pH near pK pH changes slowly near

completion.

Near endpoint, those ratios

vanish making [H+] verysensitive to titrant. pH changes very rapidly near

endpoint!

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Strong/Strong Titration Curve

Vbase V total [H+] pH

0 100 1 M 0

50 150 .5/1.5 0.48

90 190 .1/1.9 1.28

95 195 .05/1.95 1.59

99 199 .01/1.99 2.30

99.9 199.9 .001/1.999 3.30

100 200 0/2 7.00

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Acid-Base Indicators

Indicators: molecules whose acid-baseconjugates have distinct colors.

Color change occurs as acid/base rationears 1, i.e., as pHpKa (of indicator!)

Extremesensitivity of pH to titrant

volume near endpoint makes use ofindicators quantitative.

Match pKindicator to pH at equivalence.

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pH at Equivalence

Sample is gone, replaced by conjugateat original number of moles. [conjugate]0 = [sample]0 (V0 / Vtotal) F

[conjugate]equilibrium = F x (back rxn with water)

Kconjugate

= x2 / (F x) or x [FKc

]

pHequivalence = px or 14 px = 8.72(acetic)

pKindicator pHequivalence is [Ind]/[Ind]1.

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pH in the Buffer Region

Ka = [H+] [A] / [HA] = [H+] [S]/[HA]

log Ka = log[H+

] + log( [S]/[HA] ) pKa = pH log( [S]/[HA] )

pH = pKa + log( [S]/[HA] ) neither S nor HA=0

Henderson-Hasselbalch Equation pOH = pKb + log( [BH

+]/[B] )

Concentration ratios = mole ratios!

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Solubility Product

AxBy(s) x Ay+(aq) + y Bx(aq)

Q = [Ay+

]x

[Bx

]y

for arbitraryconcentrations K =[Ay+]eqx [Bx]eqy for saturation conc.

Q < K implies no solid

Q = K implies saturated solution Q > Ksupersaturation difficult to

achieve! Spontaneously precipitates.

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Calculating Solubility Product

Make a saturated solution.

Remove it from its precipitate. Evaporate to dryness and weigh solid.

Convert to moles n of solid in original V.

If AxBy then [Ay+]=x(n/V) ; [Bx]=y(n/V) Ksp = (xn/V)

x (yn/v)y x and y have enormous influence

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Solubility and pH

If dissolved ions are conjugates of weakacid, say, bothKsp and Kb must besatisfied. Ksp fixes [A

] at equilibrium value, and Kbestablishes [OH] and [HA], for example.

If Ka1 and [H+] can lower [A] belowthe solubility limit, acid can dissolve thesolid. (Assuming solid is limiting reactant.)

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Dissolving Oxides

Ag2O + H2O 2 Ag+ + 2 OH (41016)

2 H

+

+ 2 OH

2 H2O (10

+14

)

2

Ag2O + 2H

+ 2Ag+ + H2O (410+12)

Equilibrium lies far to right for modest acid.

Cu2O + H2O 2 Cu+

+ 2 OH

(41030

) Cu2O + 2H

+ 2Cu+ + H2O (4102)

Only concentrated acids will suffice.

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Complex Equilibria

Empty or unfilled metal d-orbitals aretargets for lone pair electrons in dativeor coordinate-covalentbonding. Square planar or octahedral (and beyond)

geometries ofligands(e pair donors)

bind to metal atoms to make complexes. Ligands can be neutral (H2O, NH3, CO )

or charged (Cl, CN, S2O32 ).

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Complex Equilibrium Constant

Exchange of ligands (labile) is governedby equilibrium constants.

Solid solubilities are thus influenced byligand availability.

H2O alwaysavailable (aq), but its not the

strongest ligand. Serial replacement ofH2O by other ligands leads to a sequenceof equilibrium constants.

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vs. K

Polyprotic acid constants proceedproton by proton: HSO4

(aq) H+(aq) + SO42(aq) Ka2=10

2

Ligand addition constants, , arecumulative instead:Ag+(aq) + 2 I(aq) AgI2

(aq) 2=1011

really Ag(H2O)4+ + 2 I Ag(H2O)2I2

+ 2 H2O