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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
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