19 Heterogeneous & complex equilibria 1 19 Heterogeneous and complex equilibria CaCO 3 exists as aragonite calcite Formation of crystals such as AgCl in a solution is a heterogeneous equilibrium, because there are more than one phase, AgCl (s) = Ag + (aq) + Cl – (aq) Species such as Ag(NH 3 ) 2 + & Ag(CN) 2 – are complexes (or complex ions). Ag + (aq) + 2 NH (aq) =
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19 Heterogeneous & complex equilibria 1 19 Heterogeneous and complex equilibria CaCO 3 exists as aragonite calcite Formation of crystals such as AgCl in.
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19 Heterogeneous & complex equilibria 1
19 Heterogeneous and complex equilibria
CaCO3 exists as aragonite calcite
Formation of crystals such as AgCl in a solution is a heterogeneous equilibrium, because there are more than one phase,
AgCl (s) = Ag+ (aq) + Cl– (aq)
Species such as Ag(NH3)2+ & Ag(CN)2
– are complexes (or complex ions).
Ag+ (aq) + 2 NH3 (aq) = Ag(NH3)2+ (aq)
19 Heterogeneous & complex equilibria 2
Beauty due to heterogeneous equilibria
There are many natural heterogeneous equilibria.
Please think of some!
19 Heterogeneous & complex equilibria 3
The solubility productFor the dissolution,
CaCO3 (s) = Ca2+ (aq) + CO32- (aq)
Ksp = [Ca2+] [CO32-] = 3.8e-9 (a constant) solubility product
Substance Formula Ksp
Aluminum hydroxide Al(OH)3 4.6e-35
Barium chromate BaCrO3 1.2e-10
Calcium phosphate Ca3(PO4)2 1e-26
Iron sulfite FeS 6e-18
Lead sulfite PbS 2.5e-27
Mercury sulfite HgS 1.6e-52
Ksp = [Al3+] [OH-]3
Ksp = [Ca2+]3 [PO4]2
Which is the most and least soluble?
19 Heterogeneous & complex equilibria 4
Solubility product
constants
Compound Ksp Compound Ksp
AgBr 5.0 x 10-13 Fe(OH)3 4.0 x 10-38
AgCl 1.8 x 10-10 FeS 6.3 x 10-18
AgI 8.3 x 10-17 HgS 1.6 x 10-52
AgIO3 3.1 x 10-8 Mg(OH)2 1.8 x 10-11
Ag3PO4 1.3 x 10-20 MgC2O4 8.6 x 10-5
Al(OH)3 2.0 x 10-32 Mn(OH)2 1.9 x 10-13
Ba(OH)2 5.0 x 10-3 MnS 2.5 x 10-13
BaSO4 1.1 x 10-10 NiS 1.0 x 10-24
Bi2S3 1.0 x 10-97 PbCl2 1.6 x 10-5
CaCO3 4.8 x 10-9 PbSO4 1.6 x 10-8
CaC2O4 4.0 x 10-9 PbS 8.0 x 10-28
CaSO4 1.2 x 10-6 SrSO4 3.2 x 10-7
CdS 8.0 x 10-27 Zn(OH)2 3.3 x 10-17
CoS 2.0 x 10-25 ZnS 1.6 x 10-23
CuS 6.3 x 10-36
Table like this is available in handbooks or data bases. Know where to find them when you need them. Write Ksp expressions.
19 Heterogeneous & complex equilibria 5
Ksp and solubilityThe Ksp = 1.0e-6 for BaF2, what are [Ba2+] and [F¯]?
Solution:BaF2 = Ba2+ + 2 F¯
assume x 2 x
Ksp = x (2x)2 = 1.0e-6x = 3 (1.0e-6 / 4) = 6.3e-3 M
[Ba2+] = x = 6.3e-3 M molar solubility = 6.3e-3 *175 = 1.1g/L[F¯] = 2 x = 0.013 M
Checking:6.3e-3 *0.0132 = 1e-6 = Ksp
Calculate solubility of BaCrO3, Ksp = 1.2e-10
Molar mass of BaF2=175 g/mol
19-2
19 Heterogeneous & complex equilibria 6
Concentrations of ions in solution
CaF2(s) = Ca2+(aq) + 2 F- (aq), Ksp know where to find
Ksp = 5.3e-9
19 Heterogeneous & complex equilibria 7
Perception of a saturate solution
Ag2S = 2 Ag+ + S2–
Ksp = [Ag+]2[ S2–]
19 Heterogeneous & complex equilibria 8
Calculate Ksp from Solubility
When 0.50 L saturated CaC2O4 solution was dried, 0.0030 g dry salt was obtained. Evaluate the Ksp.
for a demonstration if you have not seen the experiment
Ag+ (aq) + Cl- (aq) = AgCl(s)
19 Heterogeneous & complex equilibria 10
Common-ion effect on solubilityLike acid-base equilibria, presence of common ions from more than one electrolyte affects the solubility, since Ksp remains constant.
For example, the Ksp = 1.8e-10 for AgCl. The maximum [Ag+] is governed by the condition,
NaCl = Na+ + Cl-0.10 0.10
AgCl = Ag+ + Cl-[Ag+] 0.10
Thus [Ag+] * 0.10 = 1.8e-10 [Ag+] = 1.8e-9 M
Solubility of AgCl = 1.8e-10 = 1.3e-5 M in pure water is 7,454 times more.
? Should we considerAgCl = Ag+ + Cl-
x 0.10+x
19-3
19 Heterogeneous & complex equilibria 11
Graph the common ion effect
AgCl = Ag+ + Cl-
NaCl = Na+ + Cl-
19 Heterogeneous & complex equilibria 12
Condition for precipitationRecall: Predicting reaction directions by comparing Qc and Kc.
Same principle applies to precipitation (ppt)
Q < Ksp, unsaturated (solution)Q = Ksp, saturated (usually two phases are present)Q > Ksp, super-saturated
(unstable, often needs a seed to start the ppt)
19-5
19 Heterogeneous & complex equilibria 13
Separation by precipitationA 10-mL solution contains 0.10 M each of Cl–, Br–, and I– ions. Micro amounts of 0.10 M AgNO3 solution is added to the system. What are the Ag+ concentrations before AgI, AgBr, and AgCl precipitate?Solution: Data sheet Ksp:AgCl 1.8e-10, AgBr 5.0e-13, and AgI 8.3e-17.
[Ag+] for AgI, AgBr, & AgCl solids to form:[I–] = 0.10 M [Ag+] = 8.3e-17/ 0.10 = 8.3e-16 AgI(s) appears
If [H2S] = 1.0 MpH [S2–] Ksp of MS [S2–] for [M2+] = 0.0011 1e-21 1.6e-52 HgS 1.6e-49 (ppt)2 1e-19 2.5e-27 PbS 2.5e-24 (ppt)2.52 1.1e-18 1.1e-21 ZnS 1.1e-18 (no ppt pH < 2.5) 4.39 6e-15 6e-18 FeS 6e-15 (no ppt pH < 4.4)7 1e-9 2.5e-13 MnS _____ (no ppt pH < ____)10 1e-3
11 0.1
19-7
Recalculate [s2-] at various pH if [H2S] = 0.10 M
19 Heterogeneous & complex equilibria 15
pH, and CO2 on CaCO3 solubilityThe [CO3
2–] in a 0.0010 M H2CO3 solution is determined by,H2CO3 = H+ + HCO3
– Ka1 = 4.3e-7HCO3
– = H+ + CO32– Ka2 = 5.6e-11
H2CO3 = 2 H+ + CO32– Koverall = Ka1*Ka2 = 2.4e-17
= [H+]2 [CO32–] / [H2CO3]
[CO32–] = (0.0010*2.4e-17) [H+]–2
= 2.4e-20 * 1e(2*pH) = 2.4e(2*pH-20)
[CO32–] affects [Ca2+] due to equilibrium
CaCO3 = Ca2+ + CO32– Ksp = 8.7e–9
[Ca2+] = 8.7e–9 [CO32–]–1
= 8.7e–9 / 2.4e(2*pH–20)
= 3.6e(20 – 9–2*pH) = 3.6e(11-2*pH)
Decrease pH by 1 increases [Ca2+] by 2 order of magnitude
pH [Ca2+]8 3.6e-57 3.6e-36 0.36
19 Heterogeneous & complex equilibria 16
Stalactites and stalagmites
stalactites
stalagmites
Rain dissolves limestone and when water drops form stalactites and stalagmites in caves. They grew about 2 cm per 1000 years.
The slightly acidic rain dissolves lime stone:CaCO3 (s) + H+ = Ca2+ (aq) + HCO3
- (aq)
When acidity is reduced, solid forms:Ca2+ (aq) + HCO3
- (aq) + OH- (aq) = CaCO3 (s) + H2O
19 Heterogeneous & complex equilibria 17
Stalactites hanging down from the ceiling formed over hundreds of years in Mercer Cavern
19 Heterogeneous & complex equilibria 18
Aragonite formations found at Mercer Caverns, California
The "Angel Wings" are two delicate and translucent crystalline formations, over 9 feet long and 2.5 feet wide in Mercer Caverns
19 Heterogeneous & complex equilibria 19
Equilibrium of complexesMetal ions tend to attract Lewis bases forming coordinated complexes, or complex ions. These formation is governed by equilibrium,
metal ion ligand Step-wise formation constantAg+ (aq) + NH3 (aq) = Ag(NH3)+ (aq) K1
What is the maximum [Cl-] before AgCl(s) forms in a solution containing 1.0 M NH3 and 0.1 M AgNO3?
Solution: Previous slide showed [Ag+] = 9.2e-9 M in a solution when [NH3] = 1.0 MKsp = 1.8e-10 for AgCl (know where to look up)
Thus, the max. [Cl-] = 1.8e-10 / 9.2e-9 = 0.02 MWhen no NH3 is present, max. [Cl-] = 1.8e-10/0.1 = 1.8e-9
What is the maximum [Br-] before AgBr(s) forms in a solution containing 1.0 M NH3 and 0.1 M AgNO3?
Ksp = 5e-13 for AgBr,Thus, the max. [Br-] = 5e-13 / 9.2e-9 = 5.4e-5 M.
0.02-------- = 368 times5.4e-5
19 Heterogeneous & complex equilibria 23
Complex and precipitate formation-2What is the maximum [Br-] in a solution suppose to containing 0.10 M AgNO3 and 0.20 M Na2S2O3 before AgBr(s) (Ksp = 5e-13) forms?
Solution: Kf = 2.9e13 for Ag(S2O3)23–;
Ag(S2O3)23– = Ag+ + 2 S2O3
2– , K = 1/2.9e13 = 3.4e-140.1-x x 2x
4x3 ——— = 3.4e-14; x = (3.4e-14*0.1)1 / 3 = 1.5e-5 = [Ag+] (0.1–x) small
max [Br–] = Ksp/[Ag+] = 5e-13/1.5e-5 = 3.3e-8 (very low)
What is [Br–] = ? If [Na2S2O3] is increased to 1.0 M? See next page
19 Heterogeneous & complex equilibria 24
Complex and precipitate formation-3What is the maximum [Br-] in a solution suppose to containing 0.10 M AgNO3 and 1.0 M Na2S2O3 before AgBr(s) (Ksp = 5e-13) forms?
Solution: Kf = 2.9e13 for Ag(S2O3)23– K = 1/2.9e13 = 3.4e-14
Ag(S2O3)23– = Ag+ + 2 S2O3
2–
0.1-x x 2x+0.8
(0.8+2x)2x ———— = 3.4e-14, x = 3.4e-14*0.1/0.82 = 5.3e-14 = [Ag+] (0.1-x) small
max [Br –] = 5e-13/5.3e-14 = 94 M, unrealistically large
What is the maximum [I – ] in a solution containing 0.10 M AgNO3 and 1.0 M Na2S2O3 before AgI(s) (Ksp = 8e-17) forms?
[I-] = 8e-17 / 5.3e-14 = 0.0015 M; small compare to 0.1 M
(a) The structure of heme is a planar porphoryin ring with iron at the center. (b) Four heme units and four coiled polypeptide chains are bonded together in a molecule of hemoglobin.
19 Heterogeneous & complex equilibria 28
Amphoteric hydroxidesAmphoteric metal hydroxides react with both acids and bases.