SOLUTION CHEMISTRY

1
SOLUTION CHEMISTRY

• Assigned reading Sparks Chapter 4 and Chapter 3
  pp. 102 - 106  
• Additional readingEssington, Chapter 5, Skip
  sections 5.6.3, 5.7 (except Table 5.11) and 5.11
  Lindsay, Chapter 2 Sparks Chapter 4 and Chapter
  3 pp. 102 - 106 McBride, 1994 Chapter 1, except
  1.2f

2
Energy and Chemical Equilibrium
3
Gibbs Free Energy

• At constant temperature (T) and pressure (P) the
  energy associated with any system is
• G H - TS
• G is Gibbs free energy, J or kJ
• H is Enthalpy (thermal energy), J
• T is the absolute Temperature, Kelvin
• S is the Entropy (degree of order), J K-1
• SI unit energy unit is Joule
• Chemists used to use calories
• 1.00 calorie is the energy needed to raise the
  temperature of 1.00 g of water 1.00 degree C

4
When a reaction occurs

• ?G ?H - T?S
• ?H change in enthalpy, J mol-1
• ?H lt 0 when heat is evolved (exothermic).
• ?S change in entropy, J mol-1 K-1
• When disorder increases entropy is increased
• Reactions spontaneously go forward when the
  energy decreases.
• Driven by ?H or ?S or both

5
Example Reaction

• Dissolution of pure AgCl in pure water.
• AgCl Ag Cl-
• How far will this reaction go to reach
  equilibrium?
• We need to develop a way to find the minimum
  energy.

6
Equilibrium at minimum energy
7
The Potential Energy of Individual Components

• Chemical potential, µ
• Potential energy for each individual component
• For any individual component, i, the number of
  moles is ni and
• The components in the example above are AgCl,
  Ag, and Cl-  
• µ is in units of J mol-1

8
Chemical potential energy

• Energy per unit mole of each component
• Need define zero point of the energy scale.
• Zero is the pure element at standard temperature
  and pressure (298 K and one atmosphere).
• For a component AgCl the chemical potential is
  the energy of formation from the pure element or
  elements.
• ?G0 f µ0

9
Example of free energy of formation data of
hydrated ions in solution, Essington Table 5.5
Element ? Ion in water
10
Formation of aqueous ions

• Removal or addition of electrons to form ion
• Endothermic (takes energy)
• Hydration in water
• Highly exothermic (releases energy)

11
The chemical potential energy associated with a
mole of pure solid is easy to describe

• It is the just the free energy of formation.
• ?G0f of AgCl is the energy that is released when
  gaseous Cl2 reacts with metallic Ag to form AgCl.
• ?G0f -109.7 kJ mol-1

12
In solution the energy of mole of dissolved
component is affected by its concentration

• Chemical potential, µi, varies with concentration
  according to
• µi µi0 RT ln ai
• ?G0 f µ0 at standard state chemical potential
• ai is activity (a concentration variable)
• R, gas constant ( 8.31 Joules mole-1 oK-1)
• At lower concentration solutes are less reactive,
  e.g. H is more reactive at high concentration.
• At low concentration the entropy is higher

13
Standard State in Solution one molal

• One molal (m) one mole per 1000 g of water
• ?G0 f µ0 is determined at 1.00 m
• ?G0 f for Cl- this is the energy for the
  formation of Cl- is formed from Cl2 and its
  dissolution to form a 1 m solution
• When a 1 than
• µi µi0 RT ln (1.00)

14
Molal and Molar

• Activity is idealized molal concentration
  relative to standard conditions (1 M)
• At low concentration molal mol L-1 M molar
• Later we will deal with the considerations of non
  ideality

15
For gases the standard state is one atmosphere
pressure

• µi µi0 RT ln ai
• Use pressure units in atmospheres
• Standard state is 1 atm
• At normal pressures gases are ideal and
• µi µi0 RT ln Pi

16
Standard states of liquids and solids

• Solids and liquids
• Standard states
• Solids a 1 for pure solid and µ µo (is
  constant)
• Liquid a 1 for pure liquid and µ µo
• For liquid and solid at constant T and P the
  reactivity pre unit mole is invariant with
  quantity in the breaker
• E.g.
• Solubility invariant with quantity
• Vapor pressure invariant with quantity

17
Standard state (cont.)

• E.g. Solubility
• At equilibrium solubility it doesnt make any
  difference if there is a milligram or many grams
  of AgCl in the bottom of the beaker.
• The energy per mole of AgCl is not dependent on
  the quantity in the beaker.

18
Standard State (cont.)

• Gases a pressure
• Standard state
• a 1 for pure gas at 1 atm pressure (101 kPa).

19
Again

• Per mole of gas or solute the potential energy
  (reactivity) increases with increasing pressure
  or increasing concentration.
• e.g. Each molecule or ion has more potential to
  react at higher concentrations.

20
For mixtures of liquids or solids activity is
related to mole fraction

• Mole fraction concentrations. X, liquids, and
  solid solutions.
• e.g. A two component mixture with a moles of
  component, A and b moles of B, ideally.
• In a 50/50 mixture of the, in the ideal case, a
  component (per mole) is 50 as reactive as the
  pure component.

21
Energy calculation for a reaction

• The energy used or produced
• Potential energy of the products minus the
  potential energy of the the reactants equals
  the energy absorbed or released during reaction.

22
?G of a reaction

• e.g. Dissolution of AgCl in pure water.
• AgCl Ag Cl-
• Change in energy is
• ?G (µAg µCl) - µAgCl
• ?G (µ0Ag µ0Cl) - µ0AgCl RT((ln aAg
  ln aCl) - (ln aAgCl))
• Standard chemical potential (when a 1),
  calculated from tabulated data
• ?G0 (µ0Ag µ0Cl) - µ0AgCl
• (?G0fAg ?G0fcl) - ?G0fcl

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?G0

• Standard Chemical Potential
• Tabulated for various reactions or
• Calculated from Standard Free Energy of formation
  ?G0f
• Sum for free energy of formation for products
  minus reactants

24
?G of reaction

• ?G ?G0 RT((ln aAg ln aCl) - (ln
  aAgCl))
• ?G0 RT ln (aAgaCl/aAgCl)

25
Use ?G0f to calculate ?G

• AgCl(s) Ag(aq) Cl-(aq)
• ?G0f kJmol-1
• AgCl(s) -109.7
• Ag(aq) 77.1 ( 1 molal)
• Cl-(aq -131.2 (1 molal)
• ?Go 55.6

26
?G AND ?Go

• Activity of a pure solid 1
• ?G ?Go RT ln (Ag)(Cl-)
• ?G ?Go RT ln IAP (IAP ion activity
  product)
• If all species are at unit activity (standard
  state, IAP 1)
• ?G ?Go
• This will be far from equilibrium
• Energy yield if in the end Cl- and Ag are 1 m
  (1M)
• 55.6 kJ mol-1 means there is a need to add
  energy

27
Equilibrium

• At equilibrium, ?G 0, sum of chemical potential
  of products equals chemical potential of
  reactants.
• IAP K (equilibrium constant)
• ?Go - RT ln (Ag)(Cl-) - RT ln K
• K (Ag)(Cl-)
• Solubility product
• At 25oC, ?Go -5.72 log K (kJ mole-1)

28
?Go and log K

• ?Go conveys the same information as log K but
  with opposite sign
• For AgCl dissolution
• ?Go 55.6 kJ mole-1
• log K -9.7
• Ksp 1.9 x 10-10
• The low K and high positive ?Go show that AgCl
  dissolves very little.

29
In Class Exercise

• Calculate the concentration of Cl- and Ag in
  equilibrium with pure AgCl assuming
  stoichiometric dissolution.

30
Answer

• K (Ag)(Cl-)
• (Ag) log K -9.7
• K (Cl-)(Cl-) (Cl-)2
• log K -9.7 K 10-9.7
• (Cl-) square root of K 10-4.85
• 1.4 x 10-5 M

31
Temperature dependence of equilibrium K

• Depends on ?H
• ?G0 ?H0 - T?S0
• -RT ln K ?H0 - T?S0
• ln K -?H0/RT ?S0/R

32
Water and Hydration of Ions in Solution
33
HYDRATION ENERGY OF IONS

• Water interacts with components in solution.
• Water is a dipole and is attracted to ions.
• ( McBride, Fig. 1.2)

34

• Hydrogen bond
• Important in the structure of water (McBride,
  1994 Fig. 1.3)

35
Bond Energy in Water

• H-O 470 kJ mol-1
• H --- O (hydrogen bond) 23.3 kJ mol-1
• Because of H bonding water has
• High boiling point
• High melting point
• Low density in solid state

36
Hydration of cations

• Thought experiment Determine the ?Go of the
  following reaction
• K(g) xH2O(l) K(aq)
• When the cation is put in water, the
  hydrogen-bonded structure of water is broken up.
• Water dipoles align themselves around the cation.

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• The hydration energy is greater (more negative)
  for smaller diameter cations
• Entropy, S, increases with hydration, the
  structure of the hydrogen bonding is broken down.
  
• -?Go is proportional to z2/r where is the
  cationic radius.
• -?H is the release of heat

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Table 1. Hydration energy of alkali metal
cations, at 25o (std temperature)
39
Spheres of Hydration

• Inner sphere of water in direct contact with an
  ion.
• Coordination number for inner sphere is like that
  of O coordination in minerals
• E.g. for Al3 the c.n. is 6
• Second sphere of water is is less tightly held

40
Overall hydrated radius an z2/r

• Hydrated size is greater with increasing z2/r
• For a fixed charge number the hydrated radius is
  inversely proportional to the ionic radius.

41
Hydrated Radii, Table 5.3
42
Non Ideality in Solution and Activity Coefficients
43
ACTIVITY COEFFICIENTS IN AQUEOUS SOLUTIONS

• Ions interact with each other in solution to
  reduce the reactivity.
• Each anion has a swarm of cations surrounding
  it.
• Each cation has a swarm of anions surrounding
  it.

44

• Adjust measured concentration of ions with an
  "activity coefficient"
• ai ?iCi
• ?i - activity coefficient
• function of ionic strength
• Note We will use ( ) for activity, and for
  concentration.

45
The activity coefficient is a function of ionic
strength

• The greater the ionic strength (concentration of
  ions) the, the lower the activity coefficient.
• Calculation of ?i is based on the ionic
  strength, I.
• I 1/2 ?Cizi2
• where z is the ionic charge

46
Debye -Hückel Equation

• Assume each cation or anion is a point charge
  surrounded with oppositely charged ions. The
  "counter ion charge" reduces the free energy of
  the ion (more stable, less reactive).
• Calculate extra stability using an approach
  similar to the Gouy-Chapman double-layer theory
  for ion adsorption on clays.
• Debye-Hückel equation (good to I 0.001M).
• log ?i -Azi2 vI
• Where A 0.512 at 25oC

47

• Extended D-H equation (good to I 0.1M)
• Corrects for the size of real ions
• a D-H radius of "closest approach" larger than
  crystal radius.
• B 0.33 at 25o C

48
Species without charge

• Species without charge e.g. dissolved CO2,
  dissolved NH3, organic solvents like benzene,
  etc., the activity coefficient is 1.

49
Extended D H activity Coefficient, Essington
Table 5.4
50
Table 5.4 (cont.)
51
Davies Equation

• Davies equation (good to I 0.5M)
• Second factor accounts for the decrease in water
  activity with increasing I, due to cation
  hydration.
• (NOTE pH is an activity variable - not a
  concentration variable - pH -log (H)
• For molecular species, z 0 and ?I 1.
• e.g. H4SiO4 and CH3OH

52
In class exercise.

• Calculate the activity of Ca2 in a 0.0002 M
  CaCl2
• Use the Debye-Hückel equation

53
Answer using D-H Equation
0.05
54
Brönsted Acidity Again
55
Acetic Acid

• HOAc --gt H OAc-

56

• Dissociation (ionization) constant
• K 1.4x 10-5 log K -4.85 K 10-4.85
• Mass balance equation.
• HOAct HOAc OAc-

57
Equations
58
Variation of acetate species with pH

• Approximations
• For KA ltlt H or pH ltlt pKA
• HOAc HOAct
• For KA gt gt H or pH gt gt pKA
• OAc- HOAct
• When pH pK
• OAc- HOAc 0.5HOAct

59
Phosphoric acid

• Ionization of a polyprotic weak acid
• Dissociation Constants log KA pKA
• H3PO4 H H2PO4- 2.1
• H2PO4 - H HPO42- 7.2
• HPO42- H PO43 12.2
• PT PO43- HPO42- H2PO4- H3PO4

60

• Calculate species
• Because of the pK values are very different, can
  treat each ionization separately
• Use the same method as above for acetic acid.

61
Variation of phosphate species with pH.

• At pH values of 3.3 to 6.0 more that 95 of
  phosphate is H2PO4-.
• At pH values of 8.4 to 12 more that 95 of
  phosphate is HPO42-.

p
K
p
K
H2 PO4
1
F
r
a
ct
i
o
n
1
o
f
Sp
eci
e
pH
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Calulatedn overall constants from step-wise
constamnts

• Log K
• H3PO4 H H2PO4- 2.1
• H2PO4 - H HPO42- 7.2
• H3PO4 2H H2PO42- 9.3

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Hydrolyzing Cations are Weak Acids
64
Weak Acid Behavior of Hydrolyzing Cations

• e.g. Al3
• Al3 H2O AlOH2 H
• pKA 5.0
• Acid strength similar to acetic acid

65
Hydrolysis and the Formation of Hydroxy Complexes
and Oxyanions

• If ionic potential, z/r, is great enough
  hydration water can lose an H.
• e.g. Al3, r 0.53 Å

66
In class exercise.

• Compare the value of z/r for Na, Al3 and S6
• S, r 0.12 Å
• Na, r 1.02 Å
• Al, r 0.54 Å

67
Answer

68
First hydrolysis constants for some important
cations

• -log K
• Mg2 11.4
• Mn2 10.6
• Fe2 9.5
• Co2 9.7
• Ni2 9.9
• Cu2 7.5
• Zn2 9.1
• Fe3 2.2
• Of these cations only Fe3, Al3, and Cu2
  hydrolyze to any great extent in soils.

69
Mulitistep hydrolysis of metal cations e.g. Al3

• Al3 H2O AlOH2 H - 5.0
• AlOH2 H2O Al(OH)2 H - 4.9
• Al(OH)2 H2O Al(OH)3o H - 5.7
• Al(OH)3o H2O Al(OH)4- H - 7.4
• These are different than used by some text books

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Mulitistep hydrolysis of metal cations e.g. Al3

• Al3 H2O AlOH2 H - 5.0
• AlOH2 H2O Al(OH)2 H - 4.9
• Al(OH)2 H2O Al(OH)3o H - 5.7
• Al(OH)3o H2O Al(OH)4- H - 7.4
• These are different than used by some books
  (still some disagreement)

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Distribution of hydrolysis species of Fe and Cr,
Fig 5.6 (Essington)
72
Acidity constants, Table 3.2, Stumm and Morgan,
3rd ed. (see also Table 5.8 in Essington)
B
73
Computer Calculation of Solution Equilibria

• The distribution of species in solutions can be
  calculated using a variety of computer programs.
• MINTEQA2, developed by USEPA is commonly used. It
  is available from EPA in a DOS format (see the
  links on the class web site).
• A new Windows, visual Minteq (Vminteq) version is
  available for free from the author
  http//www.lwr.kth.se/english/OurSoftware/Vminteq/
  index.htm
• We will use this in problem sets.

74
In Class Exercise Use VMINTEQ to Calculate
Hydrolysis

• .000010 M Al3 in a 0.001 M NaCl solution at pH
  4.5 and 5
• What happens at pH 5 in 0.5 M NaCl

75
Oxyanions
76
S(VI) forms an oxyanion

• If z/r is even greater water can lose both H and
  an oxyanion can form.
• Sulfuric acid
• In water the H ionizes, and sulfate is formed.
• pKa1 -3 pKa2 1.99

77
Hydrolysis Groups, Sparks p.103

• Oxocomplexes (yellow) assumes cationic charge,
  rule of 8.
• Hydrolyzes at higher environmental pH (dark).
• Do not greatly hydrolyze at environmental pH
  (light grey).

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Henrys law and the dissolution of CO2

• CO2 is a very important weak acid in soils
• For dissolved volatile compounds (e.g. benzene,
  chloroform, volatile pesticides, carbon dioxide,
  etc. )
• P Kx
• where K is the Henrys law constant, x is the
  mole fraction in water and P is the partial
  pressure in air.

79

• At low concentration the equation can be
  rewritten in terms of molar concentration and
• P K?C
• If the solute his uncharged ? 1, and
• P KC
• Example CO2 dissolution

80
In class exercise.

• If the partial pressure of carbon dioxide in the
  air is .00035 atm. At equilibrium what is the
  concentration of dissolved molecular carbon
  dioxide if the Henrys Law constant is 30 L atm
  mol-1.

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Answer

• CO2 H2O --gt H2CO3 (also know as CO2 aq)
• (30 L atm mol-1)H2CO3 (0.00035 atm)
• H2CO3 1.2 x
  10-5mol L-1

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Dissolution of CO2

• H2O CO2 H2CO3 log K - 1.46
• Dissolved CO2 is CO2(aq) or H2CO3
• H2CO3 is only a function of PCO2
• Dissolved CO2 (carbonic acid) is a weak acid and
• log K
• H2CO3 H HCO3- - 6.35
• HCO3- H CO32- -10.33
• For some calculations we need the mass balance
  equation for carbon
• CT H2CO3 CO32- HCO3-
• CT Dissolved Inorganic Carbon (DIC)

83
The Stability of Complexes

• Complex of sulfate with Fe3
• Fe3 SO42- FeSO4
• ligand complex ion
• Formation constant
• K 104.04
• log K 4.04

84
In class exercise.

• If the concentration of uncomplexed sulfate ion
  is 0.01 M or 0.001 M what is the ratio of complex
  iron to uncomplexed iron?

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Answer
86
Pearson Hardnesssee Chap. 3 pp. 102 - 106

• Hard acids complex with hard bases and soft acids
  complex with soft bases.
• Hard metals and ligands are ions that do not
  readily form covalent bonds.
• Soft acid and base species readily deform and
  form covalent bonds.

87
Table 1.3 in McBride
88
Irving-Williams series and transition metals

• Transition Metal Complexes
• The ability of transition metals to covalently
  bond with ligands is enhanced by d-orbitals
• Relative stability of inner sphere complexes
  generally follows the Irving-Williams series
• Mn2 lt Fe2 lt Co2 lt Ni2 lt Cu2 gt Zn2

89
Complexes in soil solution, Cu2, Fig, 5.15
(Essington)
90
Complexes in soil solution, Zn2, Fig, 5.15
91
Quick Summary

• The point of equilibrium in a chemical reaction
  is the point of lowest energy .
• Free energy minimization, ? G O, can be used to
  find equilibrium constants.
• Ions in solution hydrate,
• Hydration is an important property for in
  solution.

92

• Can use Davies or Extended Debye-Hukel equation
  to correct for ionic interaction effects
• Complex formation is important for many ions in
  soil solution.
• Acid-base equilibria of weak acids is important
  in soils.
• Hydrolysis to form hydroxy-ions is a property of
  some cations.

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