coordination chemistry the thermodynamics of metal …...3b. ligand coordination shifts the e⁰ of...
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![Page 1: Coordination Chemistry The Thermodynamics of Metal …...3B. Ligand coordination shifts the E⁰ of metal ions NOTE: Oxidation-reduction (Redox) reactions are written from the reduction](https://reader036.vdocuments.net/reader036/viewer/2022063002/5f25df7b5deb9306b070ff8d/html5/thumbnails/1.jpg)
Coordination ChemistryThe Thermodynamics of Metal-Ligand Binding
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Review of the Previous Lecture
1. Discuss Crystal Field Theory
2. Determined how to calculate Crystal Field Stabilization Energy (CFSE)
3. Evaluated the different factors that contribute to the magnitude of ∆
4. Discussed different crystal field for different geometries Introduced the Jahn Teller Effect
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1. Metal-ligand complexation
M + L M-L
M + L
M-L
ΔG≠
1 2
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1. Metal-ligand complexation
Kinetic Standpoint:
Tells how slow or fast the complexation event is
Later we will discuss inertness (slow ligand exchange) vs lability (rapid ligand exchange)
The ΔG≠ values correspond to the activation barriersfor the forward and reverse reactions and define the rate constants (k)
ΔG≠ , rate of the reaction
M + L M-Lkforward
kreverse
M + L
M-L
ΔG≠
1 2
kforward kreverse
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1. Metal-ligand complexation
Thermodynamic Standpoint:
Tells about the relative ratio of product to reactants at equilibrium
The ΔG⁰ values corresponds to the stability of the M-L complex
ΔG⁰ , stability of the complex
M + L M-L
M + L
M-L
ΔG≠
1 2
K =[M-L]
[M] [L]
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2. Defining AffinityA. Single-step metal ligand interactions
When considering a single metal ligand interaction, we treat the interaction as a single ligand addition event regardless of the denticity of the ligand
M + L M-L
K =[M-L]
[M] [L]Formation (Stability) Constant =
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Say a second ligand can coordinate, now we would have more thana single-step process…
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2A. Single-step metal ligand interactionsThe first ligand binding step:
M + L M-L
K1 =[M-L]
[M] [L]
The second ligand binding step:
M-L + L M-L2
K2 =[M-L2]
[M-L] [L]
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Let’s consider the metal ligand binding process in a cumulative manner.
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2B. Cumulative M-L interactionsWhen considering metal ligand interaction in a cumulative process, we introduce the term β
M + L M-L
β 1 =[M-L]
[M] [L]
Now consider both ligands binding to the metal:
M + 2L M-L2
β 2 =[M-L2]
[M][L]2
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2B. Cumulative M-L interactionsGeneral expression for describing the cumulative process of metal ligand interactions:
M + x L M-Lx
β x =[M-Lx]
[M] [L]x
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2C. Metal ions are never “free” in solutionI. In aqueous solutions, metal ions are water bound:
M M(H2O)xH2O
Some metals interact so strongly with water that they cause hydrolysis
M(H2O) M(OH)- + H+
Metal as Brønsted-Lowry Acid
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M(H2O) M(OH)- + H+
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2C. Metal ions are never “free” in solution
Metal as Brønsted-Lowry Acid
Brønsted-Lowry Acid Relative Acidity: Alkali metal cations- Not acids
Alkaline earth- Slight acidity
2+ Transition metals: Weak acidity
3+ Transition metals: Moderate acidity
4+ and higher: Strong acidity, typically oxygenated ions• Vanadium(V) usually exists as dioxovanadium (VO2
+)
Metal ions lower the effective pKw of water and pKa of ligands.
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M(H2O)x + L M(H2O)x-1L + H2O
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2C. Metal ions are never “free” in solution
II. Ligand binding can be seen as a competition with solvent binding When you write formation constants (K) you ignore the bound water
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2D. Metal-ligand binding preferences
I. Hard Soft Acid Base Theory
log K1
Metal ion F- Cl- Br- I-
Fe3+ (aq) 6.04 1.41 0.5 -
Hg2+ (aq) 1.0 6.7 8.9 12.7
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2D. Metal-ligand binding preferencesII. The Chelate Effect
When coordinating through the same type of atom, a chelating ligand willoutcompete a monodentate ligand for metal binding.
Chelates are favorable when they form five/six membered rings when metalbound
Smaller rings are strained
Larger rings result in unfavorable ligand distortion
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2D. Metal-ligand binding preferencesLet’s consider thermodynamic factors for the stability afforded by chelators.
ΔG⁰ = ΔH ⁰ - TΔS⁰
Enthalpy (ΔH ⁰): Bond breaking/bond forming
Entropy (ΔS⁰): Tendency toward “disorder”
Compare metal binding by:
CH3NH2 vs
en
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2D. Metal-ligand binding preferencesOctahedral Cd2+ complexes:
A. [Cd(H2O)6]2+ + 4 CH3NH2 [Cd(CH3NH2)4(H2O)2]
2+ + 4 H2O
B. [Cd(H2O)6]2+ + 2 en [Cd(en)2(H2O)2]
2+ + 4 H2O
K (M)
3.3 x 106
4.0 x 1010
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2D. Metal-ligand binding preferencesOctahedral Cd2+ complexes:
A. [Cd(H2O)6]2+ + 4 CH3NH2 [Cd(CH3NH2)4(H2O)2]
2+ + 4 H2O
B. [Cd(H2O)6]2+ + 2 en [Cd(en)2(H2O)2]
2+ + 4 H2O
5 molecules
3.3 x 106
4.0 x 1010
K (M)
5 molecules
3 molecules 5 molecules
2 more molecules¨.
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2D. Metal-ligand binding preferencesOctahedral Cd2+ complexes:
A. [Cd(H2O)6]2+ + 4 CH3NH2 [Cd(CH3NH2)4(H2O)2]
2+ + 4 H2O
B. [Cd(H2O)6]2+ + 2 en [Cd(en)2(H2O)2]
2+ + 4 H2O
5 molecules
3.3 x 106
4.0 x 1010
Rxn.
5 molecules
3 molecules 5 molecules
K (M)
ΔH⁰ (kJ/mol) ΔS⁰ (kJ/mol) ΔG⁰ (kJ/mol)
A
B
-57.3
-56.5
-67.3
+47.1
-37.2
-60.7
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3. Redox Stability
The stability of the oxidation state of a metal ion in solution is highly dependent onthe biochemical conditions and the coordination environment. Both can dictate the“preference” of M-L interactions.
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3A. DefinitionsOxidation: Loss of one or more electrons
Reduction: Gain of one or more electrons
Oxidation-reduction (Redox) reactions are thermodynamically driven.
ΔG⁰ = - nFE⁰
n = # of electrons involved
F = Faraday’s constant (96,485 C/mol or J/V)
E⁰ = Electromotive force: The potential energy for electron (or charge) movement
If E⁰ is +, ΔG⁰ is - ; Spontaneous reaction
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3B. Ligand coordination shifts the E⁰ of metal ions
NOTE: Oxidation-reduction (Redox) reactions are written from the reduction perspective.
Consider Fe3+:
Half-reaction- Fe3+(aq) + e- Fe2+(aq) E⁰ = +0.77 V vs Standard Hydrogen Electrode(SHE)
In a reducing environment, ligand-free Fe has an oxidation state of 2+
But we live in an oxidizing environment, Fe3+ dominates
P = 1 atm; T = 25 ⁰C, pH =0
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3B. Ligand coordination shifts the E⁰ of metal ions
NOTE: Oxidation-reduction (Redox) reactions are written from the reduction perspective.
Consider Fe3+:
Half-reaction- Fe3+(aq) + e- Fe2+(aq) E⁰ = +0.77 V vs (SHE)
+ e- E⁰ = -0.53 V vs (SHE)pH = 7.0
Fe(III) Fe(II)
The ligand stabilized the oxidation state of Fe(III).
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3C. Redox potentials for metal ions can be found in tables or formatted in simplified diagrams.
Latimer Diagram: Summarizes a considerable amount of thermodynamic information about the oxidation states of an element.
• Diagrams are written for acidic, neutral, and basic conditions
• Omit H2O, H3O+, OH-
• Write oxidation state, highest to lowest, left to right
Fe3+(aq) Fe2+(aq) Fe(s) Acidic solution (pH 0)
+0.77 V -0.44 V
-0.04 V
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3C. Redox potentials for metal ions can be found in tables or formatted in simplified diagrams.
Latimer Diagram: Summarizes a considerable amount of thermodynamic information about the oxidation states of an element.
• Diagrams are written for acidic, neutral, and basic conditions
• Omit H2O, H3O+, OH-
• Write oxidation state, highest to lowest, left to right
Fe3+(aq) Fe2+(aq) Fe(s) Acidic solution (pH 0)
+0.77 V -0.44 V
Fe3+(aq) + e- Fe2+(aq)
Fe2+(aq) + 2e- Fe (s)
Fe3+(aq) + 3e- Fe (s)
-0.04 V