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

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.

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