Topic 1: Inorganic Chemistry I - Chelate Effect

Effective Nuclear Charge (Z_eff) and Ionic Size

As one moves across a row of transition metals (left to right), the nuclear charge increases and electrons are added to the same shell, causing ion sizes to decrease and Z_eff to increase, which influences stability constants.

Gibbs Energy (ΔG)

ΔG = ΔH - TΔS = -RTlnK

Where:

• ΔG - Gibbs free energy: measures the spontaneity of a reaction. ΔG < 0 means the reaction is spontaneous, ΔG > 0 means the reaction is not spontaneous

• ΔH - Enthalpy change: the heat absorbed or released during a reaction. ΔH < 0 means the reaction is exothermic, ΔH > 0 means the reaction is endothermic

• T - Temperature: measured in kelvins (K). Higher temperatures can affect reaction spontaneity

• ΔS - Entropy change: the change in disorder or randomness of the system. ΔS > 0 means increased disorder, ΔS < 0 means decreased disorder

• R - Universal gas constant: equal to 8.314 J·mol⁻¹·K⁻¹

• K - Equilibrium constant: indicates the extent to which a reaction proceeds toward products

• ln - Natural logarithm: used to relate Gibbs energy to the equilibrium constant through a logarithmic relationship

Stability Constant (β)

• The stability constant β is the equilibrium constant for the formation of a complex in solution

• Also called the formation constant (K_f).

• Cumulative constant: β often represents the complete complexation process even when complexes form in steps

Stability Prediction

Larger β (or log β) means a more stable complex.

Thermodynamic Nature of β

β is thermodynamic—it indicates equilibrium composition but not the speed of formation (kinetics).

Dissociation Constant (K_d)

• K_d = 1/β.

• The smaller the K_d, the more stable the complex.

Stability Constant Formula

For the ligand displacement reaction: M(H₂O)_xⁿ⁺ + yL ⇌ ML_yⁿ⁺ + xH₂O

β = [ML_yⁿ⁺] / ([L]^y [M(H₂O)_xⁿ⁺]).

• Water is omitted from the equilibrium expression because its concentration is effectively constant in aqueous solution.

Ligand Displacement Reactions

A new ligand forms a more stable complex, displacing the existing ligand.

• Examples:

  • Cyanide and Iron: [Fe(H₂O)₆]²⁺ + 6CN⁻ ⇌ [Fe(CN)₆]⁴⁻ + 6H₂O.

  • Nickel and Copper: [Cu(H₂O)₆]²⁺ + 4NH₃ → [Cu(NH₃)₄(H₂O)₂]²⁺.

Chelate Effect

Complexes with multidentate ligands are more stable than those with monodentate ligands because they form ring structures.

Chelate Geometry

Chelates form 5- or 6-membered rings, which are usually most stable.

Thermodynamic Origin of Chelate Effect

The chelate effect is driven by entropy (ΔS):

• From the ligand displacement reaction, the amount of discrete molecules released increases

  • E.g: [Ni(NH₃)₆]²⁺ + 3 en ⇌ [Ni(en)₃]²⁺ + 6 NH₃, the reaction starts with 3 discrete molecules, but ends by releasing 6 discrete molecules

• More particles → more disorder → more entropy (ΔS) → thermodynamically favoured → more stability

  • From the Gibbs free energy equation, a greater entropy leads to greater spontaneity, and hence more stability

Optimum Chelate Effect (EDTA)

Hexadentate ligands like EDTA⁴⁻ create highly stable complexes, displacing multiple water molecules and increasing entropy.

• When one EDTA⁴⁻ binds, 6 water molecules are released (2 → 7 particles), giving a large entropy gain.

Factors Affecting β: Charge-to-Radius Ratio

Higher charge and smaller radius increase β, strengthening metal-ligand attraction.

• Example:

  • Higher Charge: Fe²⁺ → Fe³⁺

  • Smaller Radius: Across transition metals with same charge, Fe²⁺ < Co²⁺ < Ni²⁺ < Cu²⁺.

Factors Affecting β: Chelation

Increased chelation raises β because it releases more discrete particles (higher entropy) and thus greater stability.

Complex Formation and Solubility

Stable complex formation with the addition of a ligand increases the solubility of sparingly soluble salts by reducing [Mn⁺].

Complex Formation and Solubility: Solubility Equilibrium

Sparingly Soluble Metal Salt: MX_n (s) ⇌ Mⁿ⁺ (aq) + nX ⁻(aq) - Equilibrium constant: K_sp

*(aq) suggests Mⁿ⁺ is surrounded by water ligands

Complex Formation and Solubility: Complex Formation

Complex Formation with the Addition of a Ligand: Mⁿ⁺ (aq) + yL (aq) ⇌ ML_y (aq) - Equilibrium Constant: β

• Forming complexes lowers [Mⁿ⁺] → shifting K_sp right → and dissolving more MX_n (s).

Beer-Lambert Law Principle

Absorbance of light (A) is directly proportional to the concentration (c) of a colored solution.

Beer-Lambert Mathematical Expression

A = log₁₀(I_o/I) = ε·c·L.

Beer-Lambert Variables

• A = absorbance

• I_o = incident light

• I = transmitted light

• ε = molar absorption coefficient (L·mol⁻¹·cm⁻¹)

• c = concentration

• L = path length (cm).

Calibration Curve

A plot of absorbance (A) vs concentration (c) gives a straight line; used to determine unknown concentrations.