Rates of Water Exchange on the [Fe₄(OH)₂(hpdta)₂(H₂O)₄]⁰ Molecule and Its Implications for Geochemistry

Abstract

The ammonium salt of [Fe₄O­(OH)­(hpdta)₂(H₂O)₄]⁻ is soluble and makes a monospecific solution of [Fe₄(OH)₂(hpdta)₂(H₂O)₄]⁰(aq) in acidic solutions (hpdta = 2-hydroxy­propane-1,3-diamino-<i>N</i>,<i>N</i>,<i>N</i>′,<i>N</i>′-tetraacetate). This tetramer is a diprotic acid with p<i>K</i>_a₁ estimated at 5.7 ± 0.2 and p<i>K</i>_a₂ = 8.8(5) ± 0.2. In the pH region below p<i>K</i>_a₁, the molecule is stable in solution and ¹⁷O NMR line widths can be interpreted using the Swift–Connick equations to acquire rates of ligand substitution at the four isolated bound water sites. Averaging five measurements at pH < 5, where contribution from the less-reactive conjugate base are minimal, we estimate: <i>k</i>_ex²⁹⁸ = 8.1 (±2.6) × 10⁵ s^–1, Δ<i>H</i>^⧧ = 46 (±4.6) kJ mol^–1, Δ<i>S</i>^⧧ = 22 (±18) J mol^–1 K^–1, and Δ<i>V</i>^⧧ = +1.85 (±0.2) cm³ mol^–1 for waters bound to the fully protonated, neutral molecule. Regressing the experimental rate coefficients versus 1/[H⁺] to account for the small pH variation in rate yields a similar value of <i>k</i>_ex²⁹⁸ = 8.3 (±0.8) × 10⁵ s^–1. These rates are ∼10⁴ times faster than those of the [Fe­(OH₂)₆]³⁺ ion (<i>k</i>_ex²⁹⁸ = 1.6 × 10² s^–1) but are about an order of magnitude slower than other studied aminocarboxylate complexes, although these complexes have seven-coordinated Fe­(III), not six as in the [Fe₄(OH)₂(hpdta)₂(H₂O)₄]⁰(aq) molecule. As pH approaches p<i>K</i>_a1, the rates decrease and a compensatory relation is evident between the experimental Δ<i>H</i>^⧧ and Δ<i>S</i>^⧧ values. Such variation cannot be caused by enthalpy from the deprotonation reaction and is not well understood. A correlation between ⟨Fe^III–OH₂⟩ bond lengths and the logarithm of <i>k</i>_ex²⁹⁸ is geochemically important because it could be used to estimate rate coefficients for geochemical materials for which only DFT calculations are possible. This molecule is the only neutral, oxo-bridged Fe­(III) multimer for which rate data are available