Dynamics of Ion Pairing in Dilute Aqueous HCl Solutions by Spectroscopic Measurements of Hydroxyl Radical Conversion into Dichloride Radical Anions

The rate of formation of dichloride anions (Cl2•–) in dilute aqueous solutions of HCl (2–100 mmol·kg–1) was measured by the technique of pulse radiolysis over the temperature range of 288–373 K. The obtained Arrhenius dependence shows a concentration averaged activation energy of 7.3 ± 1.8 kJ·mol–1, being half of that expected from the mechanism assuming the •OHCl– intermediate and supporting the ionic equilibrium-based mechanism, i.e., the formation of Cl2•– in the reaction of •OH with a hydronium–chloride (Cl–·H3O+) contact ion pair. Assuming diffusion-controlled encounter of the hydronium and chloride ions and including the effect of the ionic atmosphere, we showed that the reciprocal of τ, the lifetime of (Cl–·H3O+), follows an Arrhenius dependence with an activation energy of 23 ± 4 kJ·mol–1, independent of the acid concentration. This result indicates that the contact pair is stabilized by hydrogen bonding interaction of the solvent molecules. We also found that at a fixed temperature, τ is noticeably increased in less-concentrated solutions (mHCl < 0.01 m). Since this concentration effect is particularly pronounced at near ambient temperatures, the increasing pair lifetime may result from the solvent cage effect enhanced by the presence of large supramolecular structures (patches) formed by continuously connected four-bonded water molecules.

1. The first order rate constants of the formation of Cl2 •-. Table S1. The first-order rate constants kobs10 -6 fitted a) to the growth of absorbance measured at 340 nm, being the absorption maximum of Cl2 •-.

Density of aqueous HCl solution in dependence of temperature T
To describe the temperature dependence for the density of aqueous HCl solution Clegg and Wexler [S1] used the following polynomial expression: the mass fraction of HCl in solution, and .pk=0,..,9 r1, r1, …, r6 are fitting parameters to the experimental data collected in Table S2. The calculated densities are given in Table S3.  Table S3. Density of aqueous solution of HCl given in kg⋅m -3 calculated from eq. (S10). Data for pure water given in the first row are from ref. [S2].

Relative permittivity of solution in dependence of acid concentration and temperature
These dependencies were obtained using the scaling procedure proposed by Artemov et al. [S3] who assumed that the hypothetical electrophoretic effect results from intrinsic high concentration of hydronium cations in HCl solution: where H 2 O is the relative permittivity of water, Δ is the concentration dependent correction resulting from the presence of HCl, and ε∞ is the high frequency dielectric constant, assumed to be 5 at 25 °C.

Mean activity coefficient in dependence of acid concentration and temperature
Debye-Hückel and Pitzer-Hückel models of electrolyte solutions treat the solvent as a dielectric continuum. and an electrolyte as an ubiquitous solute. Under these assumptions. the activity of the electrolyte depends on the concentration and the activity coefficient γ±.
describing the interaction energy of ions in solution. To calculate γ± we have selected the two most commonly used expansions for 1:1 electrolyte. respectively given by eqs. (S12) and (S13).

Calculated UV-Vis spectra of representative chlorine complexes
UV-Vis spectra of two representative, optimised complexes were calculated using Gaussian 09W software and time dependent (TD) DFT method coupled with UB3LYP functional and 6-311++g(3df,3pd) basis set. The polarizable continuum model with integral equation formalism (IEFPCM) was assumed for the aqueous solvent. Six excited states were considered. The calculated spectra are presented in Figure S1.
S8 Figure S1. UV-Vis spectra of two chlorine complexes calculated using TD-DFT method: before (green) and after (blue) the concerted electron-proton transfer. Geometries of the respective complexes are also shown in the figure.