Limiting Conductivities of Strong Acids and Bases in D₂O and H₂O: Deuterium Isotope Effects on Proton Hopping over a Wide Temperature Range

Abstract

The molar conductivity (Λ°) of hydrochloric acid, potassium hydroxide, and sodium hydroxide has been measured in both light and heavy waters from 298 to 598 K at p = 20 MPa using a high-precision flow-through alternating current (AC) conductance instrument. The results were used to explore the deuterium isotope effect on ionic transport by proton hopping mechanisms under hydrothermal conditions. Extrapolations of published transport number data to elevated temperature were used to calculate the individual ionic contributions (λ°) for H3O+, D3O+, OH–, and OD–, from which the excess molar conductivities due to proton hopping were calculated. These are the first reported values for the excess conductivities for D3O+ and OD– at temperatures above 318 K. The excess conductivities indicate a strong deuterium isotope effect whereby the transport of D3O+ by proton hopping is reduced by ∼33% relative to H3O+, and OD– is reduced by over 60% relative to OH–, over the entire temperature range. A well-defined maximum in the excess conductivities of D3O+ and H3O+ at ∼420 K suggests that the Eigen cation (H2O)4H+ and the Zundel transition-state cation (H2O)2H+ are destabilized at elevated temperatures as the three-dimensional, tetrahedrally hydrogen-bonded networks in water break down. The less pronounced maximum for OD– and OH– suggested that their Eigen and Zundel anions, (H2O)3OH– and (H2O)OH–, are less destabilized in the two-dimensional networks and chains that dominate the “structure” of liquid water under these conditions.

Second ionization constant of sulfuric acid in H2O and D2O from 150 to 300 °C at p = 11.5 MPa using flow AC conductivity

“…where k pure solv is the conductivity of the pure solvent calculated by the method of Marsh and Stokes. 35 The values of l H þ ; l OH À ; l D þ ; l OD À were taken from combined fits of this and other works 33,36,37 as given in Section 4.2.…”

“…Expressions for the limiting conductivities, l1, for the individual ions Cl À , K + , H + , OH À , HSO 4 and the ion pair KSO 4 À , have been reported in light water. 23,24,33,36,37,[48][49][50][51] Values of l1 for the simple ions in D 2 O have been reported, 33,37,51 but there are no values of l1 for DSO 4 À , SO 4 2À , or KSO 4 À in heavy water.…”

“…Fig. 1 and 2 show the logarithm of the individual ion limiting equivalent conductivities plotted against the logarithm of the solution viscosity from this study and from the literature 23,24,33,36,37,[48][49][50][51] in light and heavy waters. The data from the thesis by Erickson 51 is given in ESI, † Table S3.…”

“…and the conductivities L 1 , L 2 , L 3 , and L 4 were calculated from the Quint-Viallard conductivity model at the solution ionic strength. Eqn (34) was rearranged for a to obtain: , 37 Sharygin et al, 36 , Hnedkovsky et al, 23,24 " Quist and Marshall, 49 Â Yokoyama and Ohta, 50 and Tomsic et al 48 and the expression for the equilibrium constant of the ion pairing reaction (R5) was solved for b in terms of a, c, and K K as:…”

“…41 The Quint-Viallard conductivity model was chosen for this work because it has been used successfully for a wide variety of mixtures of electrolytes [63][64][65][66][67][68][69] and it can also be used for asymmetric electrolytes. Plumridge et al, 33 Erickson, 51 and Arcis et al 37 chose to use the simpler Fuoss-Hsia-Ferna ´ndez-Prini (FHFP) conductivity model 70 for their studies of dilute purely symmetric electrolytes.…”