The limiting conductivity of the borate ion and its ion-pair formation constants with sodium and potassium under hydrothermal conditions

Abstract

Frequency-dependent molar electrical conductivities for aqueous solutions of potassium borate, and sodium borate have been measured from ambient to near-critical temperatures and pressures to an accuracy of ±3 percent, using a unique high-precision flow-through AC conductance instrument. The concentration dependence of these conductivities was analyzed with the Turq-Blum-Bernard-Kunz ("TBBK") theoretical model to yield (i) limiting conductivities of the borate ion, λ(0)[B(OH)4(-)], and (ii) ion-pair formation constants, KA, for the species NaB(OH) and KB(OH) from T = 298 K to T = 623 K at a constant pressure p ∼ 20 MPa. The ion-pair formation constants for both borate salts were found to be consistent with previous literature studies at temperatures below 473 K. No significant difference in KA was observed between the species NaB(OH) and KB(OH). As temperature was increased from 473 up to 623 K, the degree of association increased significantly, and was found to be considerably higher than for any other 1-1 electrolyte previously studied. For instance, at 623 K, the association constant log KA[NaB(OH)] = 2.75 ± 0.21 was an order of magnitude higher than log KA[NaCl(0)] = 1.53 ± 0.03, and approximately equal to that of a 2 : 1 electrolyte, log KA[SrCF3SO3(+)] = 2.58 ± 0.06. Deviations in the limiting conductivities from Stokes Law show that the borate ion's unusual "structure making" effect, observed by other workers at sub-ambient conditions, persists up to temperatures above 500 K. The temperature dependence of the Walden product ratio is very different from that observed for other monovalent anions for which experimental data are available over this wide range of temperatures.

Thermodynamics of Polyborates under Hydrothermal Conditions: Formation Constants and Limiting Conductivities of Triborate and Diborate

“…The TBBK Model. The concentration dependence of the solution conductivity was modeled with the same data treatment strategy used in previous work on ion association in metal borate solutions, 9,10 in which the TBBK model 20 was used together with the mixing rule reported by Sharygin et al 22…”

“…The relative standard uncertainties for conductivity depend on concentration [8,15], and range from u r (κ) = 0.003 for the lowest concentration measured (∼10 −4 m) to u r (κ) = 0.01 for the highest concentration measured (∼0.8 m). These relative standard uncertainties were calculated following the methodologies described in ref 18 ] were taken from Arcis et al, 10 while values for K A,m [NaOH 0 ] and K A,m [KOH 0 ] were taken from Ho et al 24 For the analysis of data below 473 K, values of the diborate formation constant K b 21,m were calculated from the expressions reported by Palmer et al 3 The TBBK model also requires knowledge of the crystallographic radius, σ i , and the limiting equivalent conductivity, λ 0 i , of each species in solution. The crystallographic radii for borate (σ = 0.244 nm) and triborate (σ = 0.4 nm) were taken from Corti and co-workers.…”

“…The radii for OH − (σ = 0.14 nm), H + (σ = 0.14 nm), Na + (σ = 0.097 nm), and K + (σ = 0.133 nm) were taken from Marcus. 28 The temperature-dependent limiting conductivities, λ 0 (H + ) and λ 0 (K + ), were calculated from Marshall's reduced density relationship, 29 and values of λ 0 [B(OH) 4 − ], λ 0 (OH − ), and λ 0 (Na + ) were taken from Arcis et al, 10 Ho et al, 24 and Zimmerman et al, 15 respectively. Below 473 K, where diborate is a minor species, values for λ 0 [B 2 (OH) 7 − ] were estimated from a simple correlation model, which is described in Supporting Information.…”

Molar Volumes and Heat Capacities of Aqueous Solutions of Potassium Hydroxide and for Water Ionization up to 573 K at 10 MPa

“…These departures are almost certainly a reflection of the much greater ion pairing in LiOH­(aq) cf. the other alkali metal hydroxides, especially at higher temperatures. − …”

Еволюція Кондуктометричного Підходу До Встановлення Поведінки Іонів Четвертинних Амонієвих Солей У Розчинах.

“…Розвиток теорії електропровідності розчинів електролітів сьогодні продовжується. Як правило, нові системи рівнянь є комбінаціями та інтерпретаціями підходів, що розглянуто в даній роботі, наприклад, модель Бартела [24,25] або Турка-Блума-Бернарда-Кунца [26]. Оскільки на сьогодні ще не створено ідеальної моделі іон-іонної та іон-дипольної взаємодії, яка б абсолютно достовірно відтворювала стан компонентів розчину через величини електропровідності, дослідники звертаються також до інших способів вивчення процесів асоціації електролітів.…”