An empirical correlation for the relative permittivity of liquids in a wide temperature range: Application to the modeling of electrolyte systems with a GE/EoS approach

Abstract

Relative permittivity, also known as static dielectric constant, is a key property of solvents in electrolyte solutions. It strongly influences the solubility of solutes and, therefore, it can be used as a predictive tool in chemical engineering processes. Relative permittivity also plays an essential role in the modeling of phase equilibria of electrolyte systems, since it is involved in the Debye-Hückel model and in the Mean Spherical Approximation, commonly used to represent long-range interactions between ions. In this paper, we propose a new temperature-dependent correlation for the relative permittivity of liquid water, methanol and ethanol, valid in a wide temperature range, including very high temperatures. Comparison with other literature equations evidenced that the main interest of the proposed correlation is to allow satisfactory predictions of the relative permittivity, not only in the range of validity of other literature models, but also in the high temperature domain, including supercritical temperatures for water. The new correlation is then used with the NRTL-PRA EoS to predict vapor pressure of water with several salts, including single electrolytes and two-salts mixtures; it must be noted that the modeling presented in this work is relevant for any G E /EoS model, since in this case (binary interactions between water and ions being equal to zero), the excess Gibbs energy reduces to the Long-Range term derived from the Pitzer-Debye-Hückel model. A temperaturedependent correction of the solvent relative permittivity is proposed to account for its dependence on ion mole fraction in this Long-Range term. Results thus obtained show that this correction leads to an accurate prediction both: for vapor pressures of aqueous electrolyte solutions in a very wide temperature domain and for the modeling of vapor-liquid equilibria of methanol-water and ethanolwater mixtures with several salts.

A Precise Thermodynamic Approach for Calculating Activity of Water in the Presence of Aqueous Alcohol + Salt Solutions and its Application to Gas Hydrate Dissociation Modeling

“…61 The dielectric constant of water is computed using the relation presented by Raspo and Neau. 62 The dielectric constant of methanol and MEG are obtained from the equation proposed by Akerlof. 65 Having determined the dielectric constants of water and alcohol, the dielectric constant of mixed solvent is calculated using a weighted average scheme 65…”

“…As such, the density and dielectric constant of mixed solvents are required in the Debye–Hückel parameter ( A γ ). Additionally, the density and dielectric constant of water are considered as functions of temperature for a better accuracy in calculations. , Water density is calculated from the correlation proposed by Hankinson and Thomson . Methanol and monoethylene glycol (MEG) densities were obtained from the DIPPR105 equation. , The density of mixed solvents can be calculated by the following relation d ms = 1 ∑ i = 1 n x s , i ′ d s , i …”

“…Additionally, the density and dielectric constant of water are considered as functions of temperature for a better accuracy in calculations. 61,62 Water density is calculated from the correlation proposed by Hankinson and Thomson. 61 Methanol and monoethylene glycol (MEG) densities were obtained from the DIPPR105 equation.…”

A Benchmark Database for Mixed-Solvent Electrolyte Solutions: Consistency Analysis Using E-NRTL

“…The mixing rules for solvent density and relative permittivity are where x i 0 is the molar fraction on the salt-free basis, w i 0 is the weight fraction on the salt-free basis, ρ i is the density of solvent i , and ε i is the relative permittivity of solvent i , as given below. The coefficients A i , B i , C i , D i , ε i 0 , and ε i 1 are obtained from or regressed to data from DIPPR and ref , as explained in detail in the Supporting Information.…”

Selective aqueous ammonia sensors using electrochemical stripping and capacitive detection

“…Avoiding these constraints in environmental waters requires alternative methods like capacitive sensing, which has been increasingly applied in other sectors due to its simplicity, range of detection, and quantification of small perturbations of aqueous relative permittivity. 29,30 Relative permittivity and thus capacitance are primarily affected by the molar fraction of different ionic species in multicomponent solutions; 31 this relationship contrasts with conductivity, which is more closely linked to total ion concentration. Thus, capacitive detection may enable sensitive yet simple detection amidst high background concentrations.…”