Diffusion with hydrolysis and ion association in aqueous solutions of beryllium sulfate

Taylor dispersion is used to measure mutual diffusion coefficients for aqueous solutions of beryllium sulfate at concentrations from 0.005 to 1 mol-L^–1 at 25°C. Least-squares analysis of the dispersion profiles shows that diffusion of the partially hydrolyzed salt produces a small additional flow of sulfuric acid, about 0.04 mol sulfuric acid per mole of total beryllium sulfate. Ternary diffusion coefficients measured for the aqueous BeSO₄–H₂SO₄ system are qualitatively consistent with Nernst-Planck predictions based on the formation of beryllium sulfate ion pairs, bisulfate ions, and the hydrolysis equilibria 2Be²⁺+H₂O= Be₂OH³⁺+H⁺, 3Be²⁺+2H₂O=Be₃(OH) ₂ ⁴⁺ +2H⁺. Except for very dilute solutions, the predicted flow of sulfuric acid is small compared to the flow of beryllium sulfate because most of the beryllium ions are protected from hydrolysis by the formation of BeSO₄ ion pairs, and most of the hydrogen ions produced by hydrolysis are converted to less-mobile bisulfate ions.     

Ternary diffusion with charged-complex formation in aqueous I2+NaI and I2+KI solutions

Diaphragm cells have been used to measure ternary diffusion coefficients for I₂+NaI and I₂+KI in aqueous solution at 25°C. Although most of the iodine molecules are bound to iodide ions and are transported as the triiodide species [I₂(aq)+I^–(aq)=I ₃ ^– (aq)], diffusion of the iodide salts produces relatively small countercurrent coupled flows of the iodine component. The ternary diffusivity of the iodine component in the solutions is 10 to 20% larger than the diffusivity of the triiodide species. This behavior can be understood by considering electrostatic coupling of the ionic flows. The diffusion equations for I₂+NaI and I₂+KI components are reformulated in terns of NaI₃+NaI and KI₃+KI mixed electrolyte components.     

Ternary Solution Mutual Diffusion Coefficients and Densities of Aqueous Mixtures of Sucrose with NaCl and Sucrose with KCl at 25°C

Ternary solution isothermal mutual diffusion coefficients (interdiffusion coefficients) have been measured for aqueous mixtures of 0.250 mol-dm^–3 sucrose (component 1) with 0.5 and 1.0 mol-dm^–3 NaCl or with 0.5 and 1.0 mol-dm^–3 KCl (salt = component 2) at 25.00°C using Rayleigh interferometry with computerized data acquisition. Densities were also measured. The volume-fixed diffusion coefficients (D _ij)_V show the following characteristics. At all compositions (D ₂₁)_V is much larger than (D ₁₂)_V and (D ₂₁)_V is a fairly significant fraction (33 to 68%) of (D ₁₁)_V. In addition, (D ₁₂)_V is slightly larger for mixtures containing NaCl than for those containing KCl at the same concentration, whereas (D ₂₁)_V is significantly larger for mixtures containing KCl. Values of (D ₁₁)_V are slightly larger for solutions containing KCl than for solutions containing NaCl. The observed trends imply that (D ₂₁)_V will probably exceed (D ₁₁)_V in both mixtures if concentrations of NaCl or of KCl are increased much further while maintaining the sucrose concentration at 0.250 mol-dm^–3. Finally, the solvent-fixed cross-term diffusion coefficients (D ₁₂)₀ and (D ₂₁)₀ are significantly larger than their corresponding (D ₁₂)_V and D ₂₁)_V.     

Hartley–Crank Equations for Coupled Diffusion in Concentrated Mixed Electrolyte Solutions. The CaCl2 + HCl + H2O System

Nernst—Planck equations and ionic conductivities are used to calculate accurate limiting interdiffusion coefficients D _ik ^o for mixed electrolyte solutions. The electrostatic mechanism for coupled electrolyte diffusion is investigated by calculating the electrostatic contribution to each D _ik ^o coefficient to give the flux of each electrolyte driven by the electric field, which is generated by the migration of ions of different mobilities. Ternary diffusion coefficients are measured for dilute aqueous K₂SO₄ + KOH and Li₂SO₄ + LiOH solutions. Because of the different mobilities of K⁺ and Li⁺ ions relative to SO ₄ ^2– ions, diffusing K₂SO₄ drives cocurrent flows of KOH, but diffusing Li₂SO₄ drives counterflows of LiOH. To describe coupled diffusion in concentrated mixed electrolyte solutions, the Hartley–Crank theory is used to correct the limiting D _ik ^o coefficients for nonideal solution behavior, viscosity changes, ionic hydration, and the zero-volume flow constraint. Diffusion coefficients predicted for concentrated aqueous CaCl₂ + HCl solutions are compared with recently reported data. The large amount of HCl cotransported by the diffusing CaCl₂ is attributed to the salting out of HCl by CaCl₂ and to the migration of H⁺ ions in the diffusion-induced electric field, which slows down the Cl^– ions and speeds up the less-mobile Ca²⁺ ions to maintain electroneutrality along the CaCl₂ gradient.     

Coupled diffusion produced by hydrolysis of aqueous potassium phosphate

Conductimetric and diaphragm cell techniques have been used to measure diffusion of aqueous potassium phosphate solutions at 25°C from 0.01 to 0.10 mol-dm^–3 (M). A significant portion of the aqueous K₃PO₄ component diffuses as equimolar amounts of potassium hydrogen phosphate and potassium hydroxide produced by hydrolysis: K₃PO₄+H₂O=K₂HPO₄+KOH. Because OH^– diffuses more rapidly than HPO ₄ ^2– , the total flow of KOH exceeds the flow of K₂HPO₄. The extra flow of KOH constitutes coupled transport of a second solute component. Ternary diffusion coefficients that describe interacting flows of K₃PO₄ and KOH components are reported. At low concentrations where phosphate is strongly hydrolyzed, the molar flux of the KOH component produced by diffusion of K₃PO₄ is six times larger than the flux of the K₃PO₄ component. Binary diffusion coefficients for aqueous K₂HPO₄ solutions are also reported. It is shown that ternary transport coefficients for K₃PO₄ solutions can be estimated from the properties of binary solutions of K₂HPO₄ and KOH.     

Ternary mutual diffusion coefficients of ZnCl2−KCl−H2O at 25°C by Rayleigh interferometry

Mutual diffusion coefficients and densities were measured for aqueous ZnCl₂–KCl mixtures at 25° by using free-diffusion Rayleigh interferometry and pycnometry, respectively. The ZnCl₂ concentrations were fixed at 1.5 mol-dm^–3, whereas those of KCl were 0.5, 1.25, 2.0, or 4.0 mol-dm^–3. This corresponds to a half charged zinc-chlorine storage battery at various suporting electrolyte concentrations. The main-term coefficient of ZnCl₂ only varies by 10% with KCl concentration, whereas that of KCl varies by about 22%. The ZnCl₂ cross-term coefficient remains small and positive; in contrast the KCl cross-term coefficient goes through a maximum and is negative at high and low KCl concentrations. At KCl concentrations of 0.5 and 4.0 mol-dm^–3, solutions with the KCl c0 are statically and dynamically (diffusively) unstable at the top and bottom of the boundary. Evaluation of the parameters of the non-linear least-squares solution to the diffusion equation is difficult for the 1.25 mol-dm^–3 KCl case, since this system has nearly equal eigenvalues in its diffusion coefficient matrix.     

Comparison of the Diffusion of Aqueous Glycine Hydrochloride and Aqueous Glycine

A Taylor dispersion tube has been used to measure mutual diffusion in aqueous solutions of glycine hydrochloride at 25°C and concentrations from 0.0005 to 0.5 M. Analysis of the dispersion profiles shows that the diffusion of glycine hydrochloride (GlyHCl) produces a subtantial additional flow of hydrochloric acid that is liberated by the dissociation: GlyH⁺ + Cl^- Gly + H⁺ + Cl^-. Diffusion in this system is, therefore, a ternary process described by the equations J ₁(GlyHCl) = – D ₁₁C ₁ – D ₁₂C ₂ and J ₂(HCl) = –D ₂₁C ₁ – D ₂₂C ₂ for the coupled fluxes of total glycine hydrochloride (1) and hydrochloric acid (2) components. The ratio D ₂₁/D ₁₁ of measured diffusion coefficients indicates that up to two moles of HCl are cotransported per mole of GlyHCl. Although protonated glycine diffuses with relatively mobile Cl^– counterions, the main diffusion coefficient of glycine hydrochloride, D ₁₁, is lower than or nearly identical to the diffusion coefficient of aqueous glycine. A model for the diffusion of protonated solutes is developed to interpret this result and the large coupled flows of HCl. Diffusion coefficients are also reported for the aqueous hydrochlorides of 3- and 4-aminobenzoic acids.     

Quinary Mutual Diffusion Coefficients of Aqueous Mannitol + Glycine + Urea + KCl and Aqueous Tetrabutylammonium Chloride + LiCl + KCl + HCl Solutions Measured by Taylor Dispersion

Taylor dispersion is widely used to measure binary mutual diffusion. Studies of three- and four-component solutions show that the dispersion method is also well suited for multicomponent diffusion measurements, including cross-coefficients for coupled diffusion. Numerical procedures are reported here to calculate mutual diffusion coefficients from dispersion profiles measured for solutions of any number of components. The proposed analysis is used to measure the sixteen quinary mutual diffusion coefficients of five-component aqueous mannitol + glycine + urea + KCl solutions and aqueous NBu₄Cl + LiCl + KCl + HCl solutions. Mannitol, glycine, urea and KCl interact weakly at the low solute concentrations used (0.010 mol·dm^?3). The diffusion coefficients of this system are compared with pseudo-binary predictions. Strong coupling of the NBu₄Cl, LiCl, KCl and HCl fluxes is interpreted by using ionic conductivities and Nernst equations to calculate limiting quinary diffusion coefficients for mixed electrolytes that interact by the electric field generated by ion concentration gradients.     

Intradiffusion coefficients for perchlorate ions in zinc perchlorate and zinc chloride solutions at 25°C: Comparing transport properties of zinc chloride and zinc perchlorate systems

Intradiffusion coefficients for³⁶ClO ₄ ^– have been measured in solutions of zinc perchlorate of concentration 0.1 to 3 mol dm^–3 at 25°C by the diaphragm cell technique. In addition, intradiffusion coefficients for perchlorate ions in zinc chloride solutions have been measured over a concentration range at 25°C. The results confirm previous work on the effect of complexation on diffusion in zinc chloride solutions above a salt concentration of 0.1M. The present data, together with literature data for diffusion coefficients of the other species present in the zinc perchlorate electrolyte system, have enabled a simple analysis of the hydration around the zinc ions to be carried out. This indicates that the water diffusion data are consistent with the zinc ions having an effective hydration sphere of 11 (±2) water molecules. This is in keeping with values obtained for other simple divalent electrolytes using the same model. The model is extended here to allow analysis of water diffusion in zinc chloride solutions taking into account the presence of complexed chloro-zinc species. The experimental data are consistent with the effective hydration of the chloro-zinc complexes being independent of the number of chloride ligands and equal to 18±3 over a concentration range of 0 tol mol-dm^–3. This postulate is discussed in terms of its consequences on the water ligand dynamics for the complex equilibria.     

Taylor dispersion measurements at low electrolyte concentrations. I. Tetraalkylammonium perchlorate aqueous solutions

An equipment for the determination of mutual diffusion coefficients using the Taylor's dispersion technique is described. The radius of the capillary was determined with the help of various calibration methods. Diffusion coefficients of aqueous tetraalkylammonium perchlorates, Me₄NClO₄, and Et₄NClO₄, were measured at 25°C in the concentration range 10^–3 to 5×10^–2 mol-dm^–3, and the slightly soluble Pr₄NClO₄ up to 1×10^–2 mol-dm^–3. The slope of linear plots ofD vs. is in agreement with theory, in contrast to the limiting valuesD ₀, which all deviate by about –5% from the Nernst-Hartley values.     

Activity coefficients of electrolytes from the emf of liquid membrane cells. III: LaCl3, K3Fe(CN)6, and LaFe(CN)6

The activity coefficients of LaCl₃, K₃Fe(CN)₆, and LaFe(CN)₆ were measured down to about 1×10^–4, 3×10^–5, and 2×10^–5 mol-kg^–1 respectively, by means of cells with ion-exchange liquid membranes. In the diluted region, the trend of lanthanum chloride agrees with the Debye-Huckel theory and corroborates earlier findings in the literature relevant to more concentrated solutions, with minor systematic corrections of the _± values. K₃Fe(CN)₆ attains (rather than tends to attain) the Debye-Huckel limiting slope at1×10^–3 mol-kg^–1, and lanthanum ferricyanide in the diluted region shows negative deviations from the limiting law, similar to the ones predicted for large-sized, highly-charged ions in the diluted region by Bjerrum's, IPBE, and Mayer's theories. The behavior of LaCl₃ in the concentrated solutions proves that lanthanum ion drags along with it into the membrane many molecules of water which were then found to be twelve. Pitzer's theory best-fit coefficients that meet the experimental curves to be reproduced satisfactorily are reported.     

Electron Transport Properties of Ions in Aqueous Solutions of Sodium Selenite

Ion diffusion kinetics has been studied using the data of conductivity measurements for aqueous solutions of sodium selenite with different concentrations and at different temperatures. Molecular and ionic self-diffusion coefficients have been determined for infinitely dilute solutions in the temperature range 288 K-313 K. The limiting values of ion mobility and changes in the energies of translation of water molecules from ions’ hydration shell have been found. At elevated temperatures, ΔE _tr ⁰ increases for both ions in direct proportion to the crystallographic radius of the latter. Ion hydration numbers at 298 K have been calculated. The results of this study are interpreted in the light of Samoilov’s theory on positive and negative hydration of ions.Original Russian Text Copyright © 2004 by L. T. Vlaev and S. D. Genieva__________Translated from Zhurnal Strukturnoi Khimii, Vol. 45, No. 5, pp. 870–876, September–October, 2004.     

Ternary diffusion coefficients of diethylene glycol and lithium chloride in aqueous solutions containing diethylene glycol and lithium chloride

In this work, ternary diffusion coefficients of diethylene glycol and lithium chloride in aqueous solutions containing diethylene glycol and lithium chloride were reported for temperatures (303.2, 308.2, and 313.2 K) using the Taylor dispersion method. The investigated ternaries contained total glycol–salt concentrations of 10, 15, and 20 wt%. The main diffusion coefficients (D₁₁ and D₂₂) and the cross-diffusion coefficients (D₁₂ and D₂₁) were discussed as function of temperature and concentration. A modified equation originally proposed by Batchelor [1] for mixture of hard spheres in a continuum solvent was used to correlate the present diffusion coefficient data and the results are satisfactory.     

Diffusion in dilute aqueous acetic acid solutions at 25°C

A conductimetric technique has been used to measure diffusion coefficients for aqueous solutions of acetic acid at concentrations from 0.002 to 0.02 mol-dm^–3 at 25°C. The acetic acid component diffuses more rapidly at lower concentrations where a higher proportion of the slower acid molecules are converted by dissociation to acetate ions and highly mobile hydrogen ions. The observed concentration dependence of the diffusion coefficient verifies the limiting law for weak electrolyte diffusion. A new type of conductimetric diffusion cell with several practical advantages over earlier designs is described together with an improved procedure for the conductimetric determination of accurate diffusion coefficients for weak electrolyte systems.     

Intradiffusion coefficients in perchloric acid solutions: Water at 5°C; water and perchlorate ion at 25°C

Intradiffusion coefficients for tritiated water (³HHO) and perchlorate ion (³⁶ClO ₄ ^- ) were measured in perchloric acid solutions. At 5°C the diffusion coefficient measured for the tritiated species increases to a maximum near 1.3 mol-dm^–3. The data at 25°C have been used to calculate distinct diffusion coefficients, D _ij ^d . As a precursor for those calculations, new estimates were made of the Onsager phenomenological coefficients, l _ij . The l _ij and D _ij ^d are similar to the respective coefficients in hydrochloric acid solutions.     

Diffusion Coefficients for Binary, Ternary, and Polydisperse Solutions from Peak-Width Analysis of Taylor Dispersion Profiles

Binary mutual diffusion coefficients D can be estimated from the width at half height W _1/2 of Taylor dispersion profiles using D=(ln 2)r ² t _R/(3W ² h) and values of the retention time t _R and dispersion tube radius r. The generalized expression D _h=−(ln h)r ² t _R/(3W ² _h ) is derived to evaluate diffusion coefficients from peak widths W _h measured at other fractional heights (e.g., (h = 0.1, 0.2,…,0.9). Tests show that averaging the D _h values from binary profiles gives mutual diffusion coefficients that are as accurate and precise as those obtained by more elaborate nonlinear least-squares analysis. Dispersion profiles for ternary solutions usually consist of two superimposed pseudo-binary profiles. Consequently, D _h values for ternary profiles generally vary with the fractional peak height h. Ternary profiles with constant D _h values can however be constructed by taking appropriate linear combinations of profiles generated using different initial concentration differences. The invariant D _h values and corresponding initial concentration differences give the eigenvalues and eigenvectors for the evaluation of the ternary diffusion coefficient matrix. Dispersion profiles for polymer samples of N i-mers consist of N superimposed pseudo-binary profiles. The edges of these profiles are enriched in the heavier polymers owing to the decrease in polymer diffusion coefficients with increasing polymer molecular weight. The resulting drop in D _h with decreasing fractional peak height provides a signature of the polymer molecular weight distribution. These features are illustrated by measuring the dispersion of mixed polyethylene glycols.     

Surfactant Diffusion Near Critical Micelle Concentrations

Taylor dispersion and differential refractometry are used to measure mutual diffusion coefficients (D) for binary aqueous solutions of octylglucopyranoside, dodecylsulfobetaine, and sodium dodecyl sulfate (nonionic, zwitterionic and ionic surfactants, respectively). Aggregation causes a sharp drop in D as the concentration of each surfactant is raised through the critical micelle concentration (cmc). Differential mutual diffusion coefficients are determined in this composition region by using small initial concentration differences (3 mmol-dm^–3) and by extrapolating the measured D values to zero initial concentration difference relative to the carrier stream. The drop in D for each surfactant is more gradual than the concentration dependence predicted by the chemical equilibrium model of surfactant diffusion. Micelle polydispersity and nonideal solution behavior are discussed as possible explanations for this discrepancy. Intradiffusion coefficients (D*) for aqueous octylglucopyranoside and dodecylsulfobetaine are evaluated by integrating the relation d(cD*) = Ddc previously derived for dilute solutions of self-associating nonelectrolyte solutes.     

Viscosities and intradiffusion coefficients in the ternary system NaCl−MgCl2−H2O at 25°C

The intradiffusion coefficients of Na⁺, Cl^– ions and water and the tracerdiffusion coefficients of Ca²⁺ ion have been measured in the ternary system NaCl–MgCl₂–H₂O at 25°C. The intradiffusion coefficients of Mg²⁺ in this system have been estimated from the corresponding Ca²⁺ diffusion measurements. Viscosities were measured at the same solution concentrations as were used for the diffusion experiments. Intradiffusion and tracerdiffusion coefficients in a range of temperatures from 5 to 45°C are reported for standard sea-water which is a member of the above ternary set.     

Diffusion of ionic species labeled with35S in various aqueous electrolyte solutions at 25°C

Composite diffusion coeffcients have been measured for the various species labeled with³⁵S which are present in a number of aqueous solutions due to the introduction of the labeled material as³⁵SO ₄ ^2– . The solutions were of two components consisting of water and either sodium sulfate. The diffusion coeffcient measured for sodium chloride solutions is similar to literature data for the corresponding diffusion in sodium sulfate solutions. The results for sulfuric acid and ammonium hydrogen sulfate have been interpreted using literature data for the relative concentrations of the hydrogen sulfate and sulfate ions to obtain estimates for the diffusion coefficents of those ions. The results for perchloric acid, regarded as representing the diffusion coefficient of the hydrogen sulfate ion, have a much different concentration dependence to that observed for the estimates for that ion in sulfuric acid and ammonuim hydrogen sulfate. The difference is attributed to the effect of the perchlorate ion on the water structure.     

Equilibrium and Transport Properties of Sodium n-Octyl Sulfonate Aqueous Solutions

Measurements of osmotic coefficients, mutual diffusion coefficients, and conductivity were performed on the binary system sodium n-octyl sulfonate (C₈SO₃Na)–water at 25°C both below and above the micellar composition range. The osmotic coefficient data were obtained through vapor-pressure osmometry, while the Taylor dispersion method was used to measure diffusion coefficients. The mass equilibrium model was applied to this self-aggregating system, taking into account the deviation of the activity coefficients from the Debye–Hückel limiting law by using the Guggenheim corrective terms for mixed electrolyte solutions. The expressions derived from the model fit the experimental osmotic and diffusion coefficient data well, when the same values of aggregation number, fraction of condensed counterions, and equilibrium constant are used. Osmotic coefficients were also used to determine the thermodynamic factor required to compute the solute mobility from diffusion data. Conductivity data were used to test two theoretical models, namely, the Onsager–Fuoss and the Mean Spherical Approximation theories. Both models have been found to yield unsatisfactory fits to our experimental data and some arbitrary terms had to be applied to the theoretical expressions to obtain good agreement between experiment and theory.