Mutual Diffusion Coefficients and Densities at 298.15 K of Aqueous Mixtures of NaCl and Na₂SO₄ with NaCl Solute Fractions of 0.9500, Trace Diffusion Coefficients of SO₄^2- in NaCl(aq), and Trace Refractive Index Increments and Partial Molar Volumes of Na₂SO₄ and NaCl

Abstract

Isothermal mutual diffusion coefficients (interdiffusion coefficients) and refractive index increments were measured for ternary aqueous mixtures of NaCl and Na2SO4 at constant NaCl molarity fraction z 1 = 0.9500 at 298.15 K, using high precision Rayleigh interferometry with computerized data acquisition. The densities of these solutions were measured using vibrating tube densimetry. The experiments were performed at seven total molarities ranging from (0.499 92 to 4.978 34) mol·dm-3. These measurements supplement our earlier ones at other compositions and composition fractions. The Na2SO4 cross-term diffusion coefficient D 21 is small and negative at nearly all of the ternary solution compositions, whereas the NaCl cross-term diffusion coefficient D 12 is larger and positive. However, at z 1 = 0.9500, D 21 changes sign as the total concentration exceeds 4.3 mol·dm-3, and above 3.2 mol·dm-3 the value of D 12 exceeds that of the corresponding Na2SO4 main-term diffusion coefficient D 22. Thus, at high concentrations, a concentration gradient of Na2SO4 causes the transport of more NaCl than of itself. At each fixed total concentration, extrapolation of Na2SO4 main-term diffusion coefficients from these and our earlier results, to zero concentration fraction of Na2SO4 (i.e., z 1 → 1), yielded the trace diffusion coefficient of the SO4 2- ion D tr(SO4 2-) in NaCl(aq). Comparing these D tr(SO4 2-) values in NaCl(aq) to published D tr(SO4 2-) values in Na2SO4(aq) shows agreement to 1−8%, when the comparisons are made at equal volumetric ionic strength. Similar extrapolations of the volumetric and refractive index increment results yielded the trace partial molar volume and trace refractive index increment, respectively. Densities of NaCl(aq) at 298.15 K were critically reanalyzed.

Cross-diffusion and pattern formation in reaction–diffusion systems

“…Such processes can be characterized by the Fickian diffusivity matrix D or by the Maxwell-Stefan diffusion matrix D, where the diffusion coefficient D ij has the physical meaning of an inverse drag coefficient in the Maxwell-Stefan equations, 22 rather than by a vector of coefficients D ii . Examples of systems that exhibit cross-diffusion include strong electrolytes, [23][24][25] micelles, 26,27 or microemulsions, 28 and systems containing molecules of significantly different sizes, for example protein-salt. [29][30][31] Similar phenomena also occur in biological systems, but since the transport process is driven by an input of energy, as, for example, in bacterial chemotaxis [32][33][34] or in predator-prey systems, [35][36][37][38] these are not true diffusion processes.…”

Diffusion Onsager Coefficients Lij for the NaCl + Na2SO4 + H2O System at 298.15 K

“…The other 21 compositions were studied with Rayleigh interferometry after data collection was automated with a computer-controlled scanner using a 6 cm linear diode array. 22,23 However, during the course of the mixture studies, [17][18][19][20][21] we made additional measurements (seven for NaCl and nine for Na 2 SO 4 ) for the binary solutions with a greater fractional precision (reproducibility) of ( 0.06 %. Extensive density data were also reported for the same NaCl + Na 2 SO 4 + H 2 O mixtures, [17][18][19][20][21] which allowed us to calculate the partial molar volumes V j i of each component.…”

“…22,23 However, during the course of the mixture studies, [17][18][19][20][21] we made additional measurements (seven for NaCl and nine for Na 2 SO 4 ) for the binary solutions with a greater fractional precision (reproducibility) of ( 0.06 %. Extensive density data were also reported for the same NaCl + Na 2 SO 4 + H 2 O mixtures, [17][18][19][20][21] which allowed us to calculate the partial molar volumes V j i of each component. These V j i values, in turn, were used with the experimental (D ij ) V to derive the corresponding solvent-fixed (D ij ) 0 values.…”

“…to assess realistic uncertainties of the individual diffusion coefficients and therefore of the derived (L ij ) 0 and (L ij ) V values. The experimental diffusion coefficients (D ij ) V from these studies and their statistical standard errors [17][18][19][20][21] are summarized below in Table 1, as are the calculated (D ij ) 0 in Table 2.…”

Screening crystallisation conditions using fluorescence correlation spectroscopy

“…To correctly describe the diffusion in terms of solute flows in multi-component solutions (cooperative diffusion) one should use the generalised diffusion equation to take into account the coupled flow of the different components (Gosting, 1956, Tanford, 1961, Fu 2002. Data pertinent to multi-component diffusion of proteins is reported by Albright and co-workers and indicates that inclusion of the cross terms describing the coupling of the transport of lysozyme and the electrolyte is essential (Albright et al, 1999;Annunziata et al 2000).…”