Dole-Jones equation

The viscosities of the acetone-bromosuccinic acid mixed solvents were derived from the Jones-Dole (33) equation and data acquired by Muller, who used the special viscometer described by Tuan and Fuoss (34). The values used for the viscosities (in poise) of solvents I-V were 3.02 X 10 3, 3.05 X 10-3, 3.08 X 10-3, 3.13 X 10-3, and 3.02 X 10-3, respectively. The literature value for the dielectric constant of acetone, 20.7, was used as the dielectric constant for each solvent. This is justified because at the highest concentration of bromosuccinic acid its mole fraction is less than 0.004. 

Viscosity data for fairly dilute salt solutions are usually discussed in terms of the Jones-Dole equation (3)... 

Fitting the Jones-Dole equation to the data was not done in the usual manner in the linearized form (17/170 — 1 )/C1 2 = A + BC1/2, since this casts a heavy burden on the required precision of 170 and also inflates the errors at the lower-concentration end. Instead, we used the form ... 

Table I contains the viscosities obtained for the solvent mixtures and the salt solutions. Table II summarizes the results for the solutions and contains the viscosity of each solvent mixture without added salt, the constants A and B of the Jones-Dole equation, the value of the density-concentration coefficient dp/dC, and the density of the solvent mixture.

The calculation of viscosities of electrolyte mixtures can be accomplished with the method of Andrade (see Ref. [40]) extended with the electrolyte correction by Jones-Dole [44]. First, the pure component viscosities of molecular species are determined by the three-parametric Andrade equation, which allows a mixing rule to be applied and the mixture viscosity of an electrolyte-free liquid phase to be obtained. The latter is transformed into the viscosity of the liquid phase using the electrolyte correction term of Jones and Dole [44], whereas the ionic mobility and conductivity are used as model parameters. 

As before, the Jones-Dole Equation (12) was fitted to the data by a least squares procedure, in the form... 

The viscosity data are shown in Table I. Table II is a summary of results, showing the solvent properties (density and viscosity) and the solution parameters the density-concentration coefficients and the constants A and B of the Jones-Dole Equation. The values of B for the four salts, for which new data are reported, are shown as functions of x2 in Figure 1. (Some data from the literature are included as noted.)... 

Jones-Dole equation, coefficients (viscosity of electrolytes) 1.5.52, table 1.5.9, I.6.78ff... 

Jones-Dole viscosity equation, 124 Jones-Partington supersaturation equation, 372... 

Concentration dependence of the viscosity of electrolyte solution has been empirically expressed by the Jones-Dole equation (eq.(l)),where r/ and rjo are the viscosities of solution 77/rjo = 1+aVc+Be (1)... 

Zi is the charge on species i, coefficient A depends on various solute and solvent properties, and the coefficients are specific to the individual ions. Parameters for the Jones-Dole equation at room temperature are tabulated by Marcus [79]. A semiempirical extension of the Jones-Dole equation to higher concentrations, and also a method for extrapolating room-temperature parameters to higher temperatures, are described by Lencka et al. [80]. Jiang and Sandler [81] have developed a different method, based on liquid-state theory, that also appears promising for correlation and limited prediction of electrolyte solution viscosities. 

Another transport property sensitive to solvent structural eflFects is the viscosity B coeflBcient obtained from the Jones-Dole equation (23),... 

The viscosity of aqueous solutions has been studied extensively some of the more pertinent data, including that for a few non-aqueous solutions, are discussed by Harned and Owen. In most cases the data can be adequately represented by the Jones-Dole equation ... 

Vosburgh and co-workers have reported for LiCl in some aliphatic alcohols up to butanol and Sobkowski and Mine have reported the same quantity for HCl in alcohols up to w-propanol. For both electrolytes increases as the number of carbons increase in the alcohol. Venkatasetty and Brown have measured the viscosities of Lil, NH4I and BU4NI in butanol at 0, 25 and 50°C and attempted to fit the data to the Jones-Dole equation. " Although measurements were made in relatively dilute solutions, deviations from linearity were observed over the concentration range studied and viscosity coefficients were not evaluated. 

Feakins and Lawrence measured the relative viscosities of sodium and potassium chlorides and bromides in NMF from 25 to 45°C and expressed the data by an expanded Jones-Dole equation. The viscosity coefficients, A, and were evaluated. While both and have positive values for every electrolyte studied in NMF, they are much smaller than the corresponding quantities in other organic solvents. The difference between the theoretical and experimental values of may be either positive or negative. 

Schmidt and co-workers ° have also measured apparent molal volumes and viscosities of several electrolytes in anhydrous ethylenediamine at 25°C and extrapolated the data to obtain F . They observed that Masson s equation (eqn 2.3.66) was valid over the concentration range studied and their data indicate that S is negative in this solvent. A theoretical value for the limiting slope, is not available. The viscosity data are in agreement with the Jones-Dole equation over the concentration range studied, but the coefficients of this equation were not reported. 

Archer and Gasser have measured the viscosity of DMSO-CsI solutions up to about 0.7 molar and employed the extended Jones-Dole equation to fit the data. The viscosities were not sufficiently accurate to evaluate consequently, this term was calculated theoretically and the Bn and coefficients evaluated by plotting — AnC -lljC... 

The terms structure making and structure breaking are attributed to Gurney (1953), but Cox and Wolfenden (1934) were the first to mention the notion of water structure in the connection of the viscosities. Furthermore, Frank and Evans (1945) have already used the term structure breaking (but not -making ) with regard to effects of the alkali metal and halide ions, except Li+ and F , on the partial molar entropies of dilute aqueous solutions. The Jones-Dole -coefficient, Eq. (2.35), is the quantitative measure of this effect, and this equation may be recast in the form ... 

Costa et al [Co 74b] employed viscosity measurements to study the effects due to the different solvating powers of the components of solvent mixtures. In lithium chloride solutions prepared with water-alcohol mixtures of various compositions, they demonstrated the dependence of the viscosity of the solution on the composition of the solvent mixture. From the nature of the viscosity curve and from the position of the extreme in the curve, conclusions were drawn on the different solvating abilities of the components of the solvent. Information appearing to be especially promising is that which may be obtained from the dependence of constant B of the Jones-Dole equation on the composition of the solvent mixture. 

Electrolyte viscosity data is frequently modeled using the Jones-Dole (JD) equation [7-9]. This equation can be extended to include a third term for concentrated electrolytes [10-13] ... 

Martinus N, Sinclair CD, Vincent CA (1977) The extended Jones-Dole equation. Electrochim Acta 22 1183-1187. doi 10.1016/0013-4686(77)80059-5... 

Tyrrell (1969), Desnoyers et al. (1969), Destroyers and Perron (1972), Abdulagatov et al. (2004, 2005, 2006a,b) and Abdulagatov and Azizov, 2006a,b), added a quadratic term Dc (extended Jones-Dole equation), as... 

Table 30.3 Jones-Dole B coefficients at T = 2.3° C (see Equation (30.11)). Source RW Gurney, Ionic Processes in Solution, Dover Publications, New York, 1 962. Data are from C Jones and SK Talley, J Am Chem Soc, 55, 624 (1 933) C Jones and RE Stauffer, J Am Chem Soc, 62, 336 (1 940) and VD Laurence and JH Wolfenden, J Chem Soc, 1144 (1934).

At 25 °C, for moderately concentrated solutions of citric acid, citric acid viscosities can be represented by the Jones-Dole type equation... 

Measured viscosities are frequently represented by the Jones-Dole equations which are valid for dilute solutions, usually for c<0.5 mol dm [151]. 

Several models were tested to describe the variation of the solution viscosity with the increase in concentration of vanadium (III) sulphates. Unfortunately, the high degree of saturation of these solutions and the imavailability of much of the information needed to apply these theoretical models made these attempts unsuccessful except for the modified form of Jones-Doles equation (Equation 10.5). 

Empirical Coefficients for the Modified Jones-Dole Equation (Equation 10.5) for 2(504)3 Solutions at Different Acid Concentrations and Temperatures... 

Correlation between measured viscosity values and those calculated from the modified Jones-Dole model (Equation 10.5). 

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