Activity coefficient calculated, tables

The individual activity coefficients calculated from (4.12), suitable for calibration of ISEs for chloride ions, the alkali metal and alkaline earth ions, are given in tables 4.1 and 4.2. Ion activity scales have also been proposed for KF [141], choline chloride [98], for mixtures of electrolytes simulating the composition of the serum and other biological fluids (at 37 °C) [106,107], for alkali metal chlorides in solutions of bovine serum albumine [132] and for mixtures of electrolytes analogous to seawater [140]. 

Rush, R. M., "Parameters for the Calculation of Osmotic and Activity Coefficients and Tables of These Coefficients for Twenty-two Aqueous Mixtures of Two Electrolytes at 25°C," ORNL-4402. Oak Ridge National Laboratory, Oak Ridge, Tenn., (April 1969). ... 

Note the use of activities, as well as of an equilibrium constant based on activities. The kinetic constants for autocatalyzed and catalyzed reactions, k and k, were determined from initial reaction rates with liquid activity coefficients calculated by UNIQUAC. Near chemical equilibrium the fCT is about 6, while Kx is about 5. Table 8.7 gives activation energies and pre-exponential factors obtained by nonlinear regression. The simulation shows tbat the autocatalysis effect is neghgible below 150 °C, but it might increase to 20% at 180 °C. 

TABLE 2.3. Single-Ion Activity Coefficients Calculated from the Extended Debye-Huckel Equation at 25°C... 

Compute logarithms of the activity coefficients from experimental X-Y data. Assuming an ideal vapor phase, the activity coefficients are given as y, = P 7, / X, P( > and y2 = PY2/X2 P2. The natural logarithms of the activity coefficients calculated using the preceding equations are shown in cols. 7 and 8 of Table 1.11. 

Table 1.12 Activity coefficient calculations for butanol(1)-water(2) system at 1 atm...

The student should construct a table giving the actual initial concentrations of the reactants IO3, I, and H. The concentrations should be calculated from the actual concentrations of NaAc and HAc in the stock solutions employed, with an activity coefficient calculated by use of the Debye-Hiickel theory for the ionic strength (/ = 0.16) of the reacting mixtures. 

Table VII. HDEHP Dimer Activity Coefficients Calculations...

Either (2-20) or (2-21) is referred to as the extended Debye-Huckel equation (EDHE) this pair of equations gives results appreciably different from the DHLL when H > 0.01 (that is, V/i > 0.1). For comparison, some ionic activity coefficients calculated from (2-15) and (2-20) are listed in Table 2-1. 

Table 2-2. As a justification of his procedure the values of mean activity coefficients calculated for various electrolytes from the individual ionic values are in satisfactory agreement with the experimental values up to an ionic strength of about 0.1.

The preceding calculations show explicitly that although the numerical values of activities and activity coefficients in Table 3.11.2 differ greatly for the different cases, the A/x values are identical within experimental error. Thus, only A/x is of fundamental significance activities or activity coefficients have only a relative significance. If deviations from ideality had been ignored the value A/x = ln(x2/xi) = i rin(0.4/0.8) = / Tln(0.500) would have been obtained, which is appreciably off the mark. One should also note that whereas for case (b) y tends to be greater than unity, y is less than unity for case (c). 

Activity Coefficients Calculated with Equation 2 of Table 3.3 for Ionic Strength... 

In dilute solutions (/ < 10 M), that is, in fresh waters, our calculations are usually based on the infinite dilution activity convention and thermodynamic constants. In these dilute electrolyte mixtures, deviations from ideal behavior are primarily caused by long-range electrostatic interactions. The Debye-Huckel equation or one of its extended forms (see Table 3.3) is assumed to give an adequate description of these interactions and to define the properties of the ions. Correspondingly, individual ion activities are estimated by means of individual ion activity coefficients calculated with the help of the Guntelberg or Davies (equations 3 and 4 of Table 3.3) or it is often more convenient to calculate, with these activity coefficients, a concentration equilibrium constant valid at a given /,... 

Kielland has estimated values of x for numerous ions from a variety of experimental data. His best values for effective diameters are given in Table 10-2. Also presented are activity coefficients calculated from Equation iO-5 using these values for the size parameter. 

Equilibrium calculations with activities yield results that agree with experimental data more closely than tho.se obtained with molar concentrations. Unless otherwise. specified, equilibrium constants found in tables are generally based on activities and are thus thermodynamic. The examples that follow illustrate how activity coefficients from Table 10-2 are applied to such data. 

The activity coefficients calculated in this manner are given in the following table. Values of G computed from. ... 

Here, (A) is the concentration of a substance measured in moles/1 and is the activity coefficient calculated as a function of the overall ionic strength in the solution. For infinitesimal diluted solutions, the activity coefficients assume the value of 1 hence, activity equals concentration. In ocean water, the various monovalent ions, or ion pairs, display activity coefficients somewhere around 0.75 whereas the various divalent ions, or ion pairs, display values around 0.2 (cf. Table 15.2, last column). 

Most vulnerable in equation (1.73) is r. value (Table 1.5). Debye and Huckel defined it as average distance at which ions are capable of approaching one another. It is associated with the diameter of a hydrated ion. It is determined experimentally by selecting it so that activities coefficients calculated from equation (1.73) coincided with the experimental. Besides, vulnerability of this value is caused by its dependence on temperature. In case of NaCl solution it may range between 3-10 and 4-10 cm. 

Using the activity coefficients calculated above we solve eqs. [A]-[E] again and use the new liquid compositions to refine the estimate of the activity coefficients. The procedure is repeated until the solution converges and the mol fractions do not change any more. A sample of the iterations are shown in the table below ... 

Nevertheless, if a comparison is made of the literature data on equilibrium measurements in dioxane-water solvent mixtures, more data are to be found which contradict the above conclusions than those which support them. In order to investigate this question, Gaizer et al [Ga 74b] determined the stability constants of the iodide mixed complexes obtained from three cobalt(III) dioxime parent complexes, in solvent mixtures with a dioxane content of 10-75%. The three dioximes were dimethylglyoxime, cyclohexanedione dioxime (Nioxime) and furil dioxime. The results are given in Table 8.4, together with the stoichiometric constants determined in solutions of ionic strengths of 0.1 m, and also the thermodynamic constants obtained with the activity coefficients calculated for the various solvent mixtures (with a knowledge of their relative permittivities). A comparison of the data obtained in the different solvent mixtures is possible only in the case of the... 

The ions charges play a very important role in the electric interactions and therefore in the values of the activity coefficients. Table 3.2 illustrates this property by giving values for ionic strength and mean activity coefficients (calculated from the previous equations) for different types of electrolytes in a concentration equal to 10 mol L . 

Table 1.11 Activity Coefficient Calculations for Butanol(l)—Water(2) System at 1 atm...

TO SET UP THE ARRAYS CONTAINING THE INTERACTION TERMS FOR THE ACTIVITY COEFFICIENT CALCULATIONS. VALUES FOR THE SYSTEM, AND OTHER SPECIES, ARE TABULATED IN APPENDIX 9.2, TABLES 3, 4 AND 5. 

A citrate buffer has recently been added to the list of standard buffers. Table 2-4. Using published pK° values of 3.13,4.76, and 6.40 and activity coefficients, calculate the pH (activity) expected at 25° and compare with the NBS value. 

Moreover, in the absence of experimental data, existing thermodynamic models (such as the FH, the Entropic-FV, and the UNIFAC-FV discussed later) can be used to predict the infinite dilution activity coefficient. Since, in the typical case today, existing models perform much better for VLE and activity coefficient calculations than directly for LEE calculations, this method is quite valuable and successful, as shown by sample results in Table 3.1. 

Table 3 shows results obtained from a five-component, isothermal flash calculation. In this system there are two condensable components (acetone and benzene) and three noncondensable components (hydrogen, carbon monoxide, and methane). Henry s constants for each of the noncondensables were obtained from Equations (18-22) the simplifying assumption for dilute solutions [Equation (17)] was also used for each of the noncondensables. Activity coefficients for both condensable components were calculated with the UNIQUAC equation. For that calculation, all liquid-phase composition variables are on a solute-free basis the only required binary parameters are those for the acetone-benzene system. While no experimental data are available for comparison, the calculated results are probably reliable because all simplifying assumptions are reasonable the... 

The values given in this table are only approximate, but they are adequate for process screening purposes with Eqs. (16-24) and (16-25). Rigorous calculations generally require that activity coefficients be accounted for. However, for the exchange between ions of the same valence at solution concentrations of 0.1 N or less, or between any ions at 0.01 N or less, the solution-phase activity coefficients prorated to unit valence will be similar enough that they can be omitted. 

TABLE I.a Comparison of Observed Activity Coefficients of Cu and Au with Values Calculated from Observed Short-Range Order Parameters by the First-Order Quasi-Chemical Theory... 

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