Activity coefficient, decrease

At ionic strengths where the activity coefficient decreases with increasing ionic strength, the product P increases because the product P is constant. 

The values of the activity coefficients decrease with increasing ionic strength I (as below). The only way for Ksp to remain constant at the same time as the activity coefficient y decreasing is for the concentrations c to increase. And this is exactly what happens the concentration of AgCl has increased by about 50 per cent when the concentration of MgS04 is 1.2 mol dm-3. 

For every hydrocarbon the activity coefficient increases with an increase of the carbon chain length. Usually, the value of activity coefficient decreases when the interaction between the solvent and the IL increases. It can be seen in Figure 1.16, where the plot of the activity coefficients, y , for different Cg hydrocarbons in [CgCiIm][Tf2N] is presented [183]. The value of the activity... 

As ionic strength increases, the activity coefficient decreases (Figure 8-4). The activity coefficient (y) approaches unity as the ionic strength (p) approaches 0. 

Effect of Ethanol on Volatility of Aroma Compounds. The activity coefficients of volatile compounds obtained by headspace method are lower in the presence of ethanol at 126 ml/L than in water (Table V). The headspace responses of aroma compounds are reduced by one-half (11-18). The aroma compoimds are not very polar and are more soluble in ethanol than in water hence the activity coefficient decreases, as shown by other authors for alcoholic beverages (19). This effect of solubilisation can be explained by the presence of interactions between aroma compound, water and ethanol. 

However, both model solutes for the n- and n-electron dispersion forces, toluene and n-heptane, respectively, show a clear trend. With increasing alkyl chain length, the activity coefficient decreases by factor 2.0 in the case of toluene, and 2.5 in the case of n-heptane, indicating stronger interactions in ionic liquids bearing longer alkyl chains. 

This equation accounts for the fact, so frequently observed, that the addition of an inert salt, not having an ion in common, will increase the solubility of a sparingly soluble salt. The inert salt increases the ionic strength of the medium, and hence the activity coefficient decreases. In order for the product Sy to remain constant the solubility S must increase correspondingly. 

The activity coefficient of a species is a measure of the effectiveness with which that species influences an equilibrium in which it is a participant. In very dilute solutions, in which the ionic strength is minimal, this effectiveness becomes constant, and the activity coefficient is unity. Under such circum.stances, the activity and the molar concentration are identical (as are thermodynamic and concentration equilibrium constants). As the ionic strength increases, however, an ion loses some of its effectiveness, and its activity coefficient decreases. We may summarize this behavior in terms of Equations 10-2 and 10-3. At moderate ionic strengths, yx< 1 tis the solution approaches infinite dilution, however, 7x —> 1 and thus ax —> [X] and X p —> K p. At high ionic strengths (/r > 0.1 M),... 

The logarithm of the activity coefficient decreases from its limiting value log / = 0 (for 7 = 0) with the square root of the ionic strength. 

Samples with a DE higher than 50% have constant calcium activity coefficients over the concentration range tested (0.8 - 3 x 10 equiv/1). In contrast, pectins with lower DE are characterized by a calcium acti ity coefficient which is decreasing above a concentration of 10 equiv/1. Furthermore, the concentration in calcium pectinates has a profound influence on the calcium activity coefficient for samples with the lowest DE or for enzyme-deesterified pectins since the calcium activity coefficient decreases to zero. With higher concentration in pectins, (c > 3 x 10 equiv/1), a... 

Therefore, we would predict an increase in Ka and in the dissociation with increased ionic strength, as the activity coefficients decrease. See Example 6.18, and Problem 21 in Chapter 6. A similar relationship holds for weak bases (see Problem 60 in Chapter 6). 

We may further speculate on the meaning of (15). It is known (Edward, 1964 Boyd, 1969 Yates and McClelland, 1974) that activity coefficients decrease in the series 7 > 7xh > 7x- This is quite reasonable since the increase in acid concentration is accompanied by a reduction in the availability of water, an excellent medium for solvating hydronium ions. This decrease will obviously tend to increase the free energy of the cationic species in particular. The extent of this increase will depend, in turn, on the ability of the individual cation to disperse the positive charge through the residues linked to the protonated atom by hydrogen bonding with the solvent. 

This illustrates the fact that as the total electrolyte concentration increases, the activity coefficients decrease. For example, the activity of in a solution containing only 0.01 M CaCla is 0.0045 M whereas if 0.1 Af NaCl is also present, the Ca activity is only 0.0019 M. 

In reality, these experimental results are not wholly inconsistent with the Debye-HOckel model, whereby the mean activity coefficient decreases as the molality increases. This comes down to taking into account the fact that a usual solute/solvent description is no longer satisfactory for concentrated electrolytes. Indeed, when dealing with concentrated electrolytes, the number of solvent molecules involved in the solvation sphere, close to the ions, cannot be ignored when compared to the total number of solvent molecules. Once one takes this phenomenon into account, then three types of adjustment emerge, each of which are laid out in detail below. 

Because of the negative sign of the partial molar excess volume the activity coefficient decrease with increasing pressure. But it can be seen that in contrast to the temperature influence caused by the pressure influence on the activity coefficients is negligible for typical pressure differences observed for VLE. But for large pressure differences the effect has to be taken into account. This is demonstrated in Section 5.8 for LLE. 

For positive deviations from Raoult s law (g >0,y > 1), depending on the sign of the excess enthalpy two cases can be distinguished. In the case of endothermic behavior (h > 0), the excess Gibbs energy and therewith, the values of the activity coefficient decrease with increasing temperature. 

The second problem is that pH should be taken from the activity of hydrogen ions, and the effect of activity coefficients 7 can be neglected in water, but when the percentage of the organic modifier in the mobile phase increases, the activity coefficients decrease and cannot be neglected. Similarly, for the dissociation constant, the concentration should be changed by activities. From the Debye-Hilckel definition, an activity coefficient depends on the ionic strength I of the solution. 

Codogan et al. [14] have studied the systems (Cg—C,) alcohols-squalane at 323,333 and 343 K the activity coefficients decrease with the increasing number of carbon atoms of the alcohol, for example from 8.19 for 2-propanol to 2.94 for 1,1-dimethyl-l-propanol at 323 K. 

The activity of an ion is affected by its surroundings. The electrostatic force varies inversely with the square root of the distance of separation of ions according to Coulomb s law. Thus, the activity coefficients decrease as the concentration of the solution increases. 

To calculate the activity coefficients, which provide an indication of how the concentration affects the activity of the species, one can use the Debye-Huckel equation, among others. By Coulomb s law, the activity coefficient decreases as the concentration increases because the electrostatic forces become stronger as the ions approach. Thus, for concentrated solutions, the repulsion effect seems to dominate. Assuming that the ions behave as charged spheres, the Debye-Huckel equation takes the form [2]... 

The value of the activity coefficient decreases from unity as the overall concentration of ions of the solution increases. Since is a constant, it follows that will increase with the ionic strength and become larger than K. The increase in the solubility of a drug by the addition of indifferent electrolytes is attributed to the increase in the ionic strength of the solution due to the indifferent electrolytes. 

Fig. 3. Water activity coefficients of (a) three bronfide and (b) three hydroxide aqueous salt solutions at 25°C as function of salt molality. Experimental data Li+ — squares, Na+ — circles, K+ — triangles. The lines represent MSA-NRTL calculations. Activity coefficients decrease with decreasing size of the cation K+ > Na+ > Li+ for bromide solutions but in the reversed order for hydroxide solutions.

Fig. 6. Mean ionic activity coefficients of five bromide salts in aqueous solution at 25 °C as fimction of salt molality. Experimental data LiBr — squares, NaBr — stars, KBr — circles, RbBr — crosses, CsBr — triangles. The dotted lines represent ePC-SAFT calculations. Activity coefficients decrease with increasing size of the cation Ii+ > Na+ > K+ > Rb+ > Cs . (From Ref. 15, Elsevier, reprinted with permission.)...

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