Apparent activity coefficient

A similar multiphase complication that should be kept in mind when discussing solutions at finite concentrations is possible micelle formation. It is well known that for many organic solutes in water, when the concentration exceeds a certain solute-dependent value, called the critical micelle concentration (cmc), the solute molecules are not distributed in a random uncorrelated way but rather aggregate into units (micelles) in which their distances of separation and orientations with respect to each other and to solvent molecules have strong correlations. Micelle formation, if it occurs, will clearly have a major effect on the apparent activity coefficient but the observation of the phenomenon requires more sophisticated analytical techniques than observation of, say, liquid-liquid phase separation. 

Figure 3 Apparent activity coefficients of Na ions in aqueous solutions of Na salts of DxS and CmDx samples with various degrees of substitution (Cp = 0.003 monomol dm" ). (O) DxS ( ) CmDx. The pH values of the sample solution are between 6 and 7.

Note Equations like (2.6) and (2.8) can also be put in a form where molarity, molality, or some other concentrative unit is used rather than mole fraction. This means that /ie has another value, but—more important—it also affects the value of the (apparent) activity coefficient. For a very dilute solution, the differences tend to be negligible, but in other cases, the concentrative unit to which the activity coefficient relates should be stated. Naturally, the various kinds of concentration can be recalculated into each other see Appendix A.7. 

The dissociated form Ac- can react with cations, whereas the undissociated form HAc may be active as an antimicrobial agent. The activities of each depend not only on the overall concentration but also on the dissociation constant (which depends on temperature), the pH, the presence and concentration of various cations, etc. It may be argued in these cases not that the activity coefficient is (much) smaller than unity but that we should take the concentration of the species involved in the reaction only. The result is, of course, the same, and we may speak of an apparent activity coefficient. 

An oil-in-water emulsion, with an oil volume fraction (fatty acid (HAc) total concentration is 0.01 mole per liter emulsion. The following data are provided the association constant for dimerization of the acid in the oil phase K — 104L-mol-1 the partitioning constant between oil and water — 1 the dissociation constant of the acid in water K0 — 1.25 10-5mol L-1 the pH is 4.90. What is the proportion of the acid in the aqueous phase and what is its (apparent) activity coefficient in the oil ... 

Electrostatic repulsion between strongly absorbed dye anions would act to increase the apparent activity coefficient of the dye anions within the fiber and hence would be acting in the right direction. Whether such a repulsion can account quantitatively for the observed results cannot be answered until a satisfactory theory has been evolved, perhaps as an outgrowth of the work of Verwey and Overbeek. ... 

Evidence for apparent activity coefficient changes has been measured on... 

Over the range of concentrations between the solubility limits the apparent activity coefficients will vary inversely as the concentrations based on the mixture as a whole. Elimination of 7 s between Eq. (3.79) and any of the integrated Gibbs-Duhem equations therefore permits the estimation of Aab and Aba from the mutual solubility. Thus, the Margules equations lead to... 

The NBS concentration scale has also been applied to seawater measurements. The measured values of pH(NBS) are, however, dependent on the change in liquid junction potential between the buffer(s) and sample, which needs to be taken into account if the measured pH values are to be used in thermodynamic calculations. This effect is often summarized as an apparent activity coefficient /h for the hydrogen ion ... 

The first term, the apparent activation energy of the encounter reaction, was evaluated from the temperature coefficient of the viscosity of sulphuric acid. 

The analogy between equations derived from the fundamental residual- and excess-propeily relations is apparent. Whereas the fundamental lesidanl-pL-opeRy relation derives its usefulness from its direct relation to equations of state, the ci cc.s.s-property formulation is useful because V, and y are all experimentally accessible. Activity coefficients are found from vapor/liquid equilibrium data, and and values come from mixing experiments. 

It follows from this discussion that all of the transport properties can be derived in principle from the simple kinetic dreoty of gases, and their interrelationship tlu ough k and c leads one to expect that they are all characterized by a relatively small temperature coefficient. The simple theory suggests tlrat this should be a dependence on 7 /, but because of intermolecular forces, the experimental results usually indicate a larger temperature dependence even up to for the case of molecular inter-diffusion. The Anhenius equation which would involve an enthalpy of activation does not apply because no activated state is involved in the transport processes. If, however, the temperature dependence of these processes is fitted to such an expression as an algebraic approximation, tlren an activation enthalpy of a few kilojoules is observed. It will thus be found that when tire kinetics of a gas-solid or liquid reaction depends upon the transport properties of the gas phase, the apparent activation entlralpy will be a few kilojoules only (less than 50 kJ). 

The reaction was followed by observing the appearance of the yellow colour of Ce(IV) at 400 m, with Pb(IV) present in excess concentration. Pb(IV) was varied in the region 8.6 x 10 M to 4.4 x 10 M while Ce(III) was kept at 4 x 10 M. A practical difficulty encountered was the photochemical instability of Ce(IV) acetate. Under the above conditions and in the temperature range 30-47 °C, the reaction is strictly first-order in each reactant. The observed rate coefficient at 30.0 °C is 1.48x10" l.mole sec and the apparent activation energy and... 

The chloride-ion dependence indicates the importance of two activated complexes, (PuOjSnCls y and (Pu02SnCl4), with AH values of 14.0 and 14.6 kcal.mole and AS" values of 4.4+7 and 8.0+5.5 cal.deg . mole respectively (as recalculated by Newton and Baker °). In terms of the apparent rate coefficient, k ... 

Similarly, concepts of solvation must be employed in the measurement of equilibrium quantities to explain some anomalies, primarily the salting-out effect. Addition of an electrolyte to an aqueous solution of a non-electrolyte results in transfer of part of the water to the hydration sheath of the ion, decreasing the amount of free solvent, and the solubility of the nonelectrolyte decreases. This effect depends, however, on the electrolyte selected. In addition, the activity coefficient values (obtained, for example, by measuring the freezing point) can indicate the magnitude of hydration numbers. Exchange of the open structure of pure water for the more compact structure of the hydration sheath is the cause of lower compressibility of the electrolyte solution compared to pure water and of lower apparent volumes of the ions in solution in comparison with their effective volumes in the crystals. Again, this method yields the overall hydration number. 

This situation is termed pore-mouth poisoning. As poisoning proceeds the inactive shell thickens and, under extreme conditions, the rate of the catalytic reaction may become limited by the rate of diffusion past the poisoned pore mouths. The apparent activation energy of the reaction under these extreme conditions will be typical of the temperature dependence of diffusion coefficients. If the catalyst and reaction conditions in question are characterized by a low effectiveness factor, one may find that poisoning only a small fraction of the surface gives rise to a disproportionate drop in activity. In a sense one observes a form of selective poisoning. 

Before terminating the discussion of external mass transfer limitations on catalytic reaction rates, we should note that in the regime where external mass transfer processes limit the reaction rate, the apparent activation energy of the reaction will be quite different from the intrinsic activation energy of the catalytic reaction. In the limit of complete external mass transfer control, the apparent activation energy of the reaction becomes equal to that of the mass transfer coefficient, typically a kilocalorie or so per gram mole. This decrease in activation energy is obviously... 

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