Activity vs. Concentration

strictly speaking, the equilibrium expressions in Eqs. 5.7 and 5.9 should be expressed in terms of the activities (a) of the entities, not their concentrations as given. Likewise, the definition of pH in Eq. 5.11 should really include the activity of H3O, not its concentration, because activity is what the pH meter really measures. 

Recall that activity was used in our development of the thermodynamic driving force for a reaction in Section 3.1.5. It is the number of free solute particles in a solution that affects the entropy of that solution, and hence the activity has to be used in thermodynamic relationships. 

The activity is related to the concentration (moles/ liter) of the compound (X) by Eq. 5.13, where y is the activity coefficient. Gamma is always less than one, and is an empirically determined factor that mediates the concentration of the compound to reflect the amount of compound free in the solution. The activity coefficient of ions can be estimated from Debye-Huckel theory. Consult any quantitative analysis textbook to get a thorough discussion of activities and activity coefficients. It is particularly important to use activities in place of concentrations for concentrated solutions in water, and for nonaqueous solvents, which are the next two topics. 

5 Acidity Functions Acidity Scales for Highly Concentrated Acidic Solutions 

The notion of pH given in Eq. 5.11 is not a sufficient measurement of the acidity of such solutions, even when activities are used instead of concentrations. Remember the leveling effect, which limits the acid strength one can achieve in a dilute solution. Therefore, now, new acidity scales are needed, giving a measurement of the effective ability of the concen- 

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Careful attention to quantitative activity vs. concentration relationships, to the effect of interaction terms in combinations (using computerized regression analysis and experimental design), and careful observation of the manner in which one mode of action supports and reinforces another, seems likely to lead us to the next generation of highly efficient flame retardant systems. 

Fig. 1. Metabolic activity vs. concentration for essential and non-essential elements reprinted from Wood and Wang, 1983.

The present report describes new results for benzene at temperatures in the range 15 to 45°C, solubilized in aqueous solutions of sodium dodecylsulfate (SDS) and 1-hexadecylpyridinium chloride (referred to as cetylpyridinium chloride or CPC). The solute activity vs. concentration data provide insight into the nature of chemical and structural effects responsible for the solubilization of benzene by aqueous micellar systems in addition, the results find direct use in predicting the performance of MEUF in removing dissolved benzene from aqueous streams. 

The table in this Handbook provides data for a number of polymer solutions as smoothed values over the complete range of solvent activities between 0 (polymer mass fraction = 1) and 1 (polymer mass fraction = 0). For this purpose, the data were selected from data books [4-6] as well as from a number of original sources [7-22] which are not included in these books. The appropriate data were smoothed. The final table provides then the polymer mass fractions at given fixed solvent activities between 0.1 and 0.9. Of course, the user must keep in mind that the activity vs. concentration range of the experimental data is sometimes smaller than the below given complete range, thus the smoothed data should be used with sufficient care. 

OmCINAL WEIGHT % Ni Pig. 26. Activity vs. concentration for benzene hydrogenation by nickel supported on alumina. 

Figure 6.5 Concentratioin esponse plot of inhibition by a slow binding inhibitor that conforms to scheme B of Figure 6.3. The progress curves of Figure 6.4A were fitted to Equation (6.1). The values of vs thus obtained were used together with die velocity of the uninhibited reaction (v0) to calculate the fractional activity (vs/v0) at each inhibitor concentration. The value of Kf9 is then obtained as the midpoint (i.e., die IC50) of die isotherm curve, by fitting die data as described by Equation (6.8).

Jarvis, N.L. and Zisman, W.A. "Surface Activity of Fluorinated Organic Compounds at Organic-Liquid/Air Interfaces Part II. Surface Tension vs Concentration Curves, Adsorption Isotherms, and Force-Area Isotherms for Partially Fluorinated Carboxylic Esters," Naval Research Labs Report 5364, Surface Chemistry Branch, Chemistry Division, October 8, 1959. 

Some of the compounds described in this chapter were studied for specific physical properties. Surface tension measurements with solutions of 9-16 in 0.01 M hydrochloric acid demonstrated that these zwitterionic X5Si-silicates are highly efficient surfactants.21 These compounds contain a polar (zwitterionic) hydrophilic moiety and a long lipophilic z-alkyl group. Increase of the n-alkyl chain length (9-15) was found to result in an increase of surface activity. The equilibrium surface tension vs concentration isotherms for 9 and 16 were analyzed quantitatively and the surface thermodynamics of these surfactants interpreted on the molecular level. Furthermore, preliminary studies demonstrated that aqueous solutions of 9-16 lead to a hydrophobizing of glass surfaces.21... 

Figure 6.23 Flotation recovery of lime-depressed pyrite activated by organic acids vs. concentration of activators...

The electromotive force (emf) of liquid membrane electrodes depends on the activity of the ions in solution and their performance is similar in principle to that of the glass electrode. To characterize the behavior of liquid membrane electrodes, the linearity of the emf measurements vs. concentration of a certain ion in solution is checked. Additional performance data are the Nernstian slope of the linear range and the pH range over which the potential of the electrode is constant. 

Very similar kinetics were observed with (SBI)ZrCl2/MAO although this catalyst is an order of magnitude less active, the concentration of active species turned out to be almost identical to the borate system kp/kp P = 0.08, with a similar accumulation of dormant states. Evidently the counteranion ([CN B(C6F5)3 2] vs. [Me-MAO] ) modulates the energetics of the chain growth cycle, i. e. the anion is intimately involved in the transition state, but does not influence the distribution between active and dormant states (Scheme 8.34) [97]. 

Antihemolytic activity. Water extract of the dried seed, administered to rabbits red blood cells at variable concentrations, was inactive vs Staphylococcus aureus a-toxin-induced hemolysis and produced weak activity vs Vibrio parahaemolyticus-induced hemolysis . ... 

Antioxidant activity. Plant juice, at a dose of 100 jiL/kg, produced weak activity vs Fenton s reagent-induced lipid peroxida-tionoco47 concentration of 1%,... 

Anti-convulsant activity. Methanol (50%) extract of the dried leaf, administered to mice, was active vs leptazol-induced convulsions . Ethanol (70%) extract of the fresh leaf, administered intraperito-neally to mice of both sexes at variable doses, was active vs metrazole- and strychnine-induced convulsions . Anti-estrogenic effect. Aqueous extract of the dried leaf smoke, administered to female adults at a concentration of 25.0 pL/plate, was active on granulosa cells. Results significant atp < 0.001 level . 

Spasmolytic activity. Ethanol (95%), ethanol/glycerin, and glycerin extracts of the leaf, administered to guinea pigs at a dose of 50 mg/kg, was active vs vasopressin-induced coronary spasms as determined from electrocardiogram ". Ethanol (30%) extract of the dried leaf, administered to rabbits at a concentration of 1 mg/mL, was active on aorta vs K -induced contractions ". Decoction of the dried leaf, administered to rats, was active on aorta, IC501.12 mg/mL. The effect of the lyophilized extract on phenylephrine-induced contraction and endothelium was present. Decoction of the dried leaf, administered to rats, was active on the aorta vs phenylephrine-induced contraction, IC501.16 mg/mL. Water extract of the dried leaf, administered to rats at a dose of 3 mg/mL, was active on trachea vs acetylcholine-induced contractions ". Superoxide production inhibition. Seed oil, administered to rats at a concentration... 

Apoptosis induction. Lipoprotein fraction of the bran, in cell culture at a concentration of 100 pg/mL, was active vs human endometrial adenocarcinoma cells " . 

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