Solute activity calculations

As we have seen, unless the pressure is considerably larger than 1 bar, T is very nearly 1. Except for special circumstances, we will assume it is unity in future calculations and discussions of activity in solution, and we will drop the designation of (1 bar) pressure for the standard state pressure. That is,/f(l bar) will be set equal to / (/>), the vapor fugacity at a pressure p, and both will be designated as/f, so that equation (6.100) can be written as... 

More recent studies on the folded toxin structure by Norton and colleagues have utilized h- and C-NMR techniques (19,20). By using 2D-FT-NMR, it was possible to localize a four stranded, antiparallel )5-pleated sheet "backbone structure in As II, Ax I, and Sh I (21,22), In addition, Wemmer et al. (23) have observed an identical )5-pleated structure in Hp II. No a-helix was observed in these four variants. In the near future, calculated solution conformations of these toxins, utilizing distance measurements from extracted Nuclear Overhauser Enhancement (NOE) effects should greatly stimulate structure-activity investigations. 

The program produces in its output dataset a block of results that shows the concentration, activity coefficient, and activity calculated for each aqueous species (Table 6.4), the saturation state of each mineral that can be formed from the basis, the fugacity of each such gas, and the system s bulk composition. The extent of the system is 1 kg of solvent water and the solutes dissolved in it the solution mass is 1.0364 kg. 

In this way and by numerical evaluation, Driessens (2) proved that the experimental activities could be explained on the basis of substitutional disorder, according to Equation (27), within the limits of experimental error. It seems, therefore, that measurements of distribution coefficients and the resulting activities calculated by the method of Kirgintsev and Trushnikova (16) do not distinguish between the regular character of solid solutions and the possibility of substitional disorder. However, the latter can be discerned by X-ray or neutron diffraction or by NMR or magnetic measurements. It can be shown that substitutional disorder always results in negative values of the interaction parameter W due to the fact that... 

Calculation of Activity of Solute from That of Solvent... 

When using standard solutions prepared on the basis of activities calculated from these activity scales, and provided there is no interfierence and that the prelogarithmic term in the E versus log a dependence is Nernstian or at least accurately known and constant, the sample activity can be determined from the ISE potentials obtained in the sample and in a standard solution (see (4.13), p. 74-6). 

Using activities, calculate the pH of a solution containing 0.010 M NaOH plus 0.012 0 M LiN03. What would be the pH if you neglected activities ... 

The final protein content of the solution is 2.8 mg/ml. The solution has 7 U/ml of specific activity, calculated using azocasein as substrate (see Basic Protocol 2, steps 1 to 8). All enzymes are available from Sigma. 

Figure C4.2.2 LOX activity measurements by both oxygen electrode (right) and UV absorbance (left). The graph shows a hypothetical reaction using identical conditions of equal substrate and LOX concentrations and temperature set at 25°C. Over the range generally used for measurement, the UV method gives a 3.24-fold greater response compared to the oxygen electrode that is, the full-scale of oxygen uptake (0 to 100) represents 0.242 pmol 02/ml of solution and the full-scale of UV-absorbance (0 to 2.0) represents 0.0746 pmol product/ml of solution. Also shown is the lag phase followed by a rapid linear rate used for activity calculation.

Thus, firstly, the choice of the pure solvent as the reference state for the definition of activities of solutes in fact impairs a fair comparison of the activity of dilute solutes such as general adds to the activity of the solvent itself. Secondly, the observed first-order rate constants k or k0 for the reaction of a solute with the solvent water are usually converted to second-order rate constants by division through the concentration of water, h2o = oA iho, for a comparison with the second-order rate coefficients HA. Again, it is questionable whether the formal h2o coefficients so calculated may be compared with truly bimolecular rate constants kUA for the reactions with dilute general acids HA. It is then no surprise that the values for the rate coefficients determined for the catalytic activity of solvent-derived acids scatter rather widely, often by one or two orders of magnitude, from the regression lines of general adds.74... 

It is merely an extension of these ideas to demonstrate the conditions that the same membrane, containing MY, should also be responsive, in a Nernstian fashion, to Y activities+in solution. These conditions are again a three-ion situation M, Y and N. The salt NY is the aqueous sample whose Y activity is to be measured. N is typically a hydrophilic ion such as Na. When aqueous NY activity is varied, the interfacial pd is again S-shaped (mV vs log[NY]). These responses are illustrated from a theoretical calculation in Figure 1. The assumed extraction parameters are given in the legend. The similarity with silver halide membrane electrodes are summarized below. 

The assay method of Dalziel is convenient. In a recording ultraviolet spectrophotometer set at 340 nm is placed a 3-mL quartz cuvette containing 2.4 mL of 0.10 M glycine-sodium hydroxide buffer solution, pH 9, 500 pL of a 54 mM solution of ethanol 1n the same buffer, and 100 pL of a 15 nM solution of NAD, also in the same pH 9 buffer. The volume is made up to 3.0 mL, and the assay initiated by the addition of 10 pL of a 1 mg per mL solution of HLADH in 0.10 M "Tris-hydrochloric acid buffer", pH 7.4. The change in optical density at 340 nm 1s monitored at 25°C and the activity calculated from the following equation ... 

We have made a number of assumptions in this calculation, the most notable being that the ionic solutions are ideal, in that there are no interactions (attractive or repulsive) between solute molecules. It is most unlikely that this is the case, especially in moderately concentrated solutions of ions. In order to correct for nonideality (interactions between solute molecules), we need to substitute the activities of solute molecules for their concentrations in all thermodynamic calculations. The activity (a) of a solute molecule is related to its concentration (C) by an activity coefficient (y). 

Solute and Solvent Activity Calculations. For the purposes of this study, the derivations necessary to the calculation of the solute and solvent activities will begin with the equation for the prediction of the excess free energy of a single electrolyte solution based on the work of Friedman (9). 

The lysozyme solubilities in aqueous solutions of sodium acetate were calculated for pH =8.3 and the results are presented in Fig. 3. The experimental preferential binding parameters are listed in Table 2 (the values for pH=4. 68-4.7 were, however, used because those for pH=8.3 were not available). The concentration dependence of the water activity in solutions of sodium chloride was obtained from Eq. (18) using the Pitzer equation for the osmotic coefficient [38]. 

Covington AK, Ferra MIA. Calculation of single ion activities in solutions simulating blood plasma. In Maas AHJ, ed. Methodology and clinical appHcations of ion selective electrodes. Copenhagen International Federation of Clinical Chemistry, 1986 239-47. 

Strictly speaking, soils are always nonequilibrium systems. With care, however, a partial equilibrium or steady state can be attained by assuming that the soil solids do not change. This is the usual assumption in cation exchange and adsorption studies. Kittrick and co-workers were able to obtain near-equilibrium measurements of some soil minerals in studies requiring -several years. From the resulting ion activities in solution, they were able to calculate some of the equilibrium constants used for the mineral stability diagrams shown later in this book. 

The value of ATeq can be calculated from the energies of formation of the components of Eq. 7.19. The equilibrium between kaolinite and montmorillonite depends on the H+, Ca2+, and Si(OH)4 activities in solution. Rearranging Eq. 7.20 yields... 

Usually, we are interested in determining the concentration of a test substance rather than its activity. Activity coefficients are not generally available, and it is inconvenient to calculate activities of solutions used to standardize the electrode. 

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