Errors activity coefficient, ignoring

The procedure outlined above is fairly typical for a number of determinations of solubility products of metal selenites. Data from such investigations have been reevaluated by the review with the accepted protonation constants of the selenite ion, corrected for the hydrolysis of the metal ion when necessary, and the value of the solubility product extrapolated to standard state conditions. It has been observed that the initial and final pH values in cases are in conflict. This has been ignored and the calculations have been based solely on the data for the equilibrium solution. Complexation of the metal ion by the anions and temperature effects were neglected, which probably introduces a negligible error compared with other sources of error. Activity coefficients were calculated by the SIT expression with s = 0 kg-mol, which is a reasonable simplification due to the low ionic concentrations. The ionic strength was obtained by an iterative procedure from knowledge of the total metal concentration and the pH of the equilibrium solution. The results of the recalculations are entered in Chapter V. 

A third (and usually more profound) cause of error lies in the way that the Nemst equation is formulated in terms of activities rather than concentration. Even if the emf and E are correct, the proportionality constant between concentration and activity (the mean ionic activity coefficient y ) is usually wholly unknown. Errors borne of ignoring activity coefficients (i.e. caused by ionic interactions) are discussed in Sections 3.4 and 3.6.3. 

The third and fourth terms in (9.43) are usually ignored. This can be accepted for very dilute aqueous solutions where the activity coefficients tend to unity, their ratio converges even faster with dilution, and water is in a larger molar excess. Unfortunately, conditions in most real measuring situations are not such that these terms can be ignored with confidence. The variability of these two terms then introduces error into the optical determination of pH or other ions. 

The magnitude of the effect of pressure on activity coefficients is much less than is the case for solubility products (see previous discussion). The errors in ignoring the compressibility term for activity coefficients are, at most, 2-5% in a pressure range up to 1000 bars (Millero 1983 Krumgalz et al. 1999). For the broad-scale FREZCHEM model, these errors are acceptable. 

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). 

The pH of a solution in equilibrium with CaC03 and atmospheric CO2 is 8.3. Equation 7.18 yields a value of pH 8.5 because activity coefficient corrections are ignored and because of rounding-off errors in the exponents of the equilibrium constants. 

The similarity with the activity coefficients or, in other words, values associated with interactions with the medium, which follows from the foregoing, suggests that Eq. (48) relates not to the usual full entropy values, but only to the contribution determined by the interaction with the medium. The full values differ by the contributions associated with intramolecular vibrations. In the case of particles with rigid internal chemical bonds, this contribution to entropy is small and can be represented in the form of Eq. (48), with the error introduced thereby being ignored. Therefore, for such particles such as, for example, HsO and, of course, monatomic ions, Eq. (48) can be considered accurate enough. 

From Fig. 10.40 it will be seen that contact between the electrolyte (soil or water) and the copper-rod electrode is by porous plug. The crystals of CUSO4 maintain the copper ion activity at a constant value should the halfcell become polarised during measurements. The temperature coefficient of such a cell is extremely low, being of the order of 1 x 10" V/°C and can thus be ignored for all practical purposes. To avoid errors due to polarisation effects, it is necessary to restrict the current density on the copper rod to a... 

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