The non-ideal case

So far the thermodynamic analysis relates only to the ideal solution, or to reaction carried out 

All the equilibrium constants discussed earlier have been quoted in terms of concentrations. 

There are two reasons for developing equilibria relations in terms of concentrations  

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If the gas is not ideal, so that the ideal gas equation cannot be used, we replace the pressurep in equations 20.198 and 20.199 by the fugacity,/, such that the ideal gas equation still holds if the pressure p is replaced by the fugacity, an effective pressure, when the real pressure is p. This form is most convenient because of the numerous ways in which non-ideality can be expressed, and we note that the fugacity is related to, but not necessarily proportional to the pressure. We can express the fugacity as a function of the pressure by introducing the fugacity coefficient, 7p, as / = y p, which then replacesp in equation 20.199 for the non-ideal case. The value of 7p tends to unity as the gas behaves more ideally, which means as the pressure decreases. 

In the non ideal case (all cases) the integral is approximated or solved numerically. 

These results show that in a MISPE procedure one may encounter substances with different patterns of behavior. In the ideal case the template (or the template and a group of its analogs which need to be carried on for further analysis) are retained 100% during the sample application and the wash step. All other substances (or at least those which interfere with further analysis) should be fully removed. In the non-ideal case some interferents will not be removed by a particular protocol. In this case it is useful to observe the behavior of these interferents on the NIP. If they are retained by the NIP, too, then their retention is likely due to nonspecific binding. In this case a better choice of the solvents in the protocol may help to eliminate the interferent. The danger here is that the new protocol may also reduce the retention of the template and reduce its recovery. It is therefore interesting to note that even in this good paper it has not been shown that the addition of 1 % methanol to the dichloromethane sample was really necessary with the real sample matrices. 

Theories of Conductance The Non-ideal Case for Symmetrical Electrolytes... 

CH12 THEORIES OF CONDUCTANCE THE NON-IDEAL CASE FOR SYMMETRICAL ELECTROLYTES... 

CH12 THEORIES OF CONDUCTANCE THE NON-IDEAL CASE FOR SYMMETRICAL ELECTROLYTES Table 12.1 Approximate t values at various concentrations of a 1-1 electrolyte... 

CH12 THEORIES OE CONDUCTANCE THE NON-IDEAL CASE EOR SYMMETRICAL ELECTROLYIES... 

Under non-ideal conditions, the external field is modified by electrophoresis and relaxation, and this modified field is (X — AX). As the concentration decreases, AX also decreases, and in the limit as c — 0, i.e. ideal conditions, AX 0. But, the velocity with which the ion migrates under this modified field is still defined in terms of the external field, even for the non-ideal case where the actual effective field under which the ion migrates is (X AX), i.e. ... 

The Hierarchical Approach developed in this chapter incorporates a knowledge-based procedure for the synthesis of separations. This consists of dividing the separation section in three subsystems gas vapour, liquid and solid separations. Each subsystem is further managed by selectors, which makes use of unit operations. Split sequencing is based mainly on heuristics, although may include algorithmic or optimisation techniques. This chapter describe in more detail the synthesis of distillation trains for zeotropic distillations, the non-ideal case being left for the Chapter 9. 

Classically, one treats phases of two components as ideal, regular, or real solutions. Usually, however, one concentrates for the non-ideal case only on solutions of salts by discussing the Debye-Huckel theory. Polymer science, in turn, adds the effect of different molecular sizes with the Hory-Huggins equation as of basic importance (Chap. 7). Considerable differences in size may, however, also occur in small molecules and their effects are hidden falsely in the activity coefficients of the general description. 

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