Error into system coefficients

The temptation to allow data systems to determine the linearity of calibration curves on the basis of the value of the correlation coefficient alone has the potential of introducing determinate errors into chromatographic quantitation. Those errors can be avoided by always studying the results carefully before drawing any conclusions. 

A linear system can be written in infinite equivalent forms in classical analysis, where round-off errors do not exist. This is also true for numerical analysis on computers, where round-off errors must be accounted for. In fact, it is possible to multiply or divide a row of the system by a nonzero coefficient (for common compilers by a power of 2 to preserve all the significant digits) without introducing any error into the system coefficients, on condition that no overflow or underflow conditions are achieved. All these systems are equivalent for the classical analysis and for the numerical computations on computers, but each of them has a different condition number for the coefficient matrix. 

For pressure-dependent reactions, both low- and high-pressure-limit rate coefficients k and k are presented where available. For the low-pressure case, collision efficiencies have been reported for several of the third-order reactions in the H2/O2/CO system. From these data it can be concluded that the temperature dependences of third-body efficiencies in this system are roughly equal for the different reactions, taking the limits of experimental errors into consideration. Exceptions are collision efficiencies in reactions where the third body interacts chemically with the collison complex, e.g.. 

Basically, the equipment is a standard Wicke-Kallenbach cell, except that provision is made for introducing a pulse of the trace component on one face of the porous sample, i.e. z=0. However the design does have to take into consideration the need to calibrate the detection unit for lags in the system.This does not seem to have been carried out in other work reported which used this technique. Failure to make this correction can lead to significant errors in the values of the diffusion coefficient which are extracted from the experimental data e.g. see Fig.l. 

The measurement of sorption, diffusion and permeability coefficients takes place as a rule using one of three methods sorption of the gases in the polymer, permeation through a membrane (film or sheet) into a sealed container or permeation through a membrane into a gas stream. As far as possible sorption methods should be used together with permeation methods that are specific for the measured gas/polymer system in order to uncover any possible anomalies or errors in the measurements by comparison of results. 

The solid lines on Figure 4 take into account the nonideal behavior of adsorbed mixtures of ethylene and ethane in NaX. This system is highly nonideal because of the interaction of the quadrupole moment of ethylene with the soditun cations of NaX. Activity coefficients at infinite dilution are unity at the limit of zero pressure and 0.27 at high pressure. The dashed lines on Figure 4 were calculated for am ideal adsorbed solution (IAS) and the resulting error in the individual isotherm for ethane at 30 bar is 20%. 

The drawback of this approach compared with that described in Section 6.5.2 is that all errors are lumped into the isotherm parameters rather than the effective mass transfer coefficient, because either the wrong column or isotherm model is chosen. This approach is thus recommended to get a quick first idea of system behavior using only little amounts of sample, and not for a complete analysis, especially if binary mixtures with component interactions are investigated. The significance of the results decreases even further if some plant and packing parameters are only guessed or even neglected. 

Without question, sodium and potassium have been the analytes receiving the most attention in conjunction with the development of new analyzers. Almost all instruments on the market utilize the potassium-selective membrane system based on the antibiotic valinomycin in a PVC membrane matrix. For blood measurements, such a membrane is quite adequate. However, in undiluted urine samples, a negative error in the measurement of potassium has been reported (KIO). Apparently, this interference comes from a negatively charged lipophilic component of the urine which can partition into the PVC membrane, reducing the membrane potential (i.e., the membrane is not permselective). Fortunately, this problem can be overcome by incorporating the valinomycin in a silicone rubber-based membrane matrix (A4) into which the unknown anionic component apparently has a less favorable partition coefficient. 

The performance of DORTHO, the double precision version of ORTHO, was a very pleasant surprise to the writers. Up through the fitting of fifteenth degree polynomials the first six digits of each coefficient were the same whether monomials or Chebyshevs were used for a coordinate system. This means that the internal orthogonalization scheme built into ORTHO and DORTHO functioned very effectively and that the double-precision arithmetic avoided meaningful roundoff errors. From this, we conclude that... 

Accurate values of Pow are clearly necessary for the ultimate calibration of all surrogate systems, but, in practice, direct measurements of Powby the traditional shake-flask method are seldom used. Particularly for compounds with low water solubility, experimental difficulties may arise from problems in phase separation without carryover, sorption to glass surfaces, or from formation of emulsions. All of these introduce serious uncertainties into the concentrations in the appropriate phases, and may consequently lead to substantial errors in the estimates of partition coefficients. The problem is particularly acute for compounds with extremely low solubility in water such as the chlorinated dibenzo[l,4]dioxins for which widely varying values have been reported (Marple et al. 1986 Shiu et al. 1988). For such compounds, use of a generator column has been advocated (De Voe et al. 1981 Woodburn et al. 1984). In essence, the following steps are carried out (1) a solution of the test substance in octanol is equilibrated with water and the concentration in the octanol phase is determined, (2) the octanol phase is... 

In terms of the isotherm formalism, the situation with regard to inert as well as interactive solutes with interactive solvents amounts to that with inert and interactive solutes with non-interactive solvents. That is, since equation 22 appears to provide a description of the partition coefficients of systems of the latter to within experimental error, empirical fitting of equation 13 would seem to be superfluous. However, it may not always be the case that solute and/or solvent positive or negative deviations from Raoult s law can be defined separately. This is particularly true of liquid chromatography, wherein the mechanisms of solute retention are at best only poorly defined. Thus, and for the purpose of achieving analytical separations, the isotherm relation may in fact prove to be advantageous insofar as it is a well-defined continuous function and, hence, can be incorporated immediately into the Laub-Purnell window-diagram scheme of optimization. We consider the matter in further detail in the Section that follows. 

So far no attention has been given in this chapter on the effect of the diffusivities. Often instantaneous reactions involve ionic species. Care has to be taken in such case to account for the influence of ionic strength on the rate coefficient, but also on the mobility of the ions. For example, the absorption of HCI into NaOH, which can be represented by H + OH HjO. This is an instantaneous irreversible reaction. When the ionic diffusivities arc equal the diffusivities may be calculated from Pick s law. But, H and OH have much greater mobilities than the other ionic species and the results may be greatly in error if based solely on molecular diffusivities. This is illustrated by Fig. 6.3c-2, adapted from Sherwood and Wei s [4] work on the absorption of HCI and NaOH by Danckwerts. The enhancement factor may be low by a factor of 2 if only molecular diffusion is accounted for in the mobility of the species. Important differences would also occur in the system HAc-NaOH. When CO2 is absorbed in dilute aqueous NaOH the effective diffusivity of OH is about twkx that of COj. 

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