Barker s method

The sum of the squared differences between calculated and measures pressures is minimized as a function of model parameters. This method, often called Barker s method (Barker, 1953), ignores information contained in vapor-phase mole fraction measurements such information is normally only used for consistency tests, as discussed by Van Ness et al. (1973). Nevertheless, when high-quality experimental data are available. Barker s method often gives excellent results (Abbott and Van Ness, 1975). 

When there is significant random error in all the variables, as in this example, the maximum-likelihood method can lead to better parameter estimates than those obtained by other methods. When Barker s method was used to estimate the van Laar parameters for the acetone-methanol system from these data, it was estimated that = 0.960 and A j = 0.633, compared with A 2 0.857 and A2- = 0.681 using the method of maximum likelihood. Barker s method uses only the P-T-x data and assumes that the T and x measurements are error free. 

The method of potentiostatic pulses is sometimes combined with the DME (called pulse polarography). hi this case the pulse frequency should match the drop frequency, where each pulse is used at a definite time in the drop life, hi Barker s method, large pulse amphrndes are used. Other versions of the potentiostatic pulse technique are square-wave and staircase voltammetry here smaU-amphtude pulses are used. 

The present author (4) has previously preferred to use raw isobaric data coupled with Barker s method (2) and the Wilson equation (5), but interpolation of the calculated discrete vapor composition values requires smoothing of boiling point-liquid composition data at some stage. 

Plot P-x,y diagram for Margules Equation with parameters from Barker s Method. 

The plot of residuals below shows that the procedure used (Barker s method with regression for H2) is not in this case very satisfactory, no doubt because the data do not extend close enough to xl = 0. 

This result is considerably improved over that obtained with Barker s method. 

If the experimental values P and uf are closely reproduced by the correlating equation for g, then these residuals, evaluated at the experimental values of Xi, scatter about zero. This is the result obtained when the data are thermodynamically consistent. When they are not, these residuals do not scatter about zero, and the correlation for g does not properly reproduce the experimental values P and y. Such a correlation is, in fact, unnecessarily divergent. An alternative is to process just the P-Xi data this is possible because the P-Xi-Ui data set includes more information than necessary. Assuming that the correlating equation is appropriate to the data, one merely searches for values of the parameters a, 3, and so on, that yield pressures by Eq. (4-295) that are as close as possible to the measured values. The usual procedure is to minimize the sum of squares of the residuals 8P. Known as Barker s method Austral. J. Chem., 6, pp. 207-210 [1953]), it provides the best possible fit of the experimental pressures. When the experimental data do not satisfy the Gibbs/Duhem equation, it cannot precisely represent the experimental yi values however, it provides a better fit than does the procedure that minimizes the sum of the squares of the 8g residuals. 

Worth noting is the fact that Barker s method does not require experimental j/f values. Thus the correlating parameters a, P, and so on, can be evaluated from a P-Xi data subset. Common practice now is, in fact, to measure just such data. They are, of course, not subject to a test for consistency by the Gibbs/Duhem equation. The world s store of VLE data has been compiled by Gmehhng et al. Vapor-Liquid Equilibrium Data Collection, Chemistry Data Series, vol. I, parts 1-8, DECHEMA, Frankfurt am Main, 1979-1990). 

Data reduction may be based on Barker s method, i.e., minimizing the sum of squares of the residuals between the experimental values of P and the values predicted by this equation (see Ex. 12.1). Assume that the activity coefficients can be adequately represented by the Margules equation. 

Smith and Brown have recently completed an extensive study of alcohol -I-alkane mixtures in which Barker s method is compared directly with chemical association models. They conclude that the equations of Barker s theory are more satisfactory than those of Kretschmer and Wiebe with concentration equilibrium constants and those of Redlich and Kister with mole fraction equilibrium constants. However, even Barker s equations are inadequate for predicting accurate excess Gibbs energies and enthalpies. Sosnkowska-Kehiaian, Hryniewicz, and Kehiaian accounted for their measurements of enthalpies of mixing of alkanes and other hydrocarbons with n-alkyl ethers using a zeroth approximation formula with one temperature-independent energy parameter. 

Reverse pulse methods Application of pulse methods Alternating current and square-wave techniques Principles of alternating current polarography Basic relationships for the AC processes Improved ACP techniques Applications of AC polarography Tensammetry and detection of surface-active substances Square-wave polarography (Barker s method)... 

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