Quartile potentials

It was shown later that a mass transfer rate sufficiently high to measure the rate constant of potassium transfer [reaction (10a)] under steady-state conditions can be obtained using nanometer-sized pipettes (r < 250 nm) [8a]. Assuming uniform accessibility of the ITIES, the standard rate constant (k°) and transfer coefficient (a) were found by fitting the experimental data to Eq. (7) (Fig. 8). (Alternatively, the kinetic parameters of the interfacial reaction can be evaluated by the three-point method, i.e., the half-wave potential, iii/2, and two quartile potentials, and ii3/4 [8a,27].) A number of voltam-mograms obtained at 5-250 nm pipettes yielded similar values of kinetic parameters, = 1.3 0.6 cm/s, and a = 0.4 0.1. Importantly, no apparent correlation was found between the measured rate constant and the pipette size. The mass transfer coefficient for a 10 nm-radius pipette is > 10 cm/s (assuming D = 10 cm /s). Thus the upper limit for the determinable heterogeneous rate constant is at least 50 cm/s. 

Writing Eq. (3.91) for p = 2, 4, and 4/3 (half-wave potential, Ein. quartile potential, 1/4, and three-quartile potential, 3/4, respectively), and combining these expressions yields... 

Alternatively, from the difference of two quartile potentials lfi3/4 - 1/4 , where 1/4 and - 3/4 are the potential values at which i and i = jh, respectively, one can find a using Tomes criterion ... 

The kinetic analysis in this case is rather straightforward. The transfer coefficient can be determined directly from the difference of two quartile potentials... 

The box plot has proved to be a popular graphical method for displaying and summarizing univariate data, to compare parallel batches of data, and to supplement more complex displays with univariate information. Its appeal is due to the simplicity of the graphical construction (based on quartiles) and the many features that it displays (location, spread, skewness, and potential outliers). Box plots are useful for summarizing distributions of treatment outcomes. A good example would be the comparison of the distribution of response to treatment at different dose levels or exposure (as measured by area under the plasma concentration-time curve) as in Figure 37.3. 

Number of Potential Outliers (0 to n) To count outliers in a distribution, we used the 1.5 x IQR [interquartile range the difference between the first quartile (Qi) and the third quartile (03)] criterion that is the basis of a rule of thumb in statistics for identifying suspected outliers (Moore and McCabe, 1999). An item of value d is considered as a suspected (mild) outlier if... 

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