detected immediately after the equilibrium of the cell had been upset by the mass of solvent vapor. All the preliminary experiments to determine the operating conditions were carried out with argon carrier gas. These conditions included : operating voltage, sample size for linear response, solvent for each compound, and optimum column temperature. Two series of runs were made, each consuming a 50-liter cylinder of krypton. ‘The first included a variety of hydrocarbons and three sulfur compounds. The second included a wider range of hydrocarbon types. A run was made with the same compounds using a’rgon as the carrier gas. RESULTS AND DISCUSSION
The results for each series of runs are shown in Tables I and 11. The first two columns of data are the sensitivities for each compound with argon md krypton. They are a measure of the signal-to-noise ratio obtained for each compound at a fixed mass flow rate of 50 mol/sec. The third column is the argon/ krypton sensitivity ratio. Results in Table I show a distinctly poorer sensitivity for the n-paraffins in krypton compared with the other compounds. It appears fro n these data that a distinct break point occurs between compounds with ionization potentials above and below 10.0. Those below 10.0 ev are detected at the same magnitude as in argon. Those above 10.0ev show much less sensitivity in krypton compared to argon. The second series of results (Table 11) confirms this same break point at an ionization potential of about 10.0 ev. The data for methyl cyclohexane, trans-l,2-dimethylcyclohexane,
and 2,2,4-trimethylpentane indicate that the change in sensitivities is not abrupt since these compounds, which would be expected to have ionization potentials close to 10.0 ev. show intermediate sensitivities. Krypton in an argon triode gives a detector for gas chromatography that is selective for compounds having ionization potentials below about 10.0 ev. The krypton detector responds readily to simple aromatics, olefins, diolefins, mercaptans, and sulfides and is therefore a valuable tool for detecting and measuring small amounts of such materials in otherwise saturated samples. Examples are: odorants in natural gas and liquefied petroleum gas (LPG), aromatics in paraffinic solvents, and olefins and aromatics in waxes. It can also be used as a dual detector system for characterizing individual components. CHARLES D. PEARSON S. SILAS ROBERT Phillips Petroleum Co Research & Development Department Research Division Analysis Branch Bartlesville, Okla. RECEIVED for review October 27, 1966. Accepted January 30, 1967. Paper presented at the 1966 Pittsburgh Conference on Analytical Chemistry and Spectroscopy (paper No. 94), February 20-26,1966.
Re-Evaluationof ChronopotentiometricData for Adsorption of Riboflavin SIR: The calculations of Tatwawadi and Bard ( I ) for the extent of electroactive adso ption of riboflavin onto mercury electrodes are generally incorrect. The unweighted least-squares analysis employed by these authors is based on the fundamental assumptions that the values of the ordinate are free from error and that the values of the abscissa are associated with equal absolute errors. These conditions are not satisfied in the present case because bot i the ordinate and abscissa are functions of the same measured variables. It is a quite general conclusion that the parameters estimated according to a correctly rormulated least-squares analysis are insensitive to mathematical reformulations of the model (2) because mathematical reformulation alters not only the quantities plotted as ordinatc: and abscissa but it also alters the function which weights 1he data in just such a fashion that there is no net effect. Thus, the observation of Tatwawadi and Bard that mathematizal reformulation of their models led to apparently different values for the parameters D and nFr is a clear indication that their data analyses are in error. We can illustrate this point by considering the analysis according to the mathematically equivalent models 3 and 3*.
(1) S . V. Tatwawadi and A J. Bard, ANAL.CHEM.,36, 2 (1964). (2) W. E. Deming, “The Statistical Adjustment of Data,” Wiley, New York, 1943; RepLblished by Dover, New York, 1964, p. 156.
Model 3:
ir Model 3*: jr1/2
- nFr
- br1I2= 0
- nFr/r1/2 - b
= 0
n F r represents the extent of adsorption expressed as charge per cm2 and the symbol b denotes the chronopotentiometric constant, n F d s C / 2 . The other symbols have their usual electrochemical significance ( I ) . n F r and b may be estimated from the chronopotentiometric data by solving the following matrix equation (3-5). Model 3:
Model 3*:
(3) Zbid.,Chap. X . (4) W. C. Hamilton, “Statistics in Physical Science,” Chap. IV, Ronald Press, New York, 1964. ( 5 ) P. J. Lingane, ANAL.CHEM.,39, 485 (1967). VOL. 39, NO. 4, APRIL 1967
541
Table I. Leastaquare Analysis of Chronopotentiometric Adsorption Data. Reduction of Riboflavin in 0.5M NaHS04 Plus 1M NazSOl Present analysis
rx
Literature analysis ( I )
D X lo6
100
r x 100
D X lo6
moles/cm2
sr“
cm2/sec
sD4
x 2 / ( N - 3)o
moles/cm3
cm*/sec
0.96
0.13 0.04 0.03
0.55 0.70 0.84
0.05 0.03 0.08
0.81 0.35 1.72
0.72 0.53 0.43
0.63 0.71 0.85
0.55
0.05
0.43
0.13 0.04 0.03
0.70 0.84
0.03 0.08
0.81 0.35 1.72
1.09 0.65 0.55
0.52 0.63 0.38
0.61 0.36 0.34
0.47 0.16 0.14
0.39 0.49 0.47
0.07 0.05
1.45 0.78 3.15
0.2 0.2 0.2
0.6 0.7 0.9
0.58 0.38 0.31
0.11 0.04 0.03
0.54 0.64 0.74
0.06 0.04 0.10
1.05 0.54
0.43 0.33 0.31
0.62 0.69 0.79
0.59 0.38 0.32
0.11 0.04 0.03
0.54 0.64 0.73
0.06
1.10
0.04 0.10
0.55
0.69 0.42 0.41
0.49 0.59 0.46
Model 1 0 . 8 mF Riboflavin 0 . 4 mF 0.2 mF Model 1* 0.8 mF 0.4 mF 0.2 mF Model 2a 0.8 mF 0.4 mF 0 . 2 mF Model 3 0.8 mF 0.4 mF 0.2 m F Model 3* 0.8 mF 0.4 mF 0.2 mF
0.60
0.43 0.96 0.60
0.09
2.55
2.65
Calculated on the basis of ur2 = (r/lO)*,
The appropriate weighting functions are (5) Model 3:
Model 3* :
It was assumed in formulating these weighting functions that the values of the current density i are known much more precisely than the values of the transition time r and hence 0 (5). urj2 is the variance of the jth transition that ui2 time measurement. If we define
To convince the pragmatically inclined, the data of Tatwawadi and Bard were re-analyzed according to these models (5) and the results are presented in the accompanying table for comparison with the results of Tatwawadi and Bard. It is evident that the correctly calculated estimates of D and of r are insensitive to these reformulations of the models. Tatwawadi and Bard estimate values for D and r according to the “reacts last” model by determining a value forb according to model 1*, calculating a value of anFT for each value of (i, T ) , and finally averaging these results. Model 2a (reacts last):
N
el
= ijrb- nFr - br,1/2
it follows directly from the definition of these weighting functions that w5 = rjwj*
+ ej/rj(ij - b / 2 ~ j l ’+~ )qq2)
In the limit of low experimental errors, el -+ 0 and w, may be set equal to rjwj*. If w, = rjwj* is substituted into either of the above matrices, the pair of matrix solutions becomes identical. Thus, the same values are obtained for nFr or for b if the data are analyzed according to either of these models. An exactly similar analysis may be performed for the models 1 and 1*. In this case, the solutions for nFr or for b are identical and there is no need to invoke a limiting process.
- nFr
Model 1:
ir
Model 1*:
i2r
542
- b2/i = 0
- inFr
ANALYTICAL CHEMISTRY
- b2 = 0
This is an unnecessarily approximate approach, singularily unworthy of the powerful CDC 1604 computer upon which the calculations were preformed (1). The parameters were recalculated as described (5) and these results are also presented in Table I. It is clear that the method of calculation espoused by Tatwawadi and Bard is inaccurate.
PETER JAMESLINGANE’ Gates and Crellin Laboratories of Chemistry California Institute of Technology Pasadena, Calif.
RECEIVED for review August 4, 1966. Accepted December 19, 1966. Work supported in part by a predoctoral fellowship from the U. s. Public Health Service, Division of General Medical Sciences. Present address: Department of Chemistry, University of Minnesota, Minneapolis, Minn.
