The Chemical Educator, Reply to Comment 1 on DOI 10.1007/s00897010465a, © 2001 Springer-Verlag New York, Inc.

Vladimir M. Petruševski* and Metodija Z. Najdoski, Chem. Educator, 2001, 6(2), S1430-4171(01)02465-3 DOI 10.1007/s00897010465a. “Spontaneous ‘Distillation.’ Approaching Thermodynamic Equilibrium, A Marathon Experiment in Physical Chemistry.”

Vladimir M. Petruševski and Metodija Ž. Najdoski

Institute of Chemistry, Faculty of Natural Sciences and Mathematics, Sts. Cyril and Methodius University, Arhimedova 5, PO Box 162, 1000 Skopje, Republic of Macedonia, vladop@iunona.pmf.ukim.edu.mk

In his letter, Clark has few comments concerning the statistical treatment of the data obtained. We have to say that he is right saying, “…modern software can do this regression as easily as polynomial fitting”. We tried WinCurveFit (this program is available as shareware) and true, all values obtained are those listed by Clark. Of the above, the first 4 are practically identical to those calculated by us, using “the little trick” and given in the manuscript (i.e. the values for A₂, k₂, A₁, k₁). The only notable difference is in the R² value: 0.9983 in the manuscript and 0.9931 calculated by Clark. 0.9931 is obtained when all four quantities are allowed to vary (as in a true least-squares refinement). On the other hand, 0.9983 is obtained using “the little trick”, because in this way k₁ and k₂ are found after many trials and only A₁ and A₂ are computed. Needless to say that 0.9931 (the value given by Clark) is the correct one. We thank Clark for pointing to the software packages that can really efficiently do the job.

As to the addition of a third exponential term resulting in an almost perfect fit, we have some doubts about its true significance. Least squares by WinCurveFit give, after few attempts, the following values: A₁ = 0.6441; A₂ = 0.6985; A₃ = 0.6439; k₁ = 3.2900; k₂ = 0.0777; k₃ = 0.0113; R² = 0.9989. The fastest process (rate constant k₁) is due to crawling, while the slowest one (rate constant k₃) may be suspected to be due to some “new” mechanism. It can not be related to “the DT pump”, since the amplitude of this process (A₃) is comparable to the other two. Thus, in the first minutes of the experiment (when the process is practically isothermal), this mechanism appears to give an important contribution, which is certainly unfeasible for “the DT pump”. By the way, the asymptotic behavior of the “the DT pump” mechanism is probably better represented by 1/t, and not by exp(-kt) function. However, one should keep in mind that the addition of more vari­ables nearly always increases the R² value and thus the third exponential term may be a pure artifact, although the very existence of a third physical mechanism can not be ruled out a priori.

Finally, considering the last sentence of Clark’s letter, we are not sure about its exact meaning. In a lack of arguments offered for such an assertion, we can only assure him that the experiments were not done hastily.