Kinetics as Spectrometry Sir: The units of a first-order rate constant, sec-’ or Hz, suggest the following analogy. Let v = l / t , where v is frequency (Hz) and t is time of reaction (sec). Then we postulate a function f ( v ) such that a peak or band is observed in the plot of f ( v ) vs. v. The maximum in this curve would be determined by a function of the rate constant k , the “resonance frequency” of the system. The band width is established by the Heisenberg uncertainty principle, which can be stated (6E)(6t)2 h ; since 6E = hsu, this becomes 6u 2 1/6t, where bt can be interpreted as the lifetime of the state, and replaced by l l h . Thus bu 2 k ; a faster reaction will be associated with a greater bandwidth 6v. Consider the reaction A Z with first-order or pseudofirst-order rate constant k . Then CA = CAO exp(-klv). An appropriate function meeting the conditions outlined above is dCAldv, Equation 1.
-
5 35-
coc
0 305
sc5
vim,
Flgure 1. Kinetic spectrum for the reaction of pnitrophenyl benzoate with hydroxylamine at pH 7.70 and 25 OC; absorbance measured at 400 nm
This can also be expressed in terms of the product concentration, since dCAldv = -dCz/du. The maximum in this curve is found by differentiation:
Combining Equations 1 and 2 gives the value of dCAldv a t the maximum:
or 0.541 C A O l k . Figure 1 shows the kinetic spectrum for the release of p nitrophenol upon reaction of p-nitrophenyl benzoate with hydroxylamine. The points were calculated from a plot of absorbance, A , against v, using a frequency interval of 5 X lo-* Hz. The smooth curve was calculated with Equation 1 (expressed for the product in absorbance units) and the values A , = 0.650 and k = 5.5 X Hz. If two reactants A and B react to give the common product Z, then -dCz/du is an additive function of two terms like that in Equation 1. The ratio of maximum peak heights from the two contributing terms (AIB) is, from Equation 3, k B C A o / k A C B o . Figure 2 is a kinetic spectrum for the hydrolysis of a mixture of p -nitrophenyl p-chlorobenzoate and p-nitrophenyl p-nitrobenzoate. Resolution of the two reactions is clearly achieved, and the relative rate estimated from the locations of the maxima, 13.6, is close to the reported value of 14.3 ( I ) . The band widths a t one-half of the maximum values are about equal to the corresponding rate constants. The ratio of chloro to nitro ester found from the peak maxima is 0.18 (uncorrected for contributions from each other); the ratio taken was 0.14. An unusual feature of the method is its capability for resolving mixtures whose faster reacting component is present in excess. The analytical potential of this approach lies in the similarity in appearance and properties of the kinetic spectrum and other spectra. Reactant concentrations can be estimated from peak heights or areas. Multicomponent mixtures might be analyzed, just as in absorption spectroscopy, by establishing systems of simultaneous equations; the optimum frequencies for the measurements can be determined by inspection of the kinetic spectra of the individual reactants. Complete line shape analysis also could be used. Manual processing of the data is laborious and could be re2066
I b
0.01
0.02
0.03
V (Hz) Figure 2. Kinetic spectrum for the hydrolysis of pnitrophenyl pchlorobenzoate (0.54 X 10-5M)and pnitrophenyl pnitrobenzoate (3.77 X lO@M) at pH 12.08 and 25 OC in acetonitrile-water medium prepared as described by Washkuhn et ai. (7); absorbance measured at 400 nm
placed by instrumental or computer processing; it may be feasible to record kinetic spectra directly. The resolution of the method is limited ultimately by the lifetime broadening effect. Although the absolute band widths are very small (in Hz), the frequency range swept in most kinetic studies is also small; Figure 2 is a typical result. The appearance of the display, though not the actual resolution, is altered by plotting on a log v scale. The spectrum can also be displayed as a plot of dCA/dv vs. time of reaction (corresponding to “wavelength”). The basic weakness of this analogy between kinetics and spectroscopy is the apparent lack of a causal relationship between the observed energy state changes and the “irradiating” frequency. The approach nevertheless seems worth exploring for its potential in the analysis of mixtures and for studying complex reactions. This viewpoint also provides a different interpretation of the nature of time and time-dependent phenomena in chemical systems.
ANALYTICAL CHEMISTRY, VOL. 47, NO. 12, OCTOBER 1975
LITERATURE CITED (1) R . J. Washkuhn, V. K . Patel, and J. R . Robinson, J. Pharm. Sei, 60, 736 (1971).
Kenneth A. Connors
School of Pharmacy University of Wisconsin Madison, Wis. 53706 RECEIVEDfor review April 30, 1975. Accepted June 25, 1975.
Auto matic Gas- Meas uring Device:
Exchange of Comments
Sir: There are serious limitations and errors in the automatic gas-measuring device proposed by Galblcs and Cslnyi ( 1 ) . Independently from other factors related to the very strict requirements for the construction of the apparatus, I want to make clear the following points. A) Times are referred to the distance between two signals (peaks of different heights) on the paper of a chart recorder (chart speed 25 cm/min). This may be the most serious source of error, in case 1 of Figure 1 of Ref. 1, the rate of gas feed is 15.81 ml/min, and since the volume between the electrodes is 0.118 ml, the time required corresponds to a distance between signals of 0.19 cm (with the given chart speed). This would represent in the case of an individual measurement, as it should be in the case of a time dependent rate of gas in a reaction, an error of about 0.5 mm, that is, 25% error. T o guarantee an error lower than 5%, the application of the device would be limited to gas rates no larger than 3 ml/min. That is to say, the device is not applicable to relatively fast reactions as the authors state. B) With the proposed device, the reaction under study could be followed up only to the point when 10 ml of gas have been produced or consumed, corresponding to only 80 signals. This limitation makes it necessary to use very small quantities of reactants and even smaller quantities of catalyst. For the study of hydrogen peroxide decomposition, shown in Figure 3, Ref. 1, the amount of H202 used is less than 0.03 gram. Such a small quantity must be handled in so!ution, and, therefore, the device does not allow the study of reactions with pure reactants. I am now studying a technique to measure and record the curves directly (rate of gas/time) which is applicable t o gas rates even larger than 50 ml/min for an unlimited time. T h e characteristics of this system will be published soon.
rates greater than 3 ml/min if a chart speed of 25 cm/min is chosen. (c) The device is suitable for measurement of not more than 10 ml of gas. We should like to make the following points. In our paper ( I ) , an automatic gas-measuring device was proposed, to follow reactions taking place with gas evolution or uptake on a (most usual) semimicro scale. We drew attention to the fact that the frictional force is proportional to the gas rate, which may result in limitations to this measuring principle a t high rates of gas (considerably in excess of 15 ml/min), when the liquid plunger (mercury) starts to disintegrate into smaller drops. On the other hand, reference was made in our paper to the possibility of extension of the range of the device, both t o greater volumes and to higher gas rates. For these purposes, five factors were mentioned: “The sensitivity of the device can be varied by selection of the diameter of the measuring tube and the distance of the electrode pairs, while the total volume to be determined can be varied by the length of the PVC tube. The range of reaction rate which can be determined automatically depends in practice on the chart speed and the response time of the recording potentiometer”. The remarks of Pascual show that the cited paragraph escaped his attention completely, as he took only one of the five factors (the recorder speed) into consideration. We may further mention that during the past year we have made efforts to enhance the sensitivity of our device in two respects (a) by increasing the number of sensor electrode pairs from 4 to 12, and (b) by integration (counting) of signals electronically and recording the number of signals vs. time curve directly. We have succeeded in enhancing the time resolution by another means: by recording the electric impulses of the Oscillotitrator on a tape recorder a t a comparatively high rate, and then playing back a t a reduced speed to evaluate the time-coordinate. T o close, we should say that it is quite usual that an instrument cannot be used over very extended ranges. This is true in the present case too. Consequently, we look forward with great interest to the new measuring principle of Pascual which will make possible the measurement of gas evolution on the macro scale.
LITERATURE CITED (1) M. 2 . GalbAcs and L. J. Csanyi, Anal. Cbem.,45, 1784 (1973).
V. L6pez Pascual Universidad de Cara!obo Facultad de Ingenieria Valencia, Venezuela
LITERATURE CITED RECEIVEDfor review March 31, 1975. Accepted June 9, 1975.
Sir: V. Ldpez Pascual suggests three shortcomings of the gas-measuring device proposed by us: (a) He found it too complicated and difficult to construct. (b) In his opinion, the time-coordinate is seriously in error a t gas evolution
(1) M. 2 . Galbbcs and L. J. Csanyi. Anal. Cbem., 45, 1784 (1973).
M. Z. Galblcs L. J. Cslnyi Department of Inorganic and Analytical Chemistry A. J6zsef University 6720 Szeged, Hungary RECEIVEDfor review May 5 , 1975. Accepted June 9, 1975.
ANALYTICAL CHEMISTRY, VOL. 47, NO. 12, OCTOBER 1975
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