ChemicaI
Kinetic Pa ra meters from Chro no pote ntiometric Potential-Time Measurements A. C. TESTA and W. H. REINMUTH Department o f Chemistry, Columbia University, New York 27,
b A method for calculation of rate constants of irreversible chemical reactions following reversible electrochemical reactions from chronopotentiometric potential-time curves is presented, and applied to the oxidation of p-aminophenol. Advantages of this method over one previously proposed by Snead and Remick are discussed. Semiquantitative calculations are given of the effect of variation of actual rate constants with distance from the electrode on apparent rate constants deduced with this experimental technique. The effect is concluded to b e negligible except when the thicknesses of the reaction layer and double layer are comparable in magnitude.
I
Snead and Remick (9) and the authors (IO) determined the formal pseudo first order rate constant for the hydrolysis of p-benzoquinone imine (PQI) under the same conditions by different electrochemical methods. Snead and Remick analyzed potential-time curves for the chronopotentiometric oxidation of p-aminophenol (PAP) and reported the value 0.020 second-I. The authors, by analyzing the ratios of transition times obtained b y chronopotentiometric oxidation of P A P followed by current reversal, obtained the value 0.140 second-1. They also pointed out a mathematical error in the treatment of Snead and Remick which raised the earlier value to 0.046 second-'. Revertheless, the disparity of the two values led naturally to a consideration of its cause. Study of this problem led to the conclusion that the discrepancy could be reduced by a different treatment of the data obtained in experiments of this type. It was thought that the effect of the electrical double layer on the chemical rate constant m-ould be more important in the potential-time technique, and that this factor might contribute to the discrepancy. However, semiquantitative theoretical calculations indicated it to be entirely negligible under the conditions of the experiment. Discussion of these tn-o points constitutes the substance of the present work. N TWO RECENT PAPERS,
1518
ANALYTICAL CHEMISTRY
N. Y.
ANALYSIS OF POTENTIAL-TIME CURVES FOR KINETIC PARAMETERS
The theory of the chronopotentiometric process which follows the scheme ne -
R
d
k
O
k
Y
(1)
was given originally by Rosebrugh and Miller (8) and later by Delahay and coworkers (3). The initial electrochemical reaction obeys the Nernst equation as signified by the double arrow, but it is followed by an irreversible chemical reaction of rate constant k. I n the present case, R, 0, and Y are p-aminophenol, p-benzoquinone imine, and p-benzoquinone, respectively. Hydrogen ions also enter the reaction scheme, but are present in large excess under the conditions of the experiment (9, 10) and can be assumed to remain at constant concentration. Assuming constant applied current, semi-infinite linear Fick's law diffusim, uniform initial concentration of R, zero initial concentration of 0 and Y , and the mechanistic scheme of Equation 1, the potential of the anode as a function of time is given b y
where E is the electrode potential; EO', the formal standard potential of the 0-R couple; t . the time from start of the experiment; T , the transition time, a t which the concentration of R a t the electrode surface becomes vanishingly small; erf is the error function; R, T,and F have their usual thermodynamic significance. Experimentally, all quantities except k and perhaps Eo' are measurable or known. Snead and Remick (9) define the quantity s s = E + - l RT n
nF
4; - 4; dt-
(3)
They plot this quantity as a function of v'f and from the slope of the resulting curve extrapolated to zero time determine the rate constant. This method, though theoretically sound, suffers from several practical disadvantages. First,
both of the terms on the right-hand side tend to infinity as t approaches zero and the error in s becomes correspondingly large. Second, E has its greatest error near time zero n-here the potential is changing rapidly and the fraction of the current devoted to nonfaradaic processes may be large. f plot still shows Third, the s us. d appreciable curvature a t the shortest times used by Snead and Remick and the uncertainty in extrapolated slope is thereby magnified. The curvature at short times also means that no weight is given to s values a t long times where the experimental errors are much smaller. An alternative method of treatment which avoids these difficulties is to construct a working curve of the function
f = In
4 7 erf (2) 22
(4)
z. On the same scale, but for convenience on a separate sheet of paper, plot nsF/RT os. log d?.Superimposition of the plots a n d , translation of the working curve to give best fit n-ith the experimental data lead directly to calculation of the rate constant. The value of the abscissa on the experimental curve corresponding to log z of zero on the working curve corresponds to kt of unity when the curves are superimposed, and from the known value of t , k can be computed. There are two degrees of freedom in the translation of the working curve to produce best fit, one along the ordinate and the other along the abscissa. One of these can be eliminated if the formal standard potential of the electrode reaction is known. The value of f asymptotically approaches zero as z approaches zero and this corresponds to a value of s of E"'. If E"' is not known, this provides a method for its determination. I n the present case, best fit with the data of Snead and Remick is obtained for an E"' of 0.471 volt os. S.C.E.This is the same as the value deduced by Snead and Remick from the same data and compares favorably ITith the value 0.470 volt determined potentiometrically by Fieser us. log
(4).
At large z corresponding to long times,
the \vorking curve approaches negative unit slope as the error function approaches unity. If the rate constant is sufficiently large, all accessible experimental points may correspond to this linear region of the curve. I n such a case, unique superimposition of the experimental and working curves ia impossible unless E O ' is known. In this situation only the quantity
0-
---.* '. \. 1
\
c a
2 ' m z
2 -
can be determined. With the data of h e a d and Remick, this difficulty does not arise. In Figure 1 the data of Snead and Remick arc plotted. The three lines correspond to theoretical curves for three different values of the rate constant. The top (dot-dash) curve corresponds to the value 0.046 second-' deduced by Snead and Remick from the same data. -4s might have been predicted from their method of treatment, the curve corresponds to the data much better a t short times than a t long. The central (solid) curve corresponds to "best" fit b y inspection and a value of 0.090 second-'. The lowest (dashed) curve corresponds to the value 0.140 second-' determined by Testa and Reinmuth (10) by independent means. Though the scatter of experimental points is unavoidably high in experiments of this sort, the difference between the best value from potentialtime measurements and that from the current-reversal technique still appears rather large to be explicable entirely in terms of experimental error. The potential-time technique, in contrast to the current-reversal technique, depends on the assumption of Yernstian behavior for the electrochemical couple. Appreciable overpotential-Le., quasi-reversibilitymight produce error in the calculated chemical rate constant. However, application of the current-reversal technique indicates the difference in potential for the oxidation and reduction processes was zero within experimental error when corrected for kinetic effects. Knobloch's polarographic results (6) for composite anodic and cathodic waves, though in different media, lead to the same conclusion. Adsorption of one or more of the species involved might again lead to spurious results. However, this factor too can be shown to he negligible from the constancy of chronopotentiometric id, plots for the oyidntion process and the analog for the reduction again corrected witahly for the kinetic complication (10). EFFECT O F CHANGE O F RATE CONSTANT NEAR ELECTRODE
A number of authors (1) have pointed
I
0.4
\
I
1
I
0.2
0.6
, IP
0.8
Lorn
Figure 1 . Variation of potential with time for chronopotentiometric oxidation of p-aminophenol
---
Experimental ( 9 ) Theoretical corresponding to different assumed values of rate constant (see text)
0
out that chemical rate constants determined electrochemically might differ from those obtained in homogeneous experiments because of the effect of the potential gradient in the electrical double layer on the activity coefficients of species therein. Jlatsuda ('7) and Gierst and Hurwitz (6) have considered the effect of the diffuse double layer on rate constants deduced from transition-time measurements. It might be expected that rate constants calculated from potential-time measurements would be more strongly influenced b y this factor than those from transition-time measurements. I n the former method the measured variable is directly dependent on instantaneous conditions a t the electrode surface, while in the latter the concentration profile, extending into the solution a distance large compared with the double layer thickness, is of importance. An approximation to the significance of this factor can be obtained as follows. The Fick's law equation for the oxidized form in the kinetic scheme of Equation 1 takes the form
with the boundary conditions
> 0, 5 -+
m
=> Co+
Col, = &/nF 6
(6)
0
(7)
D
(9)
A first approximation to the effect of variation of rate constant with distance on this quantity can be obtained b y assuming that a t distances from the electrode less than d the rate constant assumes one constant value kl while a t distances larger than d a second value k? obtains. The distance d can presumably be associated with the dimensions of the electrical double layer. The steady state form of Equation 5 can be solved under these conditions with the additional assumptions of continuity of concentration and flux a t x = a, The surface concentration takes the form COa =
t=O=>Co=O 1
this steady state corresponds in Equation 2 to arguments of the error function large enough that its value is unity and in Figure 1 to data on the right-hand side of the plot where the curve attains negative unit slope. Under these conditions Equation 5 can be set equal to zero. The steady state concentration of the oxidized form a t the electrode surface for a rate constant independent of x is
i0
nF d ./kl.D sinh (a 4 k T D ) cosh (a d/lC,TD)
+ l/kl/k2coeh (a d/kllD) + dkl/k2sinh (,adVD)
- 2 (8)
(10)
where the symbols have their usual conventional meaning ( 2 ) . Exact solution of the problem for the case of a rate constant k, which is a function of distance, appears a forbidding task. However, it should be noted that a t long times the concentration of the oxidized form approaches a steady state value dependent on x but independent of t . The attainment of
When the argument of the hyperbolic terms is large or when kl/kz is close to unity, the surface concentration is essentially determined by the surface rate constant, k,. On the other hand, when the argument of the hyperbolic terms is small, the bulk rate constant kz determines the surface concentration. I n any given experimental case, estimation of the ratio kJk5 requires knowledge of the exact mechanism of
t>O,s=O=>D
- =
nF
VOL. 32, N O . 1 1 , OCTOBER 1960
1519
reaction and of the double layer charxtcristics. I n the case of the oxidation of P I P , even with the overly gencrous estimates of 3 = 1000 -4. and k l / k z = 100 or 0.01, and using Testa and Reinniuth’s value for bulk rttte constant, 0.140 second-’, the effect n-ould be cntircly negligible. Thus, llatsuda’s conclusion (?) that double layer effects are of importance in transition-time measurements only when the double layer and reaction layer thick-
nesses are comparable in magnitude appears to be valid in the case of potential-time measurements as well. LITERATURE CITED
(1 j Breiter, XI., Kleinerman, M.,Delahay, P., J . A m . Chern. SOC.80, 5111 (1058). (2) Delahay, P., “ S e w Instrumental hlethods in Electrochemistry,’’ p. l i 9 ff, Interscience, New York, 1954.
(3) Delahay, P., hlattax, C. C., Berzins, T., J . Am. Chem. SOC.76, 5314 (1954).
( 4 ) Fieser, L., Zbid., 52, 4915 (1930). (5) Gierst, L., Hurwitz, H., 2. Elektrocheni. 64,36 (1960). ( 6 ) Knobloch, E., Collection Ctechoslov. Chem. Conimuns. 14,508 (1949). ( 7 ) hlatsuda, H., J . Phys. Chem. 64, 336 ilSGOi. ( 8 ) Rosebrugh, T. R., Miller, K. L., Ibid., 14, 816 (1910). ( 9 ) Snead, W.K., Remick, A. E., J . A m . Chem. SOC.79, 6121 (1957). (10) Testa, -1.C., Reinmuth. I\-. H., ‘ . 4 s a ~CHEM. . 32, ‘1512 (1960): RECEIVEDfor review June 5 ) 1960. Accepted August 15, 1960.
Quantitative Determination of Ethylene Epoxide, Propylene Epoxide, and Higher Molecular Weight Epoxides Using Dodecanethiol BENJAMIN J. GUDZINOWICZI Petrochemicals Department, National Research Carp., Cambridge, Mass.
,An original, rapid, and quantitative method for determining epoxides directly in aqueous and organic sohtions with dodecanethiol as reagent has been developed. The mercaptan approach i s novel as well as different from the other methods employed; this difference makes possible the direct determination of epoxides in mixtures to which the hydrochloric acid, periodic acid oxidation, or sulfite methods cannot b e applied. However, aldehydes in high weight per cent concentration (-50%) interfere with the accuracy of the method, which yields high values of the order of 0.5 to 8%.
A
of the literature reveals many rapid, precise, and accurate techniques for the determination of ethylene and propylene oxides in multicomponent aqueous and organic solutions. These are based on hydrochlorination ( B ) , ring scission by reaction with amines (6)) hydration of the a-epoxy group followed by periodic acid oxidation of the a-glycol formed (4), esterification with thiosulfate (g), and reaction with sodium sulfite (9). However, many methods are limited to the direct determination of epoxides in either aqueous or organic mixtures because of interfering reactive substances ( 9 ) . l I a n y suffer from limited Jolubility of the epoxide in the reagent solution or, in some instances, long reSURVEY
Present address, Special Projects DeResearch and Engineering Monsanto Chemical Co., Everett, Mass.
f%:zz.”,”’ 1520
ANALYTICAL CHEMISTRY
action periods to obtain quantitative data. This paper describes a rapid, quantitative method for determining epoxides directly with dodecanethiol. This procedure has also been satisfactorily extended to the analysis of higher molecular weight epoxides. The mercaptan approach is novel in that it is applicable to the direct analysis of epoxides in aqueous and organic mixtures to which the hydrochloric acid, periodic acid oxidation, or sulfite methods cannot be applied. Culvenor, Davies, and Heath ( 2 ) isolated the products from the reaction of isoamyl and n-butyl mercaptans with ethylene oxide in an alcoholic medium. This reaction was first adapted to the determination of ethylene and propylene epoxides with dodecanethiol using a procedure similar to that described by Beesing et al. ( 1 ) for the determination of a,p-unsaturated nitriles, aldehydes, esters, and ketones. The excess of dodecanethiol is conveniently measured by an iodometric titration. CH2-CH2 ‘0’
+ RSH
OH-
+
excess
CHt-CH2 I
RSH SR
1
OH
This mercaptan reaction has been widely applied in the production of nonionic surface-active agents from ethylene and propylene oxides ( 7 ) . EXPERIMENTAL
Reagents. Prepare alcoholic mercaptan solution (O.lAr), basic catalyst,
and standard iodine solution (0.liY) as described previously (1). Procedure. I n t o a 250-ml. iodine flask containing 40 ml. of 0.1N dodecanethiol solution, weigh or pipet a sample containing 2.0 t o 2.5 meq. of t h e reactive compound. After analyzing for acidity on another portion of t h e sample, add 3 ml. of alcoholic potassium hydroxide in excess of t h e amount necessary t o neutralize t h e total acidity in t h e test sample. Stopper the flask, swirl, and allow the mixture t o react for 20 minutes. At the end of this reaction period, add 10 ml. of glacial acetic acid and 100 ml. of 2-propanol. Titrate immediately with standard iodine to a faint yellow end point which will remain for 30 seconds. This is value A . Titrate several blanks of dodecanethiol (no potassium hydroxide added) to which 10 ml. of acetic acid and 100 ml. of 2DroDanol have been added. This is t i t 6 B. Run several blanks on dodecanethiol, along with the flasks Containing the samcles, th-oughout the entire- procedure, adding an amount of the alcoholic potassium hydroxide solution equal to that used in the sample flask. This solution will determine the extent of air oxidation of the mercaptan in the basic solution. After the required 20minute reaction interval, add the necessarv amounts of acetic acid and 2pro”pano1 and then titrate the mixture. This is value C. Calculations. Let N = normality of the iodine solution, and D the corrected milliliters of iodine required for the direct mercaptan blank corrected for air oxidation in t h e basic solution.
