A'OTES
Jan., 1960 1.o
li7
NON-ADDITIVE POLAROGRAPHIC WAVES I N THE ANODIC OXIDATION OF IODIDE
0.8
BY ALVINL. BEILBY'AND A. L. CRITTENDEN Department of Chemistry, University of Waehinoton, Seattle, Tashinoton Received Auurst 6 , 1969
al
20.4
w
Cases of failure of polarographic waves to be additive have been discussed by Miller and Orlemann2 and more recently by Anson and Lingane3 and g0.2 by A ~ e r b a c h . ~I n these cases, ope of the products of the electrode reaction diffuses from the electrode 0 and reacts with incoming reducible species to form 1000 2000 3000 4000 5000 a reducible species having a different diffusion coTemp., OK. efficient. Fig. 5.-The composition of dissociated water vapor from Kolthoff and Jordan6 have observed two waves 2000 to 5000°K.; total pressure 10 atm. in the anodic oxidation of iodide in chloride medium a t rotating platinum electrodes; the first corresponding to oxidation to iodine, the second to oxidation to iodine monochloride. The second step was found to be lower than the first step when .-b_ _._-_ the electrode was rotated but of equal height when the electrode was stationary. The explanation given was that iodine is formed very rapidly but - ~ _ - _- _ _ ~ that its subsequent oxidation to iodine chloride is slow enough to permit some iodine to escape from the electrode. A similar lowering of the second step was observed by Morgana at stationary electrodes. It appears that the lowering of the second -L ---+wave can be explained adequately, a t least for stationary electrodes, by the reaction of iodine chloride with incoming iodide to form slower-diffusing 1000 2000 3000 4000 6000 iodine. h numerical calculation of the magnitudes Temp., OK. of the two waves expected as a result of these ideas Fig. 6.-The total number of moles of gas (2)formed by the has been made. It has been assumed that, for the dissociation of water vapor. second step, both iodine and iodide are oxidized immediately to iodine monochloride a t the electrode and that the concentrations of iodine and GOO iodide are zero a t the electrode surface. It is assumed that the three species, together with chloride, are in equilibrium except a t the electrode sur500 face. The initial solution contains only iodide and chloride. It is further assumed that the concen400 tration of chloride is sufficiently large that its concentration may be regarded as constant through300 out. Linear diffusion is assumed.
' 7 r=
200 100
0 1000
Fig. 7.-The
3000 4000 5000 Temp., O K . enthapy of dissociated water vapor.
2000
various temperatures are also availahle.3-s The results of the enthalpy calculations are shown in Fig. 7 in which values of H/RTo ( R = gas constant, TO= 273.16"K.) are plotted as a function of temperature for various pressures. Values of H/RTo for constant values of 2 are also indicated. ( 5 ) F. D. Rossini, et al., ref. 4. Circ. 500,1952. (ti) J. Hilaenrath, et a l . , ref. 4, Circ. 564, 1955.
Experimental The electrical charge transferred during a fixed period of electrolysis from a fixed time ( h ) after application of cell potential to a second fixed time ( t t ) a t constant potential was measured using previously described equipment .7 The microelectrode was in the form of a square plate forged on the end of a platinum wire and sealed into the end of a vertically-mounted glass tube. Such an electrode should be more nearly planar than a cylindrical wire. Also it has been shown that diffusion to cylindrical electrodes is essentially linear under the conditions used .7 Measurements were made at 25.0'. ( 1 ) Based on the Ph.D. thesis of Alvin L. Beilby, 1958. Standard Oil Company of California Fellow. 1057-1958. (2) 8. L. Miller and E. F. Orlemann, J . A m . Chem. Soc., 7 6 , 2001
(1953). (3) F. C. Anaon and J. J. Lingane, ibid., 19, 1015 (1957). (4) C. Auerbach, Anal. Chem., SO, 1723 (1958). (5) I. M. Kolthoff and J. Jordan, J. A m . Chem. Soc., 76, 1571 (1953). (6) E. Morgan, Thesis, University of Washington. 1956. (7) G. L. Booman, E. Morgan and A. L. Crittenden, J. Am. Chem. SOC.,18, 6533 (1956).
1'78
Vol. 64
NOTES
points corresponding to a particular time, the area is computed by the summation m
C0
Area B = h [ * / L ' g ( O , t j
\-
+ i = l CB(ih,t ) ] = h z B
(5)
Since neither the time or volume increments, h and = Dck/h2, a t constant time ( t = n k )
k, need be specified, but only the ratio r
z
Area B = (Dct/m)1/2Z:8
0
where n is the number of rows computed. The constancy of the quantity ZB/nl/z with increasing n serves as a test for the convergence of the computations, similar tests being used for the other species. I n addition, conservation of mass requires that the ratio Z A / ~ B 2Zc be unity. The total charge transferred should be proportional to area B plus area C, or to area -4 minus area C. If no reaction between iodide and iodine chloride were to occur, t'he charge could be calculated by'
Ia
a c
z W 0
(6 )
+
z
0
0
Q
0
Dl STAN C E
Fig. 1.-Concentration gradients near the electrode surface: solid lines, oxidation of iodide in hydrochloric acid, K' = dashed lines, oxidation of iodide in sulfuric acid, K' = 1.4. Both scales are arbitrary.
Numerical Calculations.-The diffusion processes can be described by the equations
acC
- =
at
DC S c - R(x, t j
ax
=
(7)
2nFACO(Dt/rj1/z
or by numerical methods similar to but simpler than that used for the case with reaction. Results of such calculations are shown as checks in the first two rows of Table I. I n both the simple case, and the case with reaction, the areas for iodine chloride, B, converged less rapidly than did the other areas, thus it is advisable to take the charge as proportional to area A minus area C. TABLE I RATIOSOF AREASFOR VARIOUSVALUESOF K' "A
-
ZC
K'
ZA(no.rx.)
S o reaction (numerical) No reaction (analyticalj 1 x 103 1 x 102 1 x 10' 1
...
...
1.003 1.001 0.993 ,958 ,914 ,891
"A
ZB
+ 2zC
0.072 1 0.924 .918 ,015 .935
,948 1 x 10-1 where the subscripts A , B and C refer to iodide, 1 x 10-2 ,953 iodine chloride and iodine, respectively, and R(z,t) 1 x 10-3 ,887 ,948 represents change in the quantity of material in the volume increment because of chemical equi- DA = 2 X 10-6, DB = 1 X 10-5,Dc: = 1 X 10-5 , nk = 25k, r = 0,100 librium. At the electrode surface Results and Discussion I n all calculations made, t.he initial concentraThe equilibrium can he written: K = CACB/CCCD tion of iodide (Co) was taken as unity. The value of or K' = K(CD) where CD is the concentration of K' must be calculated with CD expressed in such chloride (assumed to be constant). The initial units as to make C2 unity. Therefore, to the exconditions are CA(Z,O) = Co, CB(Z,O)= 0 , Cc(x,O) tent that results vary with K', linearity between bulk concentration and wave height is not to be = 0. LilSo CA(0,t) = 0, Cc(O,t) = 0. A finite difference method8 has been applied to expected. Table I shows results computedg for various valobtain solutions for the above equations using an International Business Machine%Type 650 digital ues of K'. Deviations from unity of data in column computer. Three networks of values of the three three may be taken as measures of the convergence concentrations a t various times (nk)and distances of the calculations. The principal discrepancy (mh) are obtained. Concentration gradients for arises from slow convergence of the area B. Colthe three species computed for two values of K' are umn 2 gives the ratio of charge transferred with shown in Fig. 1. The quantity of iodine chloride reaction to the charge expected if no interaction (9) Computations in Tables I and 111 were carried out only t o a produced may be computed from the area under its curve. At the end of calculation of each row of few iterations in order t o demonstrate the effects involved. Com(8)
W. E. X l n e , "Numerical Solution of Differential Equations,"
John Wilrv and Sons, Inc., New York, N. Y., 1953, Chap. 8.
putations for cases investigated experimentally were carried out to a sufficient number of iterations to obtain convergence t o three significant figures. usually about seventy rows (nk = 70) being required.
NOTES
Jan., 1960 were to occur. It is seen that the magnitude of K’ affects the results only in a limited range. At values of lo2or greater results are essentially the same as without reaction. With values of K’ less than about little change occurs; the reaction between iodide and iodine chloride can be considered to go to completion. The effect of various values of diffusion coefficients can be seen for the case of complete reaction in Table 11. Although the diffusion coefficients D A and D c affect results significantly, little effect is found by changing D g . It is interesting to note that if the values of D A and Dc are the same, the charge transferred is the same as that expected in the absence of reaction. The same result may be obtained by adding equations l and 3 and making the substitution CY = CA Cc. Also, the charge transferred is proportional to the flux of species A plus the flux of species C a t the electrode surface. Thus, the same equations and boundary values are obtained as those applying to the simple case without reaction, and the charge transferred is the same. If the diffusion coefficient of the iodine formed by reaction is greater than that of the incoming iodide, a higher than normal charge is to be expected, and vice versa.
+
TABLE I1 EFFECTOF D I F F U ~ I OCOEFFICIENTS N o s W AE~HEIGHT Z A - ZC DA
x
105
DB
1 1 0 5 0 5 2 2 3 2
x
105
1 1 1
2 1 2 1
0 5
K’
= 1x
DC X
105
0 5 1 1 1 3 1 1
1 nk = 35X-
ZA (no.rx)
0 885 1 000 1 143 1 138 1 000 0 885 887 889
Oxidation of Iodide in Hydrochloric Acid.-The oxidation of iodide was studied in 0.25 M hydrochloric acid solution. For a bulk concentration of iodide of 0.001 M , the equilibrium constant K‘ was taken as 1.9 X lo+, based on the data of Latimer,loa value small enough to allow the reaction to be considered to go to completion. The diffusion coefficient of iodide was taken as 1.99 X l o + cm.2 set.-' for reasons discussed below. The diffusion coeficient of iodine chloride is uncertain but was taken as equal to that of iodine, for which a value of 1.11 X 10+ cm.2 set.-' was taken.6 Using these values, the ratio of charge transferred with reaction to charge expected in absence of reaction was computed to be 0.899. The two wave heights were measured a t +0.60 and +0.85 volt versus S.C.E., correcting for small residual charges. Without reaction, the second wave should be twice the height of the first. I n Table I11 are shown values of the ratio of total height of the second wave to twice the height of the first. The results agree well with the calculated value, indicating that the interaction of iodide and iodine chloride is sufficient to explain the lowering of the second wave. The Interaction of Iodide and Iodine.-The (IO) W. M. Latimer, “Oxidation Potentials,” 2nd Ed., PrenticeHall Ino., New York, N. Y . , 1952, pp. 54, 63.
179
TABLEI11 OXIDATIOX OF IODIDE IS HYDROCHLORIC ACID Electrolysis time - t z (see.)
Concn., mmoles
Height-2nd wave 2 X height 1st wave
0.5-0.6 3.0-2.4 4 0-4.8 0.1-0.2 1.0-1.2 4.0-4.8 0.5-0.6 2.0-2.4 4.0-4.8
0.500
0.899
tl
.so0 .so0 1,000 1,000 1.000 1,500 1.500 1 ,500
.899
,889 ,893 ,890 ,888 .881 ,880 890
height of t’he wave observed in the oxidation of iodide to iodine should be affected in a manner similar to the case described above through t,he format’ion of triiodide ion from iodine liberated a t the electrode surface. The equilibrium constant K’ has a value of 1.4 for millimolar iodide solutions,“ t’hus the effect should be much smaller t,han that due to iodine chloride. The ratio of charge with reaction to charge without reaction was computed to be 0.983 for millimolar iodide solutions and should be slightly different for different iodide concentrations. The experimental verification of this ratio is difficult. However, the wave height for the oxidation of iodide to iodine in 0.125 M sulfuric acid was found to be slightly lower than the first wave in 0.25 N hydrochloric acid. I n sulfuric acid, triiodide is presuma,bly formed; but in hydrochloric acid, complexing of iodine with chloride probably occurs a t the concentrations used. The ratio of the charges in the two acids varied from 0.977 to 0.990, with a mean value of 0.987. The difference appears to be greater than that due to viscosity alone. Diffusion coefficients for iodide in various concentrations of sulfuric acid were calculated from diffusion charges using equation 7. If interaction between iodide and iodine is not considered, the value of the diffusion coefficient of iodide obtained by extrapolation to infinite dilution is too low. However, if the factor for interaction is applied, the value of 2.05 X sec.-l previously reported fur infinite dilutionI2 is obtained. The diffusion coefficient for iodide in 0.125 M sulfuric acid solution which would be observed if no interaction occurred was calculated to be 1.99 X cm.2 sec.-’. The same result was obtained for iodide in 0.25 114 hydrochloric acid solution by application of equation 7 to the first wave in the oxidation of iodide. (1I ) J. J. Lingano, “Electroanalytical Chemistry.” Interscience l’ublishers, Inc., New York, N. Y., 1953, p. 116. (12) 11. 8. Harned and B. B. Owen, “The Physical Chemisty for Electrolytic Solutions,” 2nd Ed., Reinhold Publ. Corji., New York, h-, Y., 1950, p . 172.
PERCHLORATE FORMATIOX COXSTAKTS FOR SOME WEAK BASES IS ACETIC ACID BYTAKERU HIGUCHIAND KENNETH A. CONXORS ContrPbutzon from the School of Pharmacy. Unzversafy of Wzsconsin, Madzson, Wzsconszn Recelved August 6, 1969
The relative basicity of a compound B in a given solvent is conveniently measured by the extent of
