3846
JOSEPH JORDAN,
R. A.
JAVICK AND
TABLE I11 COMPARISON OF POTENTIOMETRIC AND VAPOR PRESSURE ~ < E S T L T SFOK
HC1 I N 50.00 WT. % DIOXANE-IVAIEK, 95.00’
712
13 50 ?C 0 3 0 0470 -0 00303 13 50 Zk . : 3 0 1230 - 0 0074j _-_ - 1000 lu e,/oz.------7
0 02467 Ii 05060
Potentiom.
m
0.02467 f~.05060
Mass ratio
7.58i.0.3 1 4 . 1 1 =k . 3
Vapor comp.
7.43f00.3 14.36f .3
7.52i0.11 15 5 6 z k . 5
the mass ratio and of the vapor composition. The mean deviation of the two sets of values was less than 0.0004, and average values are listed in Table IV. The calculation requires prior knowledge of y+ as a function of m, but the results are very insensitive to the exact function chosen, as illus.. trated for two plausible functions in Table IV. FOR
TABLE IV KaOH it1 50.00 WT. yo DIOXANE-TVATER AT 25.00“ y t from limiting law
m
In aduz
B*
0 00000
. . .. . . .
- 29.63‘3’
,01189
,02415 ,03910 ,0523
-0.00985 - ,01840 ,02922 ,03815
-
Av. a
“b
yi same a s for NaCl
In .
-30.70 -29.78 -30.40 -30.70
- 29, GgnzC
-0
00987
-
,01846
-
02935 ,03835 Av.
-
-30.4
B*
uda2
.,....
-30.76 -29,84 -30.51 -30.82 -30.5
UB’d ,,
0.Y ,3 .3
.2
Computed by weighted least squares via equation 5 . -20.46. b = -21.65, Standard deviatioii.
=
The calculation of O H - was based on the power series expansion, equation 20 of the preceding paper,2which was used in the form p*
(1000
L -
- 2i.,i9ntt/2
111 ol,/az)/M,~m
=
+ +
. . . (5) P brn A t low molalities, 0” should vary linearly with m.
[CONTRIBUTION FROM THE
DEPARTMENT OF
W. E. RANZ
Vol. 80
For the data in Table XV, there is a slight but statistically insignificant drift in /?* with increasing m. The most probable value for /3 is -29.7, obtained by least-squares fitting of the data to equation 5. The most probable value for 6, -21, is nearly equal to the corresponding quantity for NaC1.2 On the other hand the data do not preclude the possibility that b = 0, in which case the limiting law is valid and /3 = -30.4. In any case, it is unlikely that the correct value of &at, 0 ~ % differs from -29 7 by more than f 1.0. d In Kw/dZ1.-It follows from the definitions of the autoprotolysis constant Kn and of /3 that d 111 RwldZi = PH+. o x ?H+.CI- T Pwa-,
oIi- -
c1-
&-a+,
(9)
Upon substitution of numerical values for HCl, NaOH and NaC1,2 d In KrV/dZ1 is predicted from vapor pressure data to be -19.8 rt 1. On the other hand, from potentiometric data for In K, (converted to the mole fraction scale),’ the corresponding value is -22.3 & 0.3. The discrepancy between the two values is significant and points to determinate error in a t least one of the two sets of measurements. In view of experimental difficulties described by Harned and Fallon,’ we believe that the determinate error may have occurred in the potentiometric measurements. The experimental difficulty was that the Ag-AgC1 electrode did not function reversibly in the alkaline solutions which one has to employ in the measurement of K w a t the higher dioxane concentrations except in the presence of a large excess of sodium chlori~le.~Although Harned and Fallon took pains to minimize this error, the fact that the vapor pressure data are not subject to difficulties of this sort would t cntl to make them seem more re1i:ihle. TALLAHASSEE. FLORIDA
CHEMISTRY OF
THEPENNSYLVANIA
STATE USIVDRSITY
]
Hydrodynamic Voltammetry at Solid Indicator Electrodes’ BY JOSEPH
JORDAN,
R. A.
JAVICK A N D
W. E. I < A N Z ~
RECEIVED NOVEMBER 20, 1957
A circulatory electrolysis cell assembly has been devised with controlled hydrodynamic characteristics, for the study a t stationary solid indicator electrodes of current-voltage curves in flowing solutions. -4 new microconical platinum electrode is described and’the relevant theoretical limiting current equation is derived. In a range of flow velocities between 25 and 500 cm./sec., oxygen, ferricyanide and aquo-ferric ion at the conical platinum microelectrode yielded sigmoid currentvoltage waves with well-defined limiting currents. Implications are discussed to quantitative voltammetric analysis in flowing media. Oscilloscopic evidence is presented that the random fluctuations of the limiting currents, normally nbserved at the rotated platinum wire electrode, are due to turbulence. A constant limiting current, free of transient fluctuations, was obtained in a purely laminar gravitational flow using a “wall-less” electrolysis cell. The conical platinum microelectrode under suitable experimental conditions approximates the behavior of an electroanalytical tl ~wrneter. Selected applications are considered as examples of a n unorthodox approach to the measurement by- electrocheini-~1kinetics of rates of physical phenomena.
A time period of more than one and a half decades The behavior of the RPWE is intermediate behas now elapsed since the invention of voltammetry tween that of a “convection electrode” and a “difa t the rotated platinum wire electrode (RPWE).3 fusion electrode ” 4 5 Mass transfer by diffusion and forced convection both are controlling factors (1) Abstracted from a doctoral thesis b y Richard A. Javick. Preof the limiting currents which depend on diffusion sented a t t h e E i g h t h P i t t s b u r g h Conference of Analytical Chemistry and Applied Spectroscopy, March, 1957. coefficients as well as on the prevailing hydrody( 2 ) Department of Engineering Research of T h e Pennsylvania S t a t e University. (3) H. A . Laitinen a n d I . M. Kolthoff, J . P h y s . Chein , 4 6 , 1070 (1941).
(4) J Jordan A I I O !C h v z
(5) I f19i4)
‘rl
IColthoR
and
27, 1708 ( 1 9 i i ) J rirrdan r~
r sTOIIRNAI
76,
38-17
Aug. 5 , 1058
HYDRODYNAMIC VOLTAMMETRY AT SOLID INDICATOR ELECTRODES
3847
namic conditions. The literature reveals numerous of turbulence. A measurement of this type (of attempts to correlate quantitatively a t the RPWE physical phenomena with the aid of electrochemical limiting currents and hydrodynamic parametersU6 kinetics) is believed to be of considerable methodoAs far as the dependence is concerned of limiting logical interest. It represents the reversal of the currents on rates of rotation of the RPWE, con- customary approach in chemical kinetics, where sistent results are conspicuous by their absence.’ reaction rates are normally determined by measureIt appears impossible to interpret the available ment of the rate of physical changes, such as volexperimental data in terms of applicable theoretical ume, pressure, etc. hydrodynamic relationships. This situation may Experimental be accounted for as follows. Chemicals.-Reagent grade chemicals and conductivity a. Because of effects such as “slipping” and fric- water were used throughout. tional l o ~ s e sthe , ~ rate of rotation of the RPWE does Apparatus. Circulatory Electrolysis Cell Assemb1y.not represent a true measure of the rate of flow of The complete set-up is illustrated in Fig. 1. I t s main comthe solution relative to the indicator electrode, ponents were a flow tube, an impeller pump and a thermowhich determines the convective mass transfer of the electroactive species and controls the limiting current. Consequently, the rate of rotation is not a significant parameter under the hydrodynamic conditions prevailing in the conventional electrolysis cells used in conjunction with the RPWE.8 b. Quite generally, the experimental situation a t solid electrodes in stirred electrolysis cells is so complex, that the theoretical interpretation of the corresponding mass transfer process meets with insurmountable difficulties.6 It was anticipated that the impasse might be broken by constructing on the basis of judicious fundamental considerations, a suitable model “solid indicator electrode system” which meets the following requirements. 1. I t should approximate geometric and hydrodynamic conditions for which a rigorous mass transfer equation is available. Fig. 1.-Circulatory electrolysis cell assembly. 2. The velocity of flow past the indicator electrode should be readily controlled, varied and measured. stating compartment. The flow tube was made of Pyres 3. In terms of indicator electrode area, cell resist- tubing, 10 cm. in diameter and 45 cm. in length, which was ance, temperature control, order of magnitude of mounted vertically on suitable supports. Both ends of the limiting currents, concentration of supporting elec- tube were constricted to nozzles about 1 cm. in diameter. trolytes and of electroactive species, i t should be An additional piece of Pyrex tubing, 10 cm. in diameter and 15 cm. in length, was ring-sealed t o the upper end of the comparable to “typical polarographic experimental flow tube and its top extremity was in turn constricted t o a conditions” under which proportionality between nozzle of 1 cm. in diameter. T h e ring-sealed portion of the limiting current and concentration is normally ex- flow tube, located between the two nozzles pointing upwards, pected to prevail. A circulatory electrolysis cell was used as the “electrode compartment.” Suitable holes bored into its sides for accommodating the indicator assembly has been constructed accordingly and is were electrode, the reference electrode and two pressure probe described in this paper. In this cell, the solution tubes. I n conjunction with a suitable manometer the presflowed past a conical platinum microelectrode under sure tubes served to determine the rate of flow of the solution conditions of negligible turbulence intensity (
