Sept., 1961 I
salts is assumed. The partial pressure of oxygen \\-as niaiiitaiiied a t 0.5 atm. a t a total pressure of one
1
1
I
.z
16'49
NOTES
1
atmosphere. Reaction temperature is 480 f lo. The slope of the line representing the order of reaction with respect to nitrite was found to be essentially unity in agreement with the previously reported results of Freeman1 obtained by a differen t met hod. Figure 1 also shows a graph of the logarithm of the rate of reaction as a function of the log of oxygen Concentration a t 450'. The points are taken from experiments conducted under partial pressures of oxygen ranging from 0.25 to 1.00 atmosphere, and a i a given weight gain corresponding to a constant concentration of nitrite. The only variable is the partial pressure of oxygen. A linear plot is obtained. The order of reaction mas calculated to be unity, indicating that the rate-controlling reaction is between nitrite ion and molecular oxygen presumably a t the surface of the melt. It has been shown that varying the interface area1 between the gaseous environment and the molten salt affects the reaction rate. This is evidence in support of the previously published hypothesis concerning the reaction mechanism.
0.9
-? 3 -a bo
0.6
0.3
ELECTltOLYSIS WITH CONSTANT POTESTIAL : EFFECT O F DIFFUSION COEFFBCIEKTS ON REVERSIBLE Fig. l.--I'Iot of the logarithm of reaction rate as a function of Y : Y (o), logarithm of nitrite mole fraction X lo3 liEhCTIONS AT A SPHERICAL ELECTRODE 2 Y.
1.5
2.5
3
0.50 atm. partial pressure of oxygen and 480"; Y ( A ) , logarithm of partial pressure of oxygen a t 450' at 10% reaction. :tt
mole fraction of nitrite; [O,] = conceiitration of O2 on surface of melt; and [ O ] = concentration of atomic oxygen. Assuming a steady-state approximation for t'he rate of change of atomic oxygen then from equation 3.
I'[
=
k1[NOz-I rgzoz ka[O1 kz[NOz-l
+
(6)
Substituting for [0]in equation 4 .~ c)[N03-J
at
=
h[NOz-I [Ozl (1
+ k,[()]kz[NOn-l Az[Nm) +
(7)
If it is assumed that k3[0] is small compared to 12,. [SO,-] then -__ = k1'[NOz-] [Ozl (8) at
where ki'
=
2ki
The decomposition of sodium nitrate is neglected. It was determined experimentally that the rate of decomposition of the nitrate under the conditions of temperature and pressure used in these experiments was negligible compared to the rate of oxidation. If equation 8 is valid, plots of the log of the rate of reaction as a function of the log of the concentration of oxygen and of nitrite should give straigh.t lines with slopes of unity. Figure 1 shows the plot of the logarithm of the rate of reaction, as a function of t#helogarithm of the mole fraction of nitrite. Ideal behavior of these
BY IRVING SHAINAXD D A ~ I ES.L POLCYN Departmenl of Chemi drld L'niuerszty of Wzsconszn, illadason, Was. Keceaued March E7, 1961
Thc use of stationary sphprical electrodes in clec~rolysisexperiments a t constant potential has hem suggmted recctitly' as an unambiguous method of determining diffusion coefficients of elcctroaclive materials. The equation describing the current-time curves obtained a t potentials relatively far from the formal Eo contains two terms : one time-dependent term containing Do'I2 and a time-independent term containing Do. Thus, values of the diffusion coefficient can be obtained from both the slope and the intercept of the i u s . 1/43 plot, and the effect of various other experimental parameters can be evaluated unambiguously.* The same approach can be extended to potentials closer to the formal EO, and, with somewhat decreased accuracy, the method can be used to determine the diffusion coefficients of the product of the electrode reaction. For the case of a reversible reaction (in which both the reactant and product are soluble in the solution) taking place a t potentials near the formal Eo, the equation for the current-time curve has been reported as where the notation is that used previous1y.l This equation holds only when the diffusion coef(1) I. Shain a n d K. J. Martin, J. Phye. Chem., 66, 254 (1961). (2) See D. J. Macero e n d C. L. Rulfs, J. A m . Chem. Soc.. 81, 2942 (195S), for a discufision of t h e interactlon of these effects, particularly electrode area, on a plane electrode.
1650
Vol. 65
NOTES
35 * o 0
no 2 30-
.-
