REACTION BETWEES SILVER AND SULFUR I N OIL
1281
ble parameter. In the reduced pressure range 0.05 to 0.30 it is by far the most successful general treatment, and permits calculation of the monolayer adsorption and therefore the area of the adsorbent, with the limitation that the area per molecule in a monolayer of a given adsorbate may vary 20 per cent or more on different adsorbents. The extensive data of Hansen, Fu, and Bartell ( 2 ) indicate that these remarks apply as well to adsorption from solution as to vapor adsorption. The authors caution that the monolayer adsorption ( Z / V Z ) ~may contain solvent as well as solute. Yet this limitation seems no more serious than the variable concentration of the monolayer found in vapor adsorption, especially if the solute is one that appreciably reduces the interfacial tension. The condensed-film hypothesis, while semiempirical in nature, directs attention to the two-dimensional film characteristics and permits a test of the data for a condensed film by application of equation 5 . The present results indicate that its general applicability, especially in the range of higher film concentrations, holds also for adsorption from solution. Once the ratio Z/A1'*for a given adsorbate is determined, the slope A of a linear plot of equation 5 gives the surface area of the adsorbent just as reliably as application of the B.E.T. theory. The two treatments supplement each other nicely and help to correlate the behavior of adsorbed films at equilibrium whether in the form of insoluble monolayers on water, of vapor films on solids, or of films adsorbed from solution. REFERENCES (1) BRCNAUER, S., EMMETT, P . H . , A N D TELLER,E.: J. Am. Chem. SOC.80,309 (1938). (2) HANSES,R . S., Fu,YIKG,ASD BARTELL, F. E . : J. Phys. & Colloid Chem. 63,374 (1949). (3) HARKIXS, .'!I D., AKD JCRA,G . : J . Am. Chem. SOC.66, 1366 (1914).
T H E MECHASISM OF T H E REACTIOX BETWEEN SILVER A S D SULFUR IX MINERAL OIL R . T . FOLEY, W. XORRILL,
AVD
S. J. WISSLOW
Transjormer and Allzed Products Laboratory, Pzttsjield W o r k s , General Electric Company, Pittsjield, Massachusetts Recezved December $2, 1949
The reaction under consideration is that occurring between metallic silver and elemental sulfur in mineral oil. The purpose of this investigation is to break down the total tarnishing process into its consecutive steps and to evaluate each step both theoretically and experimentally. It is hoped to establish the ratedetermining or slow step in the overall reaction. Several consecutive or simultaneous steps might well be involved in this heterogeneous reaction. I . Dzffuszon zn solution: The sulfur in molecular solution must diffuse to the site of the reaction. The factors that control this process have been elucidated
1282
R. T. FOLEY, W. MORRILL, AND S. J. WISSLOW
in many diffusion studies. Recently, however, a better understanding of diffusion in solution, supported by “free convection,” has been reached by Wagner’s (14) theoretical and experimental study of the dissolution of sodium chloride in water. From equations derived for convection about a heated vertical plate he arrived at an analogous relationship between the rate of solution per unit area, n/A, and the diffusion coefficient, D .
The saturation concentration in solution is given by c. v is the kinematic viscosity of the medium of density p , and H is the vertical height of the plate. Ap is the density difference between the solution with concentration c and the solvent itself. Excellent agreement was obtained by Wagner between the calculated and experimental rates of solution of panels of rock salt of various heights. This relationship might well be applied to the diffusion of sulfur in mineral oil to the silver surface. For a given concentration of sulfur the resulting density difference may be calculated. An approximate value of the diffusion coefficient, D , might be reached from the known behavior of sulfur in solution in organic solvents. If it happens that sulfur reacts immediately upon its arrival at the silver surface or at the silver sulfide-oil interface, then n/,4, calculated by this diffusion equation, will agree with the rate of reaction per unit area. ZZ. Adsorption: This term is used to generalize the process by which the molecular sulfur makes the transition from the solution to the silver surface or to the silver sulfide reaction product. This might be an adsorption phenomenon or it might be the formation of a reaction intermediate made necessary by the existence of sulfur in solution as a polymer incapable of direct ionization. In connection with this step the competitive adsorption of other compounds capable of arising in the oil through oxidation or aging of the oil must be considered. The adsorption of carbon disulfide (9) and methyl violet (11), the inhibiting action that amines (1) and amine salts (8) have on the tarnishing of sterling silver, and the classical usage of silver as a catalyst in the hydration of olefins and the oxidation of allyl alcohol are indications of the adsorptive character of the silver surface. That adsorption at the interface beheen the reaction product and the corrosive atmosphere may be a rate-determining influence has been shown by Reinhold and Seidel in the closely related reaction between silver and hydrogen sulfide (6). I I I . Diffusion in the reaction product: The diffusion of metal outnard and of sulfur and oxygen inward through the reaction product film has been considered by many workers as rate determining for reactions of this type. In studying the action of iodine on silver, Tammann (10) empirically arrived at a parabolic law, y= = 2pt
(2)
relating the thickness of the film, y, after the reaction has progressed for a time t . The constant in this equation has been given theoretical significance by C. Wagner (12, 13) in terms of transference numbers, conductivities, and the
REACTION BETIYEEN SILVER AND SULFUR I N OIL
1283
of the cell involved. Wagner’s hypothesis is based on the diffusion of cations and electrons rather than of neutral atoms through a reaction product film, and good agreement between calculated and experimental reaction rates has been obtained in several cases. The purpose of this work, then, is to appraise each of these steps, if possible quantitatively, so that the mechanism of the reaction between metallic silver and sulfur in mineral oil may be depicted with accuracy.
E.Y.F.
EXPERIMENTAL
The reaction between silver and sulfur was carried out in mineral oil. This petroleum fraction is a naphthene-base oil with approximately 18 per cent aromatic and 3 per cent unsaturation. I t is a type commonly used in the electrical industry to fill transformers using oil as an insulation medium and has been characterized with respect to its physical properties in connection with other tests made in this Laboratory (2). Fine silver (99.9 per cent) was rolled from 0.32 cm. to 0.05 cm. in thickness, annealed, and cut into strips whose total projected surface area was approximately 20 cm.2 I t was found that these strips had to be anodically cleaned to get consistent results during the kinetic study. A cleaned strip was suspended from an S-shaped glass hook. The samples were transferred and weighed in this form. A sample, by means of the glass hook, was suspended from a glass rod which passed through a cork stopper. This stopper fitted tightly into a 38 x 200 mm. Pyrex test tube which contained 125 ml. of the reaction medium. In many experiments 120 ml of this reaction medium was mineral oil and 5 ml. was a benzene solution of sulfur (2.00 mg. of sulfur per milliliter of solution). The benzene used to prepare this solution and to clean the samples in a manner described below was free of thiophene. The large test tube was held in a rack and placed in a constant-temperature oil bath at the desired temperature. The usual procedure was to clean, dry, and weigh a strip before suspension in the middle of the reaction medium. The test tube containing the corrosive medium was held in a rack in a constant-temperature oil bath for the desired time, dependent on the nature of the test. After this immersion the reacted sample was removed from the test tube, rinsed in benzene, and then allowed to stand overnight in benzene. The sample was finally rinsed with benzene and acetone, dried, and weighed. The gain in weight was recorded. Owing to the adherency of silver sulfide films of the thicknesses studied, this proved to be a reliable technique. During several experiments it was necessary to strip the reaction product quantitatively. This was accomplished with 5 per cent sodium cyanide solution, a slight correction in the order of tenths of a milligram being made for dissolved silver. KINETICS AKD DIFFUSION
The course of the reaction was studied in some detail at 60°C. over a period of time required for the silver to react with approximately 95 per cent of the sulfur in solution. The original concentration of elemental sulfur was 4.38 x 10-6 equiv. cm.? Figure 1, in which the fraction of sulfur reacted is plotted against
1284
R. T. FOLEY, V'. MORRILL, .4ND S. J. WINSLOW
the time in hours, traces the course of the reaction. The curve is suggestive of a first-order reaction in which the rate is proportional to the first power of the sulfur concentration, and indeed this law is followed quite closely for the first 30 hr. of the reaction. However, after this length of time reaction rate constants calculated on the basis of a first-order dependence show a regular trend to lower numerical values. The data may also be expressed in equivalents of sulfur reacted per unit time per unit area of silver, written as n / A . These values as crosses are plotted against the time in figure 2. The decrease in rate with increase in time is at once conspicuous. If the rate n / A is governed by diffusion supported by convection, it should be predictable by equation 1 and entirely
n
K0 U
$ -
1.0
-
Q
0.80.6-
I
/ c D / O
00
0 9 4
/ 96O
$0
I-
2a 0.4 LL
[ -3
0.2
01
I
I
I
I
I
I
independent data. A diffusion constant for the sulfur in this medium, D, may be approximated from the equation
D
=
kT- 1
6~7r
(3)
where k = R/N = 1.380 X ergs deg.-', T = 333"C., 9 = 0.026 poise, and r = 2.70 X 10-8 em. The "radius" of the sulfur molecule, T , was calculated from what seemed to be a reasonable geometrical picture of. sulfur existing as an eight-membered ring with an S-S bond distance of 2.08 A. (4). At this temperasec.-l is estimated. In ture an approximate value of D = 0.35 X equiv. cm.-a, g = 981 cm. Y = 0.0301 equation 1 c = 4.38 X see.-', H = 5 cm., and ( A p / p ) = 1.63 X lo-'. These values give an average sec.-l rate of diffusion to the silver surface of n / A = 2 3 1 X 10-ln equiv. This is represented by the dotted horizontal line in figure 2. This average value falls within the range of the experimental sulfiding rates. Further calculations can be made to see if the diffusion equation, in general,
REACTION BETWEEN SILVER . 4 S D SULFUR I N OIL
1285
follows the reaction rate data actually observed. This may be done from a knoivledge of the average sulfur concentration in solution during reaction over a specific time interval. This will give a lower rate than that calculated above, because as the sulfur concentration decreases the rate must decrease. This is seen from equation 1, in which the rate is proportional to the first power of the sulfur concentration and to the 0.25 power of the “density difference.” The density difference in turn is proportional to the sulfur concentration. In table 1 rate values calculated from the known concentrations of sulfur and the corresponding density differences are compared with the observed sulfiding rate. It should be pointed out that this comparison has not been made independent of the known rate of consumption of sulfur, but it does establish the extent to which the diffusion process follows the reaction of sulfur with silver. These calculated
+
3.0
OBSERVED SULFIDING
0 CALCULATED DIFFUSION
+
loo Q
i++
2.0
I .o
20
40
60 80 TIME (HOURS)
100
120
FIG.2 . The observed sulfiding of silver compared with the calculated diffusion rate of sulfur.
values are plotted as circles in figure 2. Fair agreement, about within the range of experimental error, exists over most of the reaction time. VISCOSITY EFFECT
The assumption has been made that the diffusion coefficient for sulfur in mineral oil can be. approximated by the equation: 1 D=kT6wr
(3)
If the radius, T , of the sulfur “sphere” is taken as constant, then at a given temperature the diffusion constant, D,vi11 be dependent only on the viscosity of the medium. The question arises as t o holy the rate of reaction, n / A , will be affected if the viscosity of the medium is varied over a wide range, for these
1286
R. T. FOLEY, W. MORRILL, AND S. J. 'WIR3LOR
two quantities must be connected by the diffusion coefficient. The viscosity of the medium may be considerably altered isothermally by change in solvent. Here, the assumption has been made and verified by many experiments in this laboratory that the hydrocarbon solvent in this system is itself an inert carrier of the sulfur which is the rea&ant. Thus it is possible to extend the range of study of the dependence of reaction rate on diffusion by observing the rate in several solvents. The rate of sulfiding of silver was measured in five solvents. Table 2 gives the
TIME
-
TABLE 1 Comparison of observed sulfiding rate and calculated diffusion rate
hours
cquiv. cm.'
.2.0 4.0 6.0 8.0 15.0 17.5 18.3 22.5 24.0 27.0 39.0
3.10 X lW1o 3.20 2.96 2.53 2.20 2.29 2.14 1.82 1.94 1.91 1.43
-
,1I
I,
OBSERVED SULFIDINO RATE, n/A
1 CAICULATW IMTE, nlA DIFFUSION
T
~
i E OBSERVED SULFIDIXG RATE,
:ALCULATED DIPPUSIOS UTE, n/A
n/A
eqrriu. cm.-l
SLC.-L
2.22 2.17 1.89 1.75 1.76 1.71
51.0 65.5 67.0 76.0 95.0 95.0
SLC.-~
1.39 x 10-lo 1.33 1.37 1.27 1.25 1.22 1.14 1.26 1.19 1.22
1.17 0.98 0.96 0.88 0.76 0.68
Rate of sulfiding of silver in different solvents VENT
~
CBEMICAL NATURE
~
Aliphatic Aromatic Aliphatic Naphthenic Mixture of aromatic and naph-: thenic
ngOoC,
'
i
n/A (OBSERVED)
~
BY
poises
cquiv. cm.+ scc.-l
Ruin. cm.* SIC:^
0.00386 0.00413 0.00513 0.0260 0.0105
6.43 X 7.60 x 6.02 X 3.22 x 1O-lo 5.19 X
20.4 x 10-10 19.0 x 10-10 15.5 X 10-lo 3.02 X 10-lo 7.5 x 10-10
chemical nature of the solvent, as well as the observed rate of reaction. The rate predicted by assuming equation 1 t o hold for solvents of all viscosities is given in the fifth column. I t is apparent that only in the case of solvents 4 and 5 (higher viscosity and lower reaction rate) is good agreement with the calculated diffusion rate obtained. I t appears that the experimental reaction rate as given in the fourth column has approached a limiting quantity,-approximately 6-8 X equiv. cm.-* set.? This suggests that diffusion is not the rate-determining influence in those solvents of low viscosity. One of the other steps in the overall reaction mechanism has assumed this role.
1287
REACTION BETWEEN SILVER AND SULFUR IN OIL TEMPERATURE EFFECT
The sulfiding of silver during a 6-hr. interval was measured at several temperatures. The temperatures and rates are given in table 3. Also, the rate of diffusion to the silver surface predicted by the Wagner diffusion equation (equation 1) is given in the third column. In the fourth column reaction rates are calculated from the extrapolated data of Reinhold and Mohring ( 5 ) . These rates would be predicted for the specific temperature if the reaction rate were controlled by diffusion of ionic silver through the silver sulfide film. To relate the reaction rate to diffusion at these temperatures it was necessary to measure the Rate of suljidii
-
TABLE 3 of silver at different temperatures #/A
IEYPXPA-
CALCULATED W
TUPK
'C.
cguiv.
40
1.95 2.82 3.34 4.19 5.0 6.5
50
60 70 80 92
* Calculated
em.* scc.-1
x
10-10
cguiv.
m EQUATION 1
cm.*
JCC.-L
1.81 x 10-10 2.05 2.98 3.86 4,72 5.92
cqub. cm.* scc.-L
2.53 4.30 6.89 10.9 17.1 27.4
x
10-10
on the basis of a 6-hr. time interval.
TABLE 4 Viscosities and diffusion coefficients calculated with eauation S
'C.
poises
40
0.0419 0.0382 0.0265 0.0210 0.0175 0.0143
50
60 70 80 92
cm.2
sec.-l
2.04 X lod 2.30 3.42 4.43 5.50 6.94
viscosity of the mineral oil reaction solution. The viscosities and the diffusion coefficients calculated with equation 3 are given in table 4. The manner in which the reaction rate (column 2) follows the diffusion rate (column 3) is very striking. SULFIDINQ AND ADSORPTION
Several polar compounds were dissolved in the mineral oil reaction solution to see what effect, if any, compounds which are likely to be adsorbed by silver would have on the rate of sulfiding. Table 5 lists the chemical compounds that were added. An attempt was made to use compounds with exemplary functional
1288
R . T. FOLET, W. MORRILL, AND 6. J. U‘INSLOW
TABLE 5 Effect of various compounds on the rate of sulfiding of silver PELATIVE
AMOUNT O F
1
COMPOUhD ADDED
FUNCTIONAL OPOUP
JCLFIDING
After 6 hr.
None. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Isoamylamine (4.3 g./l.), ......................... Acetic acid (8.0 g./l.).. . . ........... Palmitic acid (6.4 g./l. Oleic acid (8.0 g./l.). . . Naphthenic acids (8.0 Butyl acetate (5.8 g./l Biacetyl (8.0 g./l.). . . . Cetyl alcohol (0.12 g./l.) ............... Quinone (8.0 g./l.). . . . . . . ............... Diphenyl sulfide (8.0 g./l.), ...................... Diphenyl disulfide (8.0 Hydrogen peroxide (5 ml. 30 per cent aqueous solution). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Benzoyl peroxide (0.8 gJ.) . . . . . . . . . . . . . . . . . . . . . . . Acetylene (saturated solution). . . . . . . . . . . . . . . . . . . .
1
After
48 hr.
--”, -COOH -COOH (=), COOH -COOH
-coo-coco-
0.60 0.90 1.00 0.15 0.95
-OH
=O -S-
-s-s-
0.75 1.00 0.96 0.12 0.98
-0-o-
-co-0-0-co-C=C-
I 0
5
1.0
-
0
5 0.8 3 v,
L
2
OLEIC ACID
0.6
0.4
-I
0.2 I
2
3
4
TIME ( D A Y S ) FIG.3. Adsorption and sulfiding
groups. It is interesting to note the effect of groupings such as -COOH, =0, -NH2, and -S-S, which are capable of being oriented. The comparative reaction figure given shows the order of magnitude of the specific surface effect. However, these values should not be accepted as quantitative, because of the
REACTION BETWEEN SILVER AND SULFUR I N OIL
1289
experimental difficulty in reproducing exactly the surface poisoning. Several of the compounds listed were investigated further to establish the time-inhibition relationship. These groups were found to show a complete range of poisoning activity. In figure 3 the comparative sulfiding rate is plotted against the time in days. Several inhibitors-hydrogen peroxide, acetic acid, and quinone-show a reasonably permanent effect. Palmitic acid, on the other hand, is illustrative of a type which, although it definitely hinders the reaction, does not form an adsorbed layer of any great degree of protection. In each case studied, the rate rather than the final amount of sulfiding was affected. The total sulfur in solution does react with the silver if the reaction time is extended sufficiently. DISCUSSION
The relative velocities of the several postulated steps may now be considered. The first step cited was that of diffusion of the sulfur in solution. By calculation based on Wagner's diffusion equation the rate at which sulfur will arrive at the silver surface may be estimated. If it is assumed that the reaction with ionic silver takes place immediately upon arrival, and if the diffusion is the slow or rate-determining step once equilibrium has been established for the other steps, the observed rate of reaction should closely follow this calculated diffusion. The plot of the data in figure 2 shows this to be the case to a remarkable degree. At certain times during the course of the reaction the rate is exactly as calculated in accordance with this mechanism. This is especially remarkable because of the method of arriving at what seemed like a reasonable value for the diffusion coefficient for sulfur in mineral oil. Sulfur dissolved in carbon tetrachloride has been found to have eight atoms in each moLecule (3). The S S bond distance has been assigned by Gingrich (4) as 2.08 A. and the S-S-Sbond angle as 100" (4a). On the basis of these data the sulfur molecule was represented as a sphere with a "radius" of 2.70 X cm. This value was used in equation 3, which is sometimes called the Sutherland-Einstein relation. This equation was derived for molecules that are spherical and large in comparison with the solvent molecules. Xeither condition holds too closely in this case, so the diffusion coefficient must of necessity be in error. In spite of this lack of refinement the calculated diffusion follows very closely the reaction rate of a great deal of the course of the reaction. The increase in rate of reaction with temperature can be explained fairly well by the expected increase in diffusion-supported, of course, by convection. In table 3 the rates calculated by equation 1 are in fair agreement with the experimental rates from 40" to 92"C., at which temperature the rate increases to about 6 X lo-'" equiv. em.-* sec.-l There apparently is an upper limit to the reaction velocity that can occur from increased diffusion. In the experiments in which the viscosity change was related to the sulfiding it was seen that an indefinite decrease in the viscosity did not cause an indefinite increase in reaction rate. I t appears that the diffusion ceased to be the rate-determining influence once the rate reached about 6-8 X 10-lo equiv. em.-* see.-'
1290
R. T. FOLEY, W. MORRILL, AND S. J. WINSLOU'
The adsorption step is postulated as the second step in the reaction series. There is not enough experimental evidence available t o show that adsorption, in the sense in which it is commonly used, is a necessary step, but it seems reasonable on the following basis. It has been shown that the silver surface can be poisoned by the adsorption of sulfides and disulfides, molecules whose structure resembles sulfur from the standpoint of coordination electrons. Moreover, other structures, polar groups, are adsorbed and inhibit the reaction in varying degree. Thus a competitive mechanism, with both sulfur and the foreign molecule exercising an affinity for the silver surface, is suggested. If these foreign groups cover the surface, the adsorption of sulfur may well be the slow step. A comparison of rates will illustrate this point. In the presence of p-quinone, the sulfur-silver reaction proceeded at an average rate of n / A = 0.9 X lo-" equiv. cm.-2 set.-' during a 48-hr. experiment. A control which was not contaminated with any known compound not a normal Constituent of this oil gave equiv. cm.-2 set.-' a result of n / A = 0.61 X Whether this phenomenon is merely adsorption or is chemical reaction or intermediate complex formation is, of course, open to question. Rudberg and v. Euler (7), in studying the adsorption of salts on silver surfaces from aqueous solutions, concluded that a surface complex, Ag:, is formed when the surface reaction takes place. After studying the catalytic decomposition of hydrogen peroxide by silver, Weigel (15) postulated a mechanism involving the precipitation of an oriented AgOOH film on the surface. I t is interesting to note that in the experiments here reported compounds with oxygen which can be oriented are particularly capable of poisoning the silver surface for the sulfide reaction. Other functional groups, such as the acid radical, which conceivably could form transitory surface salts are also active in this regard. It is apparent from figure 3 that the adsorption of these foreign compounds affects the rate rather than the final amount of sulfiding. Even in the case of hydrogen peroxide it has been established that if the silver is removed from the constant supply of volatile gas the sulfiding will proceed unabated. In this case it has been shown that the sulfur has not been destroyed but is available for reaction with silver if the decomposing hydrogen peroxide is removed from the scene. Although these results are presented here in only a semiquantitative manner, it would be intriguing to study the mechanism involved in the passivation of the silver surface by means of agents which are not film formers in the usual sense. The third step which could be rate determining is the diffusion of the reactants through the silver sulfide reaction product. Fortunately, by means of the theoretical equations of Wagner (12) and the experimental data of Reinhold and Mohring (5), we can approximate what the rate would be if the reaction were controlled by this mechanism. The latter two investigators studied the reaction between silver and sulfur in the temperature range of 130'C. to 172OC. As the reaction was carried out with a silver wire in molten sulfur it seems logical to assume that in their case the rate-determining step was the diffusion of the reactants through the reaction product film. The following values were taken
1291
REACTION BETWEEN SILVER AND SULFUR IN OIL
from their paper: I
k X 1010 (POUND)
"C.
rquio. cm.-l sec.-l
1
k X 10'O
cquiv. cm.-l scc.-L
0.83 2.64 3.61 5.51 9.31
1.41 2.72 3.68 5.69 7.21
130 148 156 162 172
(CALCULATED)
The calculated values in the third column were obtained from the Arrhenius type equation which best fitted their data: k = 17e-10,500/T
(4)
At GOOC. the extrapolated value of k = 3.4 X lo-'* equiv. cm.-' sec.?
(5)
This may be converted to m/A(g. cm.-')
= d 1 . 0 3 2 X 10-l1t(sec.)
(6)
by formulas given by Wagner (12). Here m/A is the sulfiding in grams per unit area. At several different times the amount of sulfiding may be compared: TIME
hr.
15 41.4 95
CALCULATED
g.
cm.*
7.47 x 10-4 12.4 X 18.8 X lo-'
I
OBSEPVED g. cm-1
4.00 x 10-4 7.05 x 10-4 8.4 x 10-4
In each case the extent of reaction as predicted on the basis of diffusion through the reaction product is greater than the observed rate. It is concluded then that this step is not usually the rate-determining step. However, in table 2 and in a discussion of abnormal viscosity effects observed at 6OOC. it was pointed out that the observed rate is far smaller than that predicted if diffusion in solution were the rate-determining step. Moreover, the observed "limiting rate" equiv. cm.+ sec.-l is in good agreement with the rate of 6.89 X of 6-8 X lO-l0 equiv. cm.-2 sec.-l calculated for 60°C. (cf. table 3) from the data of Reinhold and Mohring, in which case the rate-determining step is assumed t o be diffusion through the silver sulfide film. It was seen in studying the temperature dependence of the reaction that the rate as calculated on the basis of diffusion in the silver sulfide layer consistently gave values too high. It may be concluded, therefore, that with a solution as viscous as the mineral oil used in the present investigation the film diffusion is not the rate-determining step. Curiously, this situation might well be changed if a different, more fluid, solvent had been chosen for the investigation.
1292
R. T. FOLEY, W. MORRILL, AND 9 . J. IVINSLOW SUMMARY
The steps involved in the total mechanism of the reaction between sulfur in mineral oil and metallic silver may be outlined. I . Difusion of the sulfur in oil: So (in molecular solution in oil) + So (in solution at the silver surface). This is normally the slow step and a good approximation of the rate of reaction may be made from the Wagner diffusion equation. I I . Adsorption: So (in solution) ---f So (adsorbed on silver surface or at silver sulfide-oil interface). Normally this is a fast step. However, when preferentially adsorbed compounds are present on the silver surface, it may be the slow and rate-determining step. I I I . Difusion in the silver suljide layer: Ag+
+ e-
(in base metal)
---f
Ag+
+ e-
(at f i l m d interface)
Usually this is a rapid step, relatively speaking. However, when the viscosity is decreased considerably an upper limit is reached in the rate. At this point, this step is rate determining. If a less viscous oil had been chosen for the kinetic study, this might well have been the rate-determining step instead of diffusion in the oil. The authors wish to express their gratitude to Dr. Carl Wagner of the Massachusetts Institute of Technology, who offered several helpful suggestions which aided in the theoretical treatment. They mould also like to thank Dr. Norman Hackerman and Dr. Robbin Anderson of the University of Texas for their constructive review of the paper. REFERENCES BRIGGMAN, G. F . : U. S.patent 2,323,369 (July 6, 1943). CLARK,F . M . , ASD RAAB,E . L . : Am. SOC.Testing Materials, Preprint 87 (1948). ODDO,G., AND SERRA,E . : Chem. Zentr. 1899, 11, 1092. PAULING, L . : The Nature of the Chemical Bond, second edition, p. 166. Cornell University Press, Ithaca, New York (1940). (4a) Reference 4, p. 79. (5) REIIVHOLD, H., AND MOHRIKG, H.: Z. physik. Chem. 28B, 178 (1935). (6) REINHOLD, H., AND SEIDEL, H.: Z . Elektrochem. 41, 499 (1936). (7) RUDBERCI, E . G . , AND EULER,H. v.: Z . Physik 13,275 (1923). (8) RUST,J. B.: U. S.patent 2,400,784 (May 21, 1946). (9) SCHLUTER, H.: Z. physik. Chem. 163A, 68 (1931). (10) TAMMANN, G . : Z . anorg. allgem. Chem. 111, 78 (1921). (11) TERWELLEN, J.: Z . physik. Chem. 16SA. 52 (1931). (12) WAGNER,C . : Z. physik. Chem. 21B, 25 (1933). (13) WAGNER, C . : Angew. Chem. 49, 735 (1936). (14) WAGNER,. C . : J . Phys. & Colloid Chem. 63, 1030 (1949). (15) WEIGEL,E . : Z . physik. Chem. M A , 81 (1929). (1) (2) (3) (4)
