REACTION VELOCITY AT A LIQUID-LIQUID INTERFACE BY RONALD PERCY BELL
Introduction. Very little work has been done upon the velocity of reaction in a heterogeneous system consisting of two non-miscible liquids, and those cases which have been studied are of the type in which a t least one of the reactants is soluble in both liquid phases. I n a reaction of this type, the reaction velocity depends upon the rate of diffusion of one or more of the reactants across the junction of the two phases, and is not due to surface phenomena. It was therefore decided to investigate a reaction between two substances ‘a’ and ‘b’ in two non-miscible solvents ‘A’ and ‘B,’ ‘a’ being insoluble in ‘B,’ and ‘b’ being insoluble in ‘A.’ In a case of this kind, the reaction can only take place at the junction of the two phases, and will depend upon the formation of adsorbed surface films. I n order to simplify matters, it was decided to use as one reactant a solution of an electrolyte in water, which gives only a slight negative adsorption, and as the other reactant a solution of non-electrolyte in a non-dissociating solvent which will give a positive adsorption. The reaction can then only take place by the ions of the electrolyte striking the adsorbed film of the non-electrolyte. Although a reaction of this kind must be a true surface reaction, it is still possible that it may be influenced by the rate of diffusion of the non-electrolyte to the surface. This will be the case if the rate a t which the adsorption equilibrium is adjusted is slow compared with the rate a t which the molecules are removed from the surface layer by reaction. I n this case the reaction velocity will be affected greatly by the rate a t which the layer is stirred, while if the reaction velocity is only a function of the equilibrium condition of the adsorbed layer, the rate of stirring should have no influence. From the small difference which is found to exist between the static and dynamic surface tensions of solutions, it appears that the oriented monomolecular films formed in solutions are not disturbed by a moderate degree of stirring. Choice of a reaction. The reaction to be examined should have the following characteristics: (a). The two solvents must not be miscible to any great extent, and neither must be very volatile. Also they must not readily form an emulsion, and they must have specific gravities differing as far as possible so that the liquid to liquid interface shall not easily be deformed by stirring either of the layers. (b). Each of the reacting substances must be insoluble in one phase and soluble in the other. (c). The products of reaction must be soluble in a t least one of the phases. (d). The electrolyte must be a neutral salt, since hydrion and hydroxidion have a disturbing effect upon surface conditions.
REACTION VELOCITY AT A LIQUID-LIQUID INTERFACE
883
(e). The reaction must proceed at a measurable velocity at ordinary temperatures. (f). At least one of the reactants must be capable of accurate determination in solution. The reaction finally chosen as suitable was the oxidation of benzoyl-otoluidide in benzene solution to benzoyl-anthranilic acid, by a neutral aqueous solution of potassium permanganate, according to the equation:-
1
1
”COCsH5
NHCOC&
-
-
~
I
Each solvent was saturated with the other before use. Experiment showed that benzoyl-o-toluidide is quite insoluble in a saturated solution of benzene in water, and that potassium permanganate is quite insoluble in a saturated solution of water in benzene, the temperature in each case being about 2 5 O C . The product of reaction, benzoyl-anthranilic acid, was found to be only slightly soluble in water, but since only initial velocities were measured and a large volume of water was present, in no experiments did it separate out. The benzoyl-o-toluidide used was prepared by the Schotten-Baumann reaction from benzoyl chloride and pure o-toluidine. It was filtered, pressed, washed with dilute hydrochloric acid and water, and dried on the water-bath. One preparation was recrystallised from alcohol and another from benzene. After drying in a steam oven each preparation melted a t I ~ I O C , and a mixture of the two also melted a t I ~ I O C . Both were therefore considered pure and were used indifferently in the subsequent work. Measurement of Reaction, Velocity. The apparatus for measuring the reaction velocity is shown in Fig. I . The glass jar ‘A’ was of about 5 litres capacity. The permanganate layer ‘a’ was stirred by the stirrer ‘B,’ and the benzene layer ‘b’ by the stirrer k J The stirrers were of glass and were connected by pulleys so that ‘B’ rotated about four times as fast as ‘c.’ ‘B’ was enclosed by the outer tube ‘D’ SO that it moved only in the permanganate solution. The progress of the reaction was followed by titrating from time to time I O ccs. of the permanganate layer which were withdrawn by a pipette attached to the rubber tubing at ‘€3.’ At the commencement of each run the permanganate solution, approximately a t 2 5 % was run into the jar clamped in the thermostat. A known volume of benzene was then added, and left for half an hour to acquire the temperature of the thermostat. The reaction was started by adding a known volume of a benzene solution of benzoyl-o-toluidide, which had previously been brought to the temperature of the thermostat. These solutions were made up by dissolving a known weight of benzoyl-o-toluidide in a known volume of benzene. Prelimznary Experiments. Two runs were first made in which the solutions used were the same in each case, but the speed of stirring of the benzene
884
RONALD PERCY BELL
layer differed in the two cases. As a temporary standard for titrating the permanganate solution an acidified solution of ferrous ammonium sulphate was used. Since comparative values only were required, the strength of the solutions used was known only very approximately. I n the preliminary experiments, as in all measurements of reaction velocity, the following points were adhered to:(a). A large volume of permanganate solution was used, so that the removal of several I O cc. portions should not affect the concentration to any considerable extent. (b). The benzoyl-o-toluidide was always present in large excess compared to the permanganate used up, so that the E concentration of the former should not change materially during the initial stages of the reaction. The results of the preliminary runs show that after a very short initial stage, the reaction attains a velocity which is not affected by increasing the rate of stirring four-fold. Thus with an initial titre in each case of 13.9 ccs. with the faster rate of stirring the titre changed from 12.35 ccs. to 11.40 ccs. in 1.5 hours, while the corresponding change at the slower rate of stirring was from 13.20 ccs. to I 2 . 2 5 ccs. in the same time. Titration of potassium permanganate. For further experiments a solution of sodium oxalate approximately N/ IOO was used for titrating the permanganate solutions. In runs 1-4 inclusive, the I O CCS. FIG.I of permanganate solution was added to about 50 ccs. of hot, joR sulphuric acid. IOO ccs. of boiling water was then added, and the solution often remained a t 80"-9o°C for some minutes before titration. I n each of these runs very erratic results were obtained, although the general trend of the titres corresponded to the progress of the reaction. It was therefore thought that the method of titration was a t fault, and after run 4 the permanganate layer (containing the products of reaction) was removed, and I O cc. portions were titrated with standard sodium oxalate under different conditions. It was found that if the procedure described above was adopted, the titre decreased on standing, to the extent of about 17in one minute. This accounts for the erratic points obtained. However, if the permanganate was added to cold sulphuric acid, then diluted with water, and warmed gradually to 7ooC, the titre was not altered by keeping the solution
+€
REACTION VELOCITY AT A LIQUID-LIQUID INTERFACE
88.5
at 7ooC for ten minutes. This procedure was therefore employed in all subsequent runs, and the results of runs 1-4 inclusive were not used. A suggested explanation of the observed decrease in titre is that the benzoyl-anthranilic acid is partially hydrolysed to anthranilic acid by contact with hot 50% sulphuric acid. The free amino-group is then oxidised by a part of the permanganate, thus reducing the titre. Experimental Results (Firstseries). I n this series of runs the temperature of the thermostat was 2 4 . 6 5 ° + o . o ~ 0 C .
FIG.2 I n all, sixteen runs were taken. Besides the first four, run No. 6 was rejected because the stirrer was broken, and run No. 11 because for some unknown reason the titres are erratic. I n each run, on plotting the titres against the time it was found that the initial portion of the graph always approximates to a straight line, though in some cases the observed initial titre does not lie upon the line which passes through the subsequent points, indicating a short initial stage. I n these cases the initial concentration is taken t o be that corresponding to the first point on the straight line. The initial reaction velocity given in the tables of results is obtained graphically from the straight portion of the curve. As an example, the full experimental figures for run No. 8 are given:Run (8). 1 2 0 0 ccs. water 400 ccs. K M n 0 4 (A) 2 5 0 ccs. benzene Initial titre = 48.12 ccs. (oxalate B). 2 5 0 ccs. benzoyl-o-toluidide B added a t 10.30. Time I O . 30 11 . o
11.30 12.0
Titre
Time
Titre
48.12 47.33 46.73 46.11
12.30
45.60 45.60 44.70 44.34
The graph of this run is given in Fig.
1.0 I
.30
2.0 2.
886
RONALD PERCY BELL
In every run the total volume of the aqueous layer was 1600 ccs., and thP total volume of the benzene layer 500 ccs. I n runs Kos. 5, 7 and 8 the concentration of the sodium oxalate used corresponded to 1.98X IO-^ gram moles K M n 0 4 per cc. In runs Nos. 10-16 inclusive the corresponding figure was 6.12 X IO^. The results of the first series are summarised in the following table, in which:h = Initial concentration of K M n 0 4in oxalate titre per I O ccs. of solution. B = Concentration of benzoyl-o-toluidide in grams per litre. R = Initial rate of reaction in ccs. oxalate solution per I O ccs. permanganate solution per hour. Run
.1
B
3
36.14 24.86
4.55 4.55 4.55 3.94
7 8
48.I 2 26.19 26.60 26.j 2 25.40 24.63 26.34
IO I2
13 I4
‘5 16
It 0.82 0.53 1.15 2.70
2.95
1.52
8.69 5.94 2.14 4.96
3.68 3.55 0.65 3 50 ’
I n runs Sos. 5, 7 and 8, ‘B’ remains constant, while ‘A’ varies. These results can therefore be used to test the dependence of the reaction velocity upon the permanganate concentration. Expressing both the quantities in the units given in the table, we have the following values for the ratio R/A:Run ( 5 ) . 0.82j36.1q= 0 . 0 2 2 7 0 . j3124.86 = 0.0214 Run ( 7 ) . Run ( 8 ) . 1.15/48.12= 0.0223 The constancy of this ratio shows that the reaction is monomolecular with respect to potassium permanganate. This being so, we can correct for the variations in initial concentration of permanganate in runs 10-16. The following table contains the initial velocities corrected to a uniform inital concentration corresponding to a titre of 26.19ccs. oxalate solution. Run IO I2
13
B
3.94 2.95 8.69
R’
Run
2.70
1.1
1.46 3.63
15
2.14
16
4.96
B 5.94
R’ 3.66 0.69 3 50 ’
These figures are plotted in Fig. 3, which represents the dependence of the reaction velocity upon the concentration of the benzoyl-o-toluidide. I t is seen that for concentrations above about j-6 grams per litre, the value of R’ becomes independent of that of B. This range of concentrations was therefore used in the second and third series of experiments undertaken to determine the temperature coefficient of the reaction velocity.
REACTION VELOCITY AT A LIQUID-LIQUID ISTERFACE
887
Experimental Results. (Second and thzrd series). I n the second series the temperature of the thermostat was z j.oSC., and in the third series it was 14.90°c. Three runs were carried out at each temperature, with concentrations of benzoyl-o-toluidide of approximately 6, 7 and 8 grams per litre. In both runs the oxalate solution used had a strength corresponding to j.61 X IO+ gram moles KRln04 per cc. In each series it was found that by plotting the points of all three runs on one graph B straight line was obtained for the initial portion which passed through the points of each separate run, thus confirming the result of the first series namely, that for concentrations of benzoyl-o-toluidide above about j-6
FIG.3
grams per litre the reaction velocity is independent of the concentration. The reaction velocity in each series was determined by measuring the slope of the line. The results obtained were as follows:-
Series ( 2 ) . At zj.oS"C with an initial titre of 16.6j ccs., the initial velocity was 3.60 ccs. per IO ccs. per hour. Series ( 3 ) . At 14.9oOC with an initial titre of 17.15 ccs., the initial velocity was 0.28 ccs. per I O ccs. per hour. If we correct the second value for the small difference in initial titre, the values become 3.60 ccs. and 0.27 ccs. respectively. Measurement of Surface Tension. I n order to determine how the interfacial tension between the two layers varied with the concentration of benzoyl-o-toluidide, the drop-weight method was used. It was of course impossible to use permanganate solutions, but since these were dilute, the error involved in using water will be small, a t least as regards the variation of the surface tension with concentration.
888
RONALD PERCY BELL
The apparatus used was a modification of that used by Harkins.' The tip was about 7 mm. in diameter and was selected to be truly circular. It was ground flat with carborundum powder and water, and finally polished with rouge. The time allowed for each drop to fall was a t least three minutes, and under these circumstances the surface tension is proportional to the dropweight. Since the density of the solutions used varied only from 0.8740 to 0.8755, the drop-volume can in this case be taken as a measure of the surface tension. The results obtained are given in the following table in which:c = concentration of benzoyl-o-toluidide in grams per litre. v = volume of one drop of water in ccs.
FIG.
4
Both the water and the benzene solutions were saturated with respect to each other by shaking in the thermostat before measuring the drop-weight. All the surface tension measurements were carried out in the thermostat at 24.65OC. C
logloc
V
C
log10c
V
1.94 2.98 4.02
0.288
0.398
5.02
0.701
0.474
7.32 8.04
0.865 0.90j
6.19
0.792
0.398 0.396 0.348
0.377 0.326
0.604
0.314
The variation of the surface tension with the concentration is shown in Fig. 4, in which the drop-volume is plotted against log&. Discussion of results. I n the introduction the theory was advanced that reaction took place by permanganate ions striking an adsorbed surface of benzoyl-o-toluidide molecules. In this case the reaction velocity at a given temperature depends only upon the nature of the surface layer, and upon the 'Harkins, etc.: J. Am. Chem. Soc., 38, 228, 252 (1916).
REACTION VELOCITY AT A LIQUID-LIQUID INTERFACE
889
rate of impact of the permanganate ions. The hypothesis is supported by the following experimental facts:(a). The preliminary experiments show that the reaction velocity is independent of the rate of stirring, and hence not dependent on the rate of diffusion of either reactant towards the interface. (21). The results of runs 5 , 7 and 8 in the first series of velocity determinations show that the velocity is directly proportional to the concentration of potassium permanganate, i.e., since the solutions are dilute, to the rate a t which the permanganate ions strike the surface. ( c ) . The reaction velocity is found to have a large temperature coefficient, increasing about 13-fold for a rise of I o O C . This shows an analogy to heterogeneous gas-reactions, in contradistinction to diffusion reactions, for which the temperature coefficient is very small. This being the case, it should be possible to observe a connection between the reaction velocity and the condition of the surface film. The fundamental equation for the extent to which adsorption a t an interface takes place is the Gibbs-Helmholtz equation:-
c = concentration of dissolved substance. (r = surface tension. I’ = increase of concentration a t the interface in moles per sq. cm. The direct confirmation of this value for the excess concentration offers great experimental difficulties. A fair agreement between calculated and observed values was obtained for the liquid-gas interface by Donnan and Barker,’ and by Frumkiq2 but the results of W. C. McC. Lewis3 on the liquid-liquid interface are not so satisfactory. Indirect confirmation has however been obtained by several workers. It is found in general that for solutions of non-electrolytes aa/a In c becomes constant above a certain limiting value of c. This means that r has reached its maximum possible value, Le. that the surface is completely covered. Values for the molecular diameter are calculated from the value of r and good agreement is found with values obtained by other methods or for other solvents. The present work gives another opportunity of testing the same point. It is seen from Fig. 3 that &/a In c becomes constant for all concentrations above about 5-6 grams per litre. It would therefore be expected that ‘ceteris paribus,’ the reaction velocity would be the same for all benzoyl-o-toluidide solutions having concentrations above this limit. The curve in Fig. 3 bewhere
l Donnan and Barker: h o c . Roy. Soo., SSA, 557 (1911). ‘Frumkin: Z.physik. Chem., 115, 253 (1925). *Lewis: Phil. Mag., 15, 499 (1908);17,466 (1909);Z.physik. Chem., 73, 129 (19x0).
,
890
RONALD PERCY BELL
comes parallel to the concentration axis for high concentrations, the point of inflection lying between j and 6 grams per litre, so that the dependence of the reaction velocity on the condition of the surface film is confirmed by experiment. The constancy of the reaction velocity a t high concentrations is shown not only by Fig. 3 j but by the agreement of the separate runs in series ( 2 ) and ( 3 ) . The present experiments therefore provide an independent verification of the presence of a saturated monomolecular adsorbed layer at the surface of a concentrated solution of a non-electrolyte. I t is suggested that this work can be extended to a general study of adsorption by other kinetic properties of interfaces, e.g., rates of evaporation. Such experiments are now in progress. For concentrations of benzoyl-o-toluidide corresponding to a complete covering of the surface, i t is of interest to compare the number of permanganate ions reduced with the total number which strike the surface. This latter number can only be calculated if we assume that the permanganate layer is homogeneous throughout, and neglect the surface film of water molecules.1 Making these somewhat doubtful assumptions, we have by the kinetic theory2:-
n = number of ions per second striking a given unit area. JV = number of ions contained in a total of S species (ions vent molecules). c = root-mean-square velocity of an ion. @b = molecular co-volume of solution. Since the solutions are dilute we can write:-
where
+ sol-
kt7 = c = concentration in gram moles per cc. where and hence :x = 3600 e A C ’ V G where
X = reaction velocity in gram moles per hour. A = area of interface.
I n the second series of velocity determinations the initial titre xas 16.6; ccs. This corresponds to a concentration of :c = 16.65 X 5.61 X = 9.37
IO-~
X
10
x IO-^ gram moles MnOa’ per cc.
Morgan and Egloff: J. Am. Chem. Soc., 38, 844 (1916); Harkins: 39, 1848 (1917); 47, 1 6 1 0 (1925); King: Kansas Exp. Sta. Tech. Bull., 9 (1922);Mathews and Stamm: J. Am. Chern.iSoc., 46, 1071 (1924). FeJTraube: W e d . Ann., 61, 380 (1897); also Dieterici: 66,826 (1898). Compare the equationused by Langmuir for gases. Trans. Faraday SOC.,1922.
REACTION VELOCITY h T A LIQUID-LIQUID INTERFACE
From the kinetic energy of the MnOd‘ ion a t 25OC. we obtain,
C=
A
2.45 X
104
= 132 sq. cm.
x
9.37 X IO-^ X 132 X 2.45 X 104 4 6 X 3.14 = 2 . 5 1 X 104gram moles K M n 0 4 per hour. The initial velocity determined experimentally was 3.60 ccs. oxalate per I O ccs. solution per hour. Since the total volume of solution was 1600 ccs., we have :X = 3.60 X 160 X 5.61 X I O - ~ = 3 . 2 2 X IO+ gram moles X M n 0 4 per hour. There is thus a ratio of about I : IO-’ between the number of M n 0 4ions which reach the surface layer and the number which react with benzoyl-otoluidide a t zs0C. There are two factors which may account for this large number of unfruitful collisions:(a). That only collisions possessing an energy of impact greater than a limiting value ‘E’ are fruitful. If the adsorbed layer can be regarded as entirely stable, then ‘E’ refers only to the energy of the permanganate ion. Probably, however, the adsorbed toluidide molecules are in varying states of vibration and strain, in which case ‘E’ refers to the joint energy of the two colliding molecules. (b). That certain ‘phase conditions,’ e.g. mutual orientation of the reacting molecules, are necessary to reaction. That the first of these factors is present seems certain on account of the very small number of fruitful collisions, and more especially on account of the high temperature coefficient. The second factor may or may not be effective simultaneously with the first. If we consider it as a case of simple thermal activation the variation of the reaction velocity with the temperature over a fairly small temperature range is given by:-d l-n k - -E dT RT2 where the ‘energy of activation,’ E, is a constant. I n the present instance, measurements have only been made at two temperatures, so that it is impossible to show that the In k - 1/T2graph is a straight line, i.e. that E is actually constant. However if we assume its constancy, a value can be calculated from the temperature coefficient. Taking the mean temperature as zo°C., Hence
X
=
3600
-~ - E 2 x 2932 (lOgio3.6 - lOgio0.28)
111~3.6- ln,o.z8 IO
E =
2
x
293’
4.343 = 43,700
calories
892
RONALD PERCY BELL
Assuming that the calculation of the total number of collisions is correct, we have:Effective collisions = 1.28 X IO+ Total collisions from which we can calculate a value for E according to the Maxwell distribution law, Effective collisions Total collisions whence
I .28
E
X IO-^ = e= =
- e--E,RT E
2 X 298 X 15.87 9.500 cals.
Thus the two values of E, 43,700 cals. and 9,500 cals. calculated on the basis of simple thermal activation are very different, and the discrepancy will be increased if a phase factor (necessarily less than unity) is present. It seems probable that although the equation used to calculate the total number of impacts may be approximately correct for an imaginary plane in the interior of the solution, it will fail entirely a t a phase interface on account of the adsorbed water layer a t the surface and the electrical action. In any case, reliance cannot be placed upon the value 43,700cals., depending as it does on a single determination, and the application of simple kinetic theory t o an ionic solution cannot give more than very approximate results. Thus in this case the results of thermal calculations are inconclusive. It appears, however, that a study of this type of reaction may prove useful in the study of thermal activation. In the ordinary heterogeneous gas-reaction, the surface is not readily reproducible, nor is its area easily measured, while in the homogeneous bimolecular gas-reaction the calculation of the total number of collisions depends on molecular diameters, which are not known accurately. In a reaction of the present type, the collisions are between moving molecules and a well-defined interface, and their number can be calculated by simple kinetic theory. It would seem that the complications met with in the present work might be obviated by the study of a reaction a t a gas-liquid surface.
SummnrP (I). The velocity of the surface reaction between benzoyl-o-toluidide in benzene solution and potassium permanganate in aqueous solution has been determined for varying concentrations of the two reactants and a t temperatures of 15°C and 25OC. Comparative measurements of the interfacial tension between water (2). and benzene solutions of benzoyl-o-toluidide have been carried out by the drop-weight method.
REACTION VELOCITY AT A LIQUID-LIQUID INTERFACE
893
(3). It has been shown that the above reaction is caused by permanganate ions striking an adsorbed layer of benzoyl-o-toluidide, and that its velocity is not dependent upon diffusion from one solvent to another. (4). Comparison of the velocity curves with the surface tension has afforded an independent confirmation of the Gibbs-Helmholtz adsorption equation. ( 5 ) . Calculations have been made t o test the hypothesis of thermal activation for this reaction, but with inconclusive results. ( 6 ) . It is suggested that more conclusive results might be obtained by the study of a reaction a t the gas-liquid interface, and that the general problem of inter-phase kinetics may provide a valuable line of approach in the study of adsorption. In conclusion, the author wishes to express his gratitude t o Sir Harold B. Hartley for his advice, encouragement and assistance throughout the work. Physical Chemistry Laboratories, BaUiol and Trinity CoUeges, Oxford. Decedber 89,lQH.
