Dec., 1963
REACTION BETWEEN HYDROCARBOSS AND PICRIC ACIDI?; SOLIDSTATE
2569
MECHANISM OF THE REACTION BETWEEN HYDROCARROKS ANI) PICRIC ACID 11s THE SOLID STATE Chrinistry I>rpnrlment, Corakhpur Un iaersity, Cl'ornl h p u r , Inrlin
Received Mal/ 8, 1963 The kinetic data for reactions between hydrocarbons, Le., naphthalene, phenanthrene, anthracene, and picric acid, in t~hesolid state are recorded. The measurements have been made at various temperatures and for particles of various sizes. For elucidating the mechanism, photoreaction in the solid state has also been studied. Experimental results are best fitted by an equation of the type E 2 = 2kite-P€, where E is the thickness of the boundary; ki and p are constants. The factor p is found to be approximately independent of temperature and particle size. The value of ki and energy of activation increase in the order: naphthalene > phenanthrene > anthracene. It was also found that ki varied linearly with the surface area of the particles. It is fairly definite that the reaction is diffusion-controlled. There is evidence to show that bulk diffusion or lattice diffusion is nonexistent. The probable diffusion mechanisms have been discussed.
Introduction It has been shown that the reaction between naphthalene and picric acid can be studied in the solid state by a simple technique' described in an earlier communication. In the present communication data are presented which throw light on the mechanism of the reaction between hydrocarbons and picric acid. For this purpose measurements have been made at various temperatures and for particles of different sizes. The studies have been extended to other hydrocarbons such as phenanthrene and anthracene. As reported earlier, the reactions axe diffusion-controlled. Diffusion may occur by various mechanisms such as lattice diffusion, vapor phase diffusion, surface migration, or grain boundary diffusion. It is the purpose of the present paper to throw light on this point. Experimental Materials and their Purification.-Naphthalene was purified by repeated sublimation under vacuum. Subsequently, it was subjected to fractional crystallization with pure ethanol. The melting point was found to be 80.3". Phenanthrene was purified by repeated crystallization with lime-distilled ethanol. Further, it was kept under vacuum for 48 hr. t o remove ethanol, etc. Its melting point was 100.3'. Anthracene was purified by crystallization from benzene (A.R. grade) thrice and was kept in a vacuum desiccator. Its melting point was found to be 216.0'. Picric acid was recrystallized from ethanol and dried in a vacuum desiccator. The melting point was found to be 121.4'. 1. Study of the Reaction Kinetics in the Solid State.-The technique used has been described earlier .1 The reactions were followed in thermostats which were maintained at temperatures lower than the eutectic lemperature. The color of the boundary in case of naphthalene-picric acid was yellow, for phenanthrenepicric acid it was orange-yellow, and for anthracene-picric acid i t was reddish yellow. The distance through which the boundary moved was noted correct to =t0.001 em. as a function of time. The reaction was followed for I to 2 weeks. The studies were made a t different temperatures and for particles of various sizes. Particles of different meshes, i.e., 25, 50, 100, and 200 mesh/ were used in the investigation. It was observed that only hydrocarbons diffused through the picrate. The results are plotted in Fig. 1-3. 2. Determination of the Reaction Temperature.-The following procedure was adopted to determine the reaction temperature as defined by Cohn.2 The apparatus consisted of a doublewalled Pyrex glass tube, provided with a side tube which was connected to a vacuum lint,. The rate of temperature rise was controlled by adjusting the order of vacuum. A rubber cork with two holes, one for the tliermotneter ( l / l o o ) and the other for the stirrer, was inserted in the mouth of the double-walled tube. (1) R. P. Rastogi, P. S. Bassi, and S. L. Chadha, J . Phya. Chem., 66, 2707 (1962). 12) G. Cohn, Chem. Rev., 42, 528 (1948).
A known amount of naphthalene was put in the inner tube and the assembly was placed in ice bath so that the temperature of naphthalene fell gradually. An equimolar amount of picric acid placed in a Pyrex tube was also cooled to the same temperature. When both the substances attained the same temperature, picric acid was dropped into the double-walled tube and the two solids were mixed thoroughly. The temperature of the contents was noted. The whole system was put into a water bath maintained at a suitable temperature, the stop-watch was switched on, and the temperature of the mixture was noted a t various intervals of time. The temperature-time graph from 0 to 78" was plotted. The temperature rise was gradual showing the absence of reaction temperature. comparative study of the 3. Study of Photoreaction.-A photoreaction and the dark reaction was made to ascertain the mechanism of diffusion of the reactants since the hydrocarbons are known to be photoc~nducting.~The study was made by keeping the capillaries filled with hydrocarbons and picric acid in the ultraviolet light and in dark. Results are given in Table V. 4. Study of Reaction with Nonporous Samples of Phenanthrene and Picric Acid.-Phenanthrene was melted in a test tube and a pellet was made having a smooth surface of thickness 0.942 em. The pellet of picric acid was made with a press. Its thickness was the same as that of phenanthrene. The two pellets were then kept in close contact by maintaining pressure on the two sides. Phenanthrene was observed to have diffused into picric acid. The reaction was noted a t different time intervals. The results are given in Table I. 5 . Gravimetric Study of the Reaction between Naphthalene and Picric Acid.-Known amounts of picric acid and naphthalene were kept in two bulbs with capacities of 20 and 30 cc., respectively. These bulbs were connected to a tube through a B-14 ground-glass joint so that the bulbs could be detached whenever required. This tube had another side tube with a stopcock which was connected to a vacuum line. The apparatus was evacuated so that the whole of i t was filled with naphthalene vapor. (The vapor pressure of naphthalene is much greater than that of picric acid.) Naphthalene vapors reacted with picric acid in the other bulb. The rate of reaction was measured by noting the weight of picric acid in the other bulb a t definite time intervals. The data are recorded in Fig. 5 , where the square of the weight of the naphthalene absorbed is plotted against time (days).
Results Results are given in Tables I and TT and in Fig. 1, 2, 3, and 5. Discussion The following equation4 was found to fit the data $' = 2kit exp(-pE)
where 5 is the thickness of the product layer; t is the time; ki and p are constants. The equation .f2 = kt (3) N. B. Hannrty, "Semi-conduotors," Reinhold Publishing Gorp., New York, N.Y . , 1959. (4) W. Jander, 2. anorg. allgem. Chem., 166, 31 (1927).
R. P. RASTOGI,P. S. BASSI,AND S. L. CHADHA
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Vol. 67
log Fig. 1.-Kinetic data for reaction between naphthalene and picric acid a t different temperatures: X, 45 f 1" (25 mesh); f3, 61 f 1" (50 mesh); +, 45 f 1' (50 mesh); A, 61 f 1" (100 mesh); 0 , 3 5 f 1" (25 mesh); 8,61 f 1 (200 mesh); 8 , 4 5 f 1" (100 mesh); h,35 f 1" (50 mesh); X , 35 f 1" (100 mesh); 0 , 45 f 1" (200 mesh); o, 35 f 1" (200 mesh). O
-350
Fig. 3.-Kinetic
-3.40
-330
.
~
~~
-320
r-
~
-3.10
data for reaction between anthracene and picric acid a t various temperatures.
TABLE I STC'DY O F
REACTION WITH
XOJPOROUS SAMPLES O F PHEK-
AWTHRENE AND
PICRIC ACID
Time, t (hr.)
Thickness of the product layer, 5 bm.)
0.0 18.0 25.0 42.0 50.0 70.0 76.0 129.0
0.0 .61 .64 .75 .79 .84 .86 .98
lO$(Y/ t)
Fig. 2.-Kinetic data for reaction between phenanthrene and picric acid a t various temperatures: I, 64 f 1" ( 2 5 mesh); 11, 45 f 1" ( 2 5 mesh); 111, 64 f 1" (50 mesh); IV, 45 + 1" (50 mesh); V, 64 f 1" (100 mesh); VI, 35 f 1" (25 mesh); VII, 45 f 1" (100 mesh); VIII, 35 f 1" (50 mesh); IX, 35 f 1" (100 mesh).
does not fit the data. For testing eq. 1, log (E2/2) was plotted against 5. Straight lines were obtained in all the cases. Figures 1 to 3 show that the kinetic data obey eq. 1. The values of ki and p as determined by the method of least squares are given in the following tables for naphthalene, phenanthrene, and anthracene. It is significant to note that p is practically independent of temperature and particle size for each hydrocarbon. Theseare0.21 f 0.01, 1.7 f 0.01, and 3.2 f
0.66 for naphthalene, phenanthrene, and anthracene, respectively. From the values of ki at different temperatures, it is easy to compute the values of the entropy of activation AS*, enthalpy of activation AH*, energy of activation E and C, if we assume that the temperature dependence of Ei is given by the equation
hi
+-E/RT
(2)
where C is the frequency factor and E is the energy of activation. The values of energy of activation for different reactions are given in Table 111. ( 5 ) There is larger uncertainty in this value because only two kinetic measurements a t 64 i lo and 45 =I= lo could be made with particles of 100 rnesh/cm.'4
REACTION BETWEEN HYDROCARBONS AND PICRIC ACIDIN SOLIDSTATE
Dec., 1963
5. The energy of activation is affected by the par-
TABLE I1 PARAMETERS O F EQUATTON 1 FOR REACTION BETWEEN CARBONS AND PICRIC ACID Temperature, "C.
Particle size, mesh/om.s
ki, mm.s/hr.
HYDRO- ticle size.
p, mm.-1
(A) Reaction between naphthalene and picric acid 61 f 1
45 zk 1
35 i 1
5.89 2.98 1.61 6.05 3.27 1.60 0.94 3.04 1.44 0.75 0.415
50 100 200 25 50 1a10 200 25 510 100 2010
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0.20 .19 .18
.21 .20 .19 .24 .22 .22 .22 .22
Mechanism of Reaction.-There are three different aspects of reactions which ought to be considered : (i) the mechanism of purely chemical reactions between hydrocarbons and picric acid; (ii) the mechanism of propagation of reaction across the product layer; (iii) the mechanism of propagation of reaction in individual grain once the coating of naphthalene-picric acid compound is formed on the surface. We may schematically represent the course of reaction in the following manner, where the encircled N, P, and N P represent naphthalene, picric acid, and picrate, respectively. (a) In the preliminary stages the reaction takes place at the boundary.
(R) Reaction between phenanthrene and picric acid 64 f 1 25 4.69 X 1.40 1.62 2.17 x 50 1.05 X 1.86 190 2.82 x 10-2 1.64 45 f 1 25 1.48 X 50 1.97 1.97 0.48 x 100 6.39 x 10-8 35 i 1 25 1.78 3.16 x lo-$ 1.68 50 1.69 x 1.79 100
(C) Reaction between anthracene and picric acid 64 i 1 45 i 1
100 io0
4.14 2.39
x x
10-4 10-4
2.55 3.93
(b) Subsequently, diffusion of hydrocarbon across the product layer occurs either by vapor phase or surface migration or grain boundary diffusion.
TABLE I11 FOR REACTION BETWEEN HYDROCARBOKS ENERGY OF ACTIVATION AND PICRIC ACID Particle size, mesh/cm.z
E', kcal./mole
C,mm.a/hr.
(A) Reaction between naphthalene and picric acid 25 13.4 8.28 x 109 50 11.4 1.86 X 10s 100 10.6 1.03 X 108 (B) Reaction between phenanthrene and picric 25 9.4 0.70 X 50 9.4 0.26 X 100 8.5 0.25 X
acid lo6 106 los
(C) Reaction between anthracene and picric acid 100 5.7 2.134
The surface migration and grain boundary diffusion may be visualized as
For the sake of comparison the values of ki for the three hydrocarbons a t 45 f 1' and with particle size 100 mesh/cm.2 are recorded in Table IV. TABLE IV Substance
kl,mm.a/hr.
Naphthalene Phenanthrene Anthracene
1.60 4.8 x 2.39 x 10-4
p , mm.-'
0.19 1.97 3.93
The broad features of the analysis of the kinetic data may be summarized as follows. 1. The parameter p is independent of temperature and particle size. 2. The value of ki increases as the particle size increases; ki appears to be directly proportional to the square of the radius of the individual particle. 3. The value of lci increase in the order: naphthalene > phenanthrene > anthracene. 4. Energy of activation increases in the order: naphthalene > phenanthrene > anthracene.
(c) Finally, there occurs propagation of the reaction in the individual picric acid grain.
@ NP N P
Now several questions arise. How is the reaction propagated in the solid state? What is the mechanism of diffusion? The diffusion in the solid state may occur by any one of the following mechanisms: (1) bulk diffusion; (2) lattice diffusion; (3) grain boundary
Vol. 67
R. P. RASTOGI, P. S. BASSI,AKD S. L. CHADHA
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TABLE V DARKAND PHOTOREACTION BETWEEN ACIDAND PHENANTHRENE Particle size = 100 mesh/cm.2
COiiiPARTSON O F
tin^. Irr.
7 25 67 97
(Radius?.
(Radrusf.
Fig. 4.-Dependence of reaction rate on particle size: A, reaction between naphthalene and picric acid; B, reaction between phenanthrene and picric acid. I
1
4
6
8
10
12
14
16
18
20
Days. Fig. 5.-Kinetic data for reaction between naphthalene vapor and picric acid (solid); w is the increase in weight of picric acid in grams.
diffusion; (4) surface diffusion; and ( 5 ) vapor phase diffusion. Bulk diffusion or volume diffusion may involve dislodging of the molecules from their equilibrium positions or may involve diffusion through lattice defects. The former positively does not appear to exist since the energy of activation is not so high as to warrant it. Following observations are relevant in this connection. (i) The dark and the photoreaction between phenanthrene and picric acid proceed with the same velocity, as is clear from Table V. In the presence of ultraviolet light, the n-electrons are excited to higher electronic levels and consequently both reaction velocity and lattice diffusion should be accelerated. Since this was not observed, evidently the role of n-electrons is secondary in influencing the reaction kinetics.
Dark reaction (tiiqtanre moved, V I I I . )
0.015 .018 ,024
.025
PICRIC'
Photoreartion (iliqlnnre m o ~ ~ rm.) d ,
0 018 .021
,026 ,029
(ii) The most important evidence against the lattice diffusion is the absence of reaction temperature for picrates. We know that the reaction temperature is a specific temperature above which reaction is quite vigorous, whereas below this temperature the reaction is very slow. Since in the picrate formation reaction no evidence of the reaction temperature was detected, there appears to be very little likelihood of bulk diffusion taking place in the solid state reaction under study. Since these hydrocarbons have appreciable vapor pressure, one may suspect that initially spaces are filled with the vapor which consequently reacts with picric acid. We shall summarize experimental observations which are in favor of vapor phase diffusion. (a) Naphthalene and other hydrocarbons diffuse through the product layer, whereas picric acid does not. (b) The hydrocarbons have appreciable vapor pressure. (c) The reaction between naphthalene and picric acid takes place even if there is empty space between the two reactants in the capillary. (d) The reaction kinetics was studied by using nonporous samples of naphthalene and picric acid in the form of tablets prepared by melting or pressing the reactants. When these were kept in adjacent positions it was found that the picric acid tablet was covered with a fine coating of picrate. The evidence against the vapor phase mechanism is recorded at this point. (i) If diffusion occurs through vapor phase, the diffusion coefficient would be proportional to vapor presssure and the activation energy of the reaction should be equal to or greater than the heat of sublimation, The energy of activation and heat of sublimation are compared in Table VI. It is clear that the energy of activation is much less than the heat of sublimation. TABLE VI Hydrocarbon
Energy of activation for particles of 100 mesh/cm.z, kcal./mole
Heat of sublimation. kcal./mole
Naphthalene Phenanthrene Anthracene
10.6 8.5 5.7
15 17 20
(ii) Observations c and d are not corroborated in the case of other hydrocarbons. It would appear from the preceding arguments that it is quite likely that diffusion of naphthalene through vapor phase may be important but it is not so in other hydrocarbons. There is another very important feature of reaction kinetics which deserves mention. The rate constant ki is directly related to the particle size. I n Fig. 4, Ici is plotted against the square of the radius of the particles for naphthalene and phenanthrene. Straight lines are
E.M.F.STUDIESIN AQUEOUS SOLUTIONS
Dec., 1963
obtained in each case, showing that the reaction rate increases with particle size. This could not have happened in the case of vapor phase diffusion, as the surface area of both ithe reactants increases in the sarne manner which would ultimately lead to the same reaction rate. This also supports the belief that surface migration of the hydrocarbon molecules also probably plays some part in the reaction. In order to study the role of vapor phase in the overall reaction, kinetic studies were undertaken by keeping naphthalene and picric acid separately in two bulbs as described earlier. Naphthalene vapor reacted with picric acid and the total weight of the bulb having picric acid increased. The increase in weight, u', was noted a t different time intervals. Figure 5 shows that after a certain time interval the relationship
2573
w2 = k't -j- IC"
(3) is obeyed by the data where IC' and IC" are certain constants. The plot resembles the one that is usually obtained in the case of tarnishing reactiom6 Acknowledgments.-Thanks are due to Council of Scientific and Industrial Research for supporting the investigation. P. S. Bassi acknowledges the award of a Junior Research Fellowship. We are aleo indebted to Professor F. C. Tompkins, F.R.S., for helpful discussions through correspondence. It is a pleasure to acknowledge that most of the experimental work was done a t the Parijale University Chemistry Department, Chandigarh. (6) A. L. G. Rees, "Chemistry of the Defect Solid State," Methuen's Monographs on Chemical Series, London, 1964, p. 103.
ELECTROMOTIVE FORCE STUDIES I N AQUEOUS SOLUTIONS A T ELEVATED TEMPERATURES. IV. THE ACTIVITY COEFFICIENTS OF HYDROGEN BROMIDE AND POTASSIUM BROMIDE IN HYDROGEN BROMIDE-POTASSIUM BROMIDE MIXTURES BY M. H. LIETZKEAND R. W. STOUGHTON Chemistry Division, Oak Ridge h~atiunalLaboratory,1 Oak Ridge, Tennessee Received May 8, 196s The activi1,y coefficient of HBr in HBr-KBr mixtures has been studied to 150". At constant temperature and ionic strength the logarithm of the activity coefficient of HBr in the mixtures varies linearly with the molality of KBr. The activity coefficient of the KBr in the mixtures was calculated by using the parameters describing this variation and those for the variation of the activity coefficients of HBr and KBr with ionic strength in pure HBr or KBr mlutions. It was found that the activity coefficient of KBr varies less with changing ionic strength and temperature than does the activity coefficient of HBr in the same mixtures.
Previous papers in this series have described the determination of the standard potential of the Ag, AgCl electrode2 to 275 O, 1;he thermodynamic properties of hydrochloric acid solutionsS to 275", and the determination of the standard potential of the Ag, AgBr electrode, and the mean ionic activity coefficient of HBr4 to 200'. I n the present work e.m.f. measurements have been made in HBr-KBr mixtures to 150" so that the activity coefficient of HBr in these mixtures could be calculated. The cell used may be represented as Pt-H2 ( p ) HBr (rnz), KBr (m3)I AgBr-Ag
1
I n addition, values of the activity coefficient of KBr in the mixtures have been computed from the results of these measurements and from literature values for pure KBr solutions. Experimental The experimental apparatus and the preparation of electrodes and solutions were the same as described previously. 2 , 4 The e.m.f. measuremeiits were made on IIBr-KBr solutions of total ionic strength, approximately 0.01, 0.02, 0.034, 0.05, 0.067, 1.O, 1.8, and 3.8, in which the ionic strength fraction of HBr in the (1) Work performed for thP U. S. Atomic Energy Commission and for the Office of Saline Water, U. S. Department of the Interlor, a t the Oak Ridge National Laboratory, operated by Union Carbide Corp. for the U. 9. Atomic Energy Commission. (2) R. S.Greeley, W. T. Smith, Jr., R . W. Stoughton, a n d M. H. Lietzke, J. Phys. Chem., 64, 652 (1960). (3) R. S.Greeley, W. T. Smith, Jr., M. H. Lietzke, and R. W. Stoughton, ibzd., 64, 1445 (1960). (4) M. B. Towns, R. S.G ~ e e l e yand , M. €1. Lietzke, ibzd., 64, 1861 (1960).
mixture was 0.5, and in solutions of total ionic strength, approximately 0.4 and 1.0, in which the ionic strength fraction of HBr was either about 0.25 or 0.75 at about 25,60,90, 125, and 150". The e.m.f. values taken at the same temperature were reproducible to ea. h1.0 mv. In general they were more reproducible in the solutions containing a higher fraction of HBr. No drift of e.m.f. with time was observed.
Results and Discussion I n treating the results, the hydrogen pressure was calculated by subtracting the vapor pressure of the solution from the observed total pressure, while the vapor pressure of the solution was obtained by taking the vapor pressure of pure water a t the temperature of measurement from the steam tables5 and correcting for the presence of KBr and HBr in solution by Raoult's law. Each e.m.f. value was corrected to 1.00 atm. of hydrogen pressure by subtracting ( R T / 2 5 ) In fHz, where the hydrogen fugacityfH, was taken equal to the hydrogen pressure. The solubility of AgBr was neglected and the ionic strength was taken to be equal to the sum of the HBr and the KBr molalities. The corrected e.m.f. values E at each ionic strength were plotted as a function of temperature and the values corrected to the round values of the temperature, 25, 60, 90, 125, and 150". The temperature of measurement was never more than 1' from the corresponding round temperature. These corrected values are given in Table I. The activity coefficient yi of HBr a t each tempera( 5 ) "VDI-Wasserdsmpftafeln," edited by E. Schmitt, 4th Ed., SpringerVerlag, Berlin, 1956.
