SOLID-STATE REACTIONS BETWEEN PICRIC ACIDAND NAPHTHOLS
3315
Solid-state Reactions between Picric Acid and Naphthols
by R. P. Rastogi and N. B. Singh Chemistry Department, Gorakhpur University, Gorakhpur, I n d i a
(Received October 29, 1965)
The solid-state reactions between naphthols and picric acid have been investigated. The kinetics have been studied a t several temperatures and for particles of different sizes. The results are fitted to an equation which has been theoretically deduced. The kinetics have also been studied when the reactants are separated spatially by a gap. Results show that surface migration is primarily involved in the diffusion process. A study of the kinetics of inward penetration of naphthols in picric acid grains has also been made. In order to understand the nature of the interaction between naphthols and picric acid, the phase diagram, ultraviolet and visible spectra, infrared spectra in trichloroethylene, and infrared spectra and reflectance spectra in the solid state have been studied. The stability constants of picrates were estimated using the distribution method. The dipole moment of picrates was also measured. The charge-transfer or hydrogen bond interaction is not involved in the formation of picrates. It is likely that dipole-dipole interactions may be prominent .
Introduction
where is the thickness of the product layer a t any time t and ICl and p are constants. On the basis of the available evidence, it was concluded that the reaction is diffusion controlled. Ah attempt was made to elucidate the mechanism of diffusion, but no definite picture could be obtained. In the present communication, results for the solid-state reaction between naphthols and picric acid have been presented and discussed in a manner which gives positive informastion about the mechanism of lateral diffusion as well as inward penetration of the reactants in the picric acid grains. A theoretical justification for eq 1 has also been given. The results of experimental studies investigating the nature of the interaction between naphthols and picric acid are also reported in this communication.
purified by repeated distillation under vacuum. The melting points of pure samples of a-naphthol and pnaphthol were 96 and 122", respectively. Picric acid (BDH) was purified by successive recrystallization from absolute alcohol. The melting point of the purified sample was 122.5". Chloroform (BDH) was washed several times with cold, distilled water to remove any ethyl alcohol present as impurity. It was dried over calcium chloride and fractionally distilled. The density of the purified sample (bp 61') at 35" was found to be 1.4603 g/ml. Dioxane (AR, BDH) was refluxed over sodium for 15-20 hr. It was fractionally distilled and stored over sodium wire (bp 101.2-11.5"). Kinetic Study of the Solid-State Reaction. The procedure employed for studying the kinetics of the reaction between a-naphthol and picric acid and pnaphthol and picric acid was the same as described earlier.' The studies were made at different temperatures and for particles of different sizes. The kinetics were also studied when the reactants were separated by a known distance. Such a study could be made for only a-naphthol since no reaction occurs witjh picric acid and @-naphtholwhen they are kept at a distance
Experimental Section Materials and Puri$cation. Both a-naphthol (Extra pure, E. Merck) and @-naphthol (AR, BDH) were
(1) R. P. Rastogi, P. S. Bassi, and S. L. Chaddha, J. P h y s . Chem., 66, 2707 (1962). (2) R. P. Rastogi, P. S. Bassi, and S. L. Chaddha, ihid., 67, 2569 (1963).
Kinetic studies of solid-state reactions between naphthalene, phenanthrene, anthracene, and picric acid have already been described in earlier communications.'t2 The kinetic results were found to obey the empirical equation ~2
= ~k,te-*~
(1)
Volume 70, Number 10 October 1966
3316
R. P. RASTOGI AND N. B. SINGH
I
-7
0
'02
'04
-
96
eo8
Figure 2. Dependence of reaction rate on temperature: 0 , reaction between a-naphthol and picric acid; 8,reaction between p-naphthol and picric acid. ,IO
,I2
3Ccm)
Figure 1. Kinetic data for the reaction between a-naphthol and picric acid at different temperatures.
apart in the Pyrex capillary. The results are plotted in Figures 1-4. Gravimetric Studies. The method used for gravimetric studies was the same as that described previously.2 Study of the Spectra. Absorption spectra of ru-naphthol, picric acid, and their complexes in alcohol in the ultraviolet and visible regions were obtained with a Carl-Zeiss spectrophotometer. The spectra are given in Figures 7 and 8. Measurements with a Gary 14 R recording spectrophotometer were also made for confirmation. Infrared spectra in Nujol mull were obtained with a Carl Zeiss U.R.-10 spectrophotometer using sodium chloride optics, The same spectra using trichloroethylene were measured employing lithium fluoride optics. The Journal of Physical C h m i s t r u
The reflectance spectra of naphthols, picric acid, and the complex were obtained with a Beckman DU spectrophotometer, using the reflectance attachment and R!IgC03 as the reference. Phase Diagrams. Solid-liquid equilibrium data were obtained by the thaw-melt method.8 The temperature was measured with a thermistor. Partition Studies. To determine the formation constant of the complex, the distribution method was e m p l ~ y e d . The ~ ~ ~ equation used by Foster, et a1.6 for calculation of the equilibrium constant is only approximate. A rigorous derivation yields
K =
Y
P[Z
+ YkZ - P
+ k Z 2 - Y - YkZ + P ]
(2)
where K = stability constant, Y = molarity of picric acid in chloroform layer in presence of napthol, P = (3) R. P. Rastogi and K. T. R. Varma, J. C h m . SOC.,2097 (1956). (4) P. D. Gardner and W. E. Stump, J. Am. Chem. SOC.,79, 2769 (1957) . (5) R. Foster, D.L. Hammick, and 9. P. Pearce, J. Chem. SOC.,244 (1959).
SOLID-STATE REACTIONS BETWEEN PICRIC ACIDAND NAPHTHOLS
3317
DK 03, Wlssenschaftlich-Technische Werkstatten, Weilheim, Germany) at 35" which was maintained by circulating water around the cell from a thermostat. The instrument was calibrated using liquids of known dielectric constants. The refractive index of solutions in dioxane was measured with a Carl Zeiss refractometer. The dipole moments were estimated by the method followed by Richards and Walker.6 The results are recorded in Table VI.
Results and Discussion The kinetic data for a-naphthol as well as p-naphtho1 at various temperatures and for particles of different sizes are best fitted to eq 1. This is supported by Figure 1. ICi is found to depend on temperature as well a~ on particle size. The values of k, and p for particles of a definite size at various temperatures are given in Table I. The values of these quantities for particles of different sizes at a fixed temperature are recorded in Table 11.
-
d(cm;) Table I: Influence of Temperature on ki"
Figure 3. Dependence of rate constant on the length of the air gap.
7
Temp,
ki,
P,
Reactants
OC
cmt/hr
cm-1
a-Naphthol
25f 1 35 f 1 45 f 1 55 f 1
3.9 X 1.84 X 5 . 7 9 x 10-4 1.45 X
41.2 48.6 45.2 42.0
@-Naphthol
35 f 1 45 f 1 55 f 1
6.74 x 9.97 X 1.87 X
74.67 f 6 . 5 64.07 f 6 . 5 55.98 f 6 . 5
I I
f2.6 f2.6 f2.6 f2.6
Particle size, below 150 mesh.
Table 11: Influence of Particle Size on kt" 1
2
3 ---f
4
5
6
7
r%oiicm)
Figure 4. Dependence of reaction rate on particle size: 0, reaction between a-naphthol and picric acid; @, reaction between @-naphtholand picric acid.
molarity of picric acid in chloroform layer in absence of naphthol, Z = molarity of naphthol in chloroform, k = solubility depression effect. I n the derivation of eq 2 higher powers of (1 kZ) have not been neglected. Equilibrium constants were calculated with the help of eq 2. These are recorded in Table V. Determination of Dipole Moment. The dipole moments of naphthols, picric acid, and picrates in dioxane were measured with the help of a dekameter (Type
Reactants
Mesh sire
ks, cml/hr
p, cm-1
a-Naphthol
100 120 170 200 240
7.0 x 4.15 x 3.97 x 1.87 x 1.15 x
10-4 10-4 10-4 10-4 10-4
19.3 f 6 . 1 3 6 . 5 f6 . 1 38.9 f 6 . 1 45.1 f 6 . 1 38.2 f 6 . 1
@-Naphthol
120 200 240
2 . 2 3 x 10-4 6.56 x 5 . 0 x 10-5
73.7 f 5 . 4 64.2 f 5 . 4 79.5 f5 . 4
+
Temperature, 45 f l o .
(6)
J. H. Richards and S. Walker, Trans. Faraday Soc., 57,
406
(1961).
Volume 70, Number 10 October 1966
3318
R. P. RASTOGI AND N. B. SINGH
16
15
I4 13 I2 II h
E, 10
\ow
9:
38
1: 5 4
3
2 1
0 20
40
60
80
-
100
120
t
140
160
180
220
200
240
(hours)
Figure 5. Kinetic data for the reaction between a-naphthol (vapor) and picric acid (solid).
Equation 1 is essentially empirical in nature. The derivation usually given is not correct.’ However, it can be theoretically justified on the basis of the following arguments. / i h G AiB
*H
Let us consider two species A and B which are in the solid state. Let EF be the surface of separation. We suppose that molecules of A alone can migrate. We further suppose that migration of A beyond EF takes place by jumps or by surface migration as shown in the illustration above. The interface reaction is practically instantaneous so that any molecule of A striking B at G or H is used up in the chemical reaction. f measures the distance of maximum penetration of A molecule in B from plane EF. The J O U Tof ~Physical Chemistry
Let f ( f ) be the probability of a free jump terminating in the adsorption of molecules of A and subsequent chemical reaction. The probability that no molecular encounter of A and B takes place between f and f df is proportional to df and would be equal to pdf, where p is independent of f . At this stage we need not bother about the factor on which p depends. The probability that the encounter occurs between E and E dE is (1 - pdf). The probability that a collision takes place in the distance (f df) is equal to the product of the independent probabilities of adsorption in f as well as in df. Hence
+
+
+
f(4 + df)
= fM(1
- PdE)
(3)
However, since
(4) (7) G . Cohn, Chem. Rev., 42, 628 (1948).
SOLID-STATE REACTIONS BETWEEN PICRIC ACIDAND NAPHTHOLS
3319
. . . k I
0
'2
11
-3
'4
e5
*6
; I
-8
'3
1.0
Mole- frotion of L- naphlhol Figure 6. Phase diagram of a-naphthol and picric acid.
0
11
*2
-3
*4
*5
-6
e7
e6
-9
0
Mole-fractiono_f p nophthol Figure 7. Phase diagram of &naphthol and picric acid.
Volume 70,Number 10 October 1968
R. P. RASTOGI AND N. B. SINGH
3320
I
?Q
240
260
280
-J
300
320
340
360
380
460
("
Figure 8. Ultraviolet spectra: 0 , a-naphthol; 0 , picric acid; €4, a-naphthol picrate.
face EF, the concentration C of the molecules striking a t t would be given by
we have (5)
Since f(0) would be unity, we have on integration of eq 5 f(t) = e-Pt (6) If Co is the concentration of the species A a t the interThe Journal of Physical Chemistry
c = CoeFPE Using Fick's law of diffusion, we have
(7)
SOLID-STATE REACTIONS BETWEEN PICRIC ACIDAND NAPHTHOLS
3321
comparison. These were calculated from the known values of heats of fusions and heats of vaporization. 9
Table 111: Energy of Activation for Diffusion
d
l 1.0 ’ k
I 380
- . 420
400
440
-A
460
480
500
(mr)
Figure 9. Absorption spectrum of a-naphthol picrate.
where A is the surface area, D is the diffusion coefficient, and bc/bx is the concentration gradient. Because of the speed of the reaction, very few molecules are actually left within a thin layer of the advancing product zone and therefore the concentration gradient can be taken to be nearly equal to C/E, where the value of C is given by eq 7. Therefore we can write
(9)
Reactants
Heat of sublimation, kcal
Energy of activation, kcal
a-Naphthol p-Naphthol
21.7 19.9
19.1 IO. 1
We shall discuss the following aspects of the reaction mechanism which are worth considering: (1) mechanism of lateral diffusion when bulk quantities of reactants are kept side by side; (2) mechanism of diffusion of the reactant in picric acid grains; (3) mechanism of chemical interaction. Mechanism of Lateral Diffusion. The lateral diffusion can occur by surface migration, grain-boundary diffusion, or diffusion through vapor phase. Experiments show that diffusion does not occur through the vapor phase. From Table 111, it is clear that the energy of activation is less than heat of sublimation. If A. is the surface area of picric acid grains, dnldt, the number of molecules of naphthols per unit time striking these grains from the vapor, would be given by dn P -=A0 ____ dt d2rMRT where P is the pressure, R is the gas constant, T is the temperature, and M is the molecular weight. If the vapor is assumed to behave ideally, it follows that
Integration of eq 9 gives
-dn= A 0 Poe - AsJr’RT dt d2nMRT ~
t2 = 2ADte-”
(10)
which is similar to eq 1 with k t =’ AD. Since the diffusion coefficient depends on temperature, we have
ICi
=
4nar2Doe-E/RT
(11)
where Dois a constant and E is the energy of activation involved in diffusion. Surface area A would be given by n(47r2),where n is the number of particles and r is the radius of particles. For particles of definite size, log k , would vary directly as the reciprocal of absolute temperature. When values of log IC, are plotted against the reciprocal of absolute temperature, straight lines are obtained (Figure 2). From (11) it follows that the slope gives the activation energy for diffusion. The energies of activation are given in Table 111. The values of heat of sublimation have also been given for the sake of
where Po is a certain constant and ASH is the heat of sublimation. The rate of reaction in the present case is diffusion controlled, and hence, if diffusion occurs through vapor phase, the energy of activation should be equal to the heat of sublimation as z/?i would not vary much within a small temperature range. Since energy of activation is less than the heat of sublimation, it follows that diffusion via vapor phase is not prominent. The rate of reaction when the reactants are kept adjacent to each other and when the reactants are separated by a distance (air gap) is not the same. I n ~
~~
(8) “International Critical Tables,” Vol. 5 , McGraw-Hill Book Co., Inc., New York, N. Y., 1929, p 134. (9) 0. E. May, J. F. T. Berliner, and D. F. J. Lynch, J . Am. Chem. SOC, 49, 1012 (1927).
Volume 70, Number 10 October 1966
R. P. RASTOGI AND N. B. SINGN
3322
I 200
1
240
280
320
360
400
440
4a0
520
560
600
640
686
560
600
640
680
----A(mF> Figure 10. Reflectance spectra: 8,a-naphthol; 0, picric acid; 0 , a-naphthol picrate.
01 200
240
320
280
360
400
4
440
480
520
A “1
Figure 11. Reflectance spectra: 8,p-naphtho1; 0, picric acid; 0 , p-naphthol picrate.
the former case the kinetic data obey eq 1, while in the latter the results are described by the equation ,$2
= kt
(14)
where k is a certain constant. Values of k for different lengths of air gap d are recorded in Table IV. I n Figure 3, log k has been plotted against d, which shows that t’hefollowing relationship is obeyed k =
Ae-pId
The Journal of Physieal Chemislry
(15)
where p’ and A are constants. The values of p’ are given in the last column of Table IV. It should be noted that eq 15 holds for the case of a-naphthol only. From eq 15 it follows that when d = 0, k = A and further when d = 00, k = 0. The analysis shows that the vapor phase diffusion is certainly not significant. No reaction occurs when the reactants are separated by a gap in the case of ,&naphthol. This further confirms that the vapor phase diffusion is not prominent. Since the magnitude of the energy of activation is
SOLID-STATE REACTIONS BETWEEN PICRIC ACIDAND NAPHTHOLS
3323
gOl
100
Table IV : Kinet,ic Parameters for the Reaction between &-Naphthol and Picric Acid When the Reactants Are Kept Apart"
80
Temp,
d,
k,
P',
O C
cm
cm*/hr
cm-1
45 & 1
1.473 0.441 0.375 0.185
1 . 0 x 10-6 7.0 x 1 . 1 x 10-5 1.4 X
1,727
1.475
4.0 x 1 . 3 x 10-5 1 . i x 10+ 3 . 7 x 10-6
2.006
55
*1
0,900 0.ii1
0.332
::p 50
PO
IO.
0
3000
' Particle size below 150 mesh.
3200
3400
3806
3600
Frequency (cmj
Infrared spectrum of a-naphthol in trichloroethylene.
not high, it appears that bulk diffusion also does not take place. The only alternative left is the surface migration or grain-boundary diffusion. Surface migration seems to be more likely since k z depends on the surface area of particles (Figure 4). From Figure 4 it follows that a relation of the type k , = er2 holds good, where r is the radius of particles and 8 is a constant. This finding is in agreement with eq 11. The value of e for a-naphthol is 12.06 hr-' and that for 6-naphthol is 5.5 hr-I. Mechanism of Diflusion of the Reactant in Picric Acid Grains. Studies on single crystals are necessary to throw light on this aspect. However, some information can be extracted from the gravimetric study of the reaction. The results of such a study are plotted in Figure 5. There is an induction period and the subsequent reaction is probably diffusion controlled. constant satisfies the data, The equation w2 = k't i is the increase in weight and t is the time. The where u reaction stops after a certain time interval. The amount of a-naphthol used up in the reaction at 55 and 64" was 0.8 and 1.6%, respectively, of the theoretical value for complete reaction with picric acid. This suggests that an interface reaction is mainly involved and the penetration of the reactant into picric acid is not deep. The mechanism of penetration is, however, not clear. The energy of activation for the case of a-naphthol is 24.5 kcal. This suggests that inward penetration may involve a vacancy mechanism. Mechanism of Chemical Interaction. I n order to have an idea of the mechanism of interaction, phaseequilibrium studies were undertaken. Solid-liquid equilibrium data recorded in Figures 6 and 7 show that 1 : l complexes are formed in the solid state. Since the maximum is flat, it appears that the complex is dissociated in the liquid state.lO
+
2 34 e
s
E
d
70-
60.
so.
40: 30
20
_c_I.
Figure 13. Infrared spectrum of picric acid in trichloroethylene.
Hypothetically, it would appear that picrates would form n-donor-n-acceptor complexes. Ultraviolet spectra of picrates as well as of naphthols and picric acid are given in Figure 8. Absence of any new absorption maximum in the case of the complex shows that a charge-transfer interaction is probably not involved. The spectrum of the complex in the visible region (Figure 9) also does not show any maximum. Since the phase diagram suggests that the picrates are dissociated in the liquid state, it was thought worthwhile to examine the reflectance spectra of the picrates in the solid state. The latter avoids the disturbing influence of the solvent if any. The reflectance spectra of the two complexes are given in Figures 10 and 11, which show that no new band is obtained. It appears that only a weak interaction is responsible for the for~
~~~
(10) R. P. Rastogi, J . Chem. Educ., 41, 443 (1964).
Volume 70, N u m b e r 10 October 1966
R. P. RASTOGIAND N. B. SINGH
3324
possibility of hydrogen-bond interaction or dipoledipole interaction. 1 1 , 1 2 However, hydrogen-bond interactions are not supported by infrared studies (Figures 12-14) since the OH stretching region ( ~ 3 6 0 0cm-l) in the case of a-naphthol picrate was exactly identical with that of a-napthol. The dipole moment of picrates shows that probably dipole-dipole interaction is most prominent. Table VI shows that the magnitude of the dipole moment is slightly greater than the sum of the dipole moments of the naphthol and picric acid.
1001
3200
3000
3400
3800
3600
4000
Table VI:
Dipole Moments of Picrates
Frequeiicv ccni;>
Figure 14. Infrared spectrum of a-naphthol picrate in trichloroethylene.
Substance
mation of picrates. The charge-transfer interaction has to be ruled out. Studies of the spectra give no information about the dipole-dipole interaction or dipole-induced dipole interaction for obvious reasons. More information about such interactions can be obtained from partition studies. Equilibrium constants and heats of formation for picrates estimated from distribution measurement are given in Table V. The values of equilibrium con-
Table V:
Heats of Formation of Picrates AH,
Reactants
K*S
K27
kcal/ mole
a-Naphthol picrate Naphthol picrate
3.00 f 0.17 5.09 f 0.07
2.32 =t0.13 4.06 f 0.22
-4.9 -4.3
@
stants were determined at 18 and 27". The magnitude of the heats of formation in the two cases indicates the
The Journal of Physical Chemistry
a-Naphthol @-Naphthol Picric acid a-Napht,hol picrate @-Naphtholpicrate
Dipole moment,a D.
2.01 (1.91)b 2.02 (2.01)* 2.04 (2.13)" 5.10 6.26
a The values in parentheses refer to the values obtained by previous workers. * A. E. Lutskii and L. A. Kochergina, Zh. See ref 6. Fiz. Khim.,33, 174 (1959).
It is clear that picrate formation is easily possible in the solid state simply because a loose type of interaction is involved. A gliding molecule is likely to enter easily into a sort of loose combination. Acknowledgment. N. B. S. is thankful to the Council of Scientific and Industrial Research for supporting the investigation. Thanks are also due to Professor C. N. R. Rao of the Indian Institute of Technology, Kanpur, for help rendered in the spectral studies. (11) D.Ross and I. Kuntz, J . Am. Chem. SOC.,76, 74 (1954). (12) P. D. Gardner, R. L. Brandon, N. J. Nix, and I. Y. Chtang, ibid., 81, 3413 (1959).
