R. P. RASTOGI AND N. B. SINGH
4446 coordinates consisting of two elements (one nonzero off -diagonal force constant) yield crossover only if the basic diagonal force field is asymmetric at one or more isotopic bonds. Many of the details of the results for two-element reaction coordinates can be related to the results obtained with single-element reaction coordinates. When the reaction coordinate contains three or more elements, crossovers in the temperature-dependent factor can be produced with symmetric diagonal force fields, as can “plateau” regions where the isotope effect is almost constant over a wide range of temperature. The details of such results, which require for their generation the use of two or more nonzero off-diagonal force constants, can be inferred only generally from those obtained with one such off-diagonal force constant value and therefore can be related to the results for single-element reaction coordinates only with difficulty. That is, with increasing complexity of the reaction coordinate, consideration of the isotope effect consequences of the motion to be those of a superposition of individual internal coordinate displacements becomes an increasingly inaccurate approximation. This research has shown that crossover and other
anomalies of temperature dependence can be generated (in a model system chosen for its impediments to such generation) by reasonable adjustments of the transition state force field. Whether or not the results reported here constitute a demonstration that such anomalies are prevalent in kinetic isotope effects is a matter of judgement and can be established firmly only by exploration of the behavior of a number of different model systems. Intermolecular isotope effects may be expected to have different properties than intramolecular isotope effects. Further, the inclusion of bending force constants among the parameters varied should drastically alter the frequency with which anomalies of temperature dependence are observed. When the possibilities thus afforded are added to those expected from selection of an imaginary frequency (as opposed to a zero frequency) for the reaction coordinate motion,27 the task of exploring even a single reaction is seen to be truly enormous, unless only four or five atoms are involved in the transition state. Methods for systematizing such exploration remain to be developed. Acknowledgment. This research was supported by the U. S. Atomic Energy Commission, COO-1142-78.
Solid-state Reactivity of Picric Acid and Substituted Hydrocarbons by R. P. Rastog?’ and N. B. Singh Department of Chemistry, Gorakhpur University, Gorakhpur, U.P . , India
+
(Received April 18, 1968)
+
+
The solid-state reactivity of picric acid acenaphthene, picric acid 0-naphthylamine, and picric acid pyrocatechol has been investigated. The results show that diffusion in the solid state is controlled by surface migration, in conformity with the earlier finding by Rastogi and Singh. It is found that molecules having a smaller size and molecules having greater symmetry are more favorable for surface migration.
Introduction Solid-state reactions between picric acid and naphthols, recently investigated by Rastogi and Singh,lb are a novel class of solid-state reactions, since the kinetics are controlled by surface migration. The rate of advance of the product layer when the reactants are kept adjacent to each other is given by (2
= 2kite-*P
(1)
where [ is the thickness of the product layer a t any time
migration of A would take place in the manner shown below
-e__t.
Using this model of surface diffusion, Rastogi and Singhlb have shown that
k,
= 4n?rr2Doe-E’RT
(2)
where Do is the diffusion coefficient, E is the energy of
t, and kl and p are constants. If A and B are the two reactants kept adjacent to each other and the reaction progresses in the direction of the arrow, the surface The Journal of Physical Chemistry
(1) (a) Visiting ‘Professor, Department of Chemistry, Indiana University, Bloomington, Ind. (b) R. P. Rastogi and N. B. Singh, J . Phys. Chem., 70, 3315 (1966).
SOLID-STATE REACTIVITY OF PICRIC ACID
4447
activation, and n and r are the number and radius of the particles of B, respectively. Very little is known about the mechanism of surface migration. The purpose of this paper is to get an insight into the nature of mechanism. Surface migration would be expected to be favored by symmetrical and planar molecules, since such molecules can move on the surface relatively easily as compared with unsymmetrical molecules, particularly when the surface is not perfectly smooth. The unsymmetric rnolecules would get entangled on the surface. I n order to examine this point, the solid-state reactivity of acenaphthene, &naphthylamine, and pyrocatechol, which have varying degrees of asymmetry, has been studied. The influence of the size of the molecules on solid-state reactivity has also been investigated. The results are reported in this article.
Experimental Section Materials and Purijications. Picric acid (BDH) was purified as described earlier.lb Acenaphthene was first distilled under vacuum and then recrystallized from absolute alcohol. The melting point of the purified sample was 94.2'- Pyrocatechol and 8-naphthylamine were purified by successive recrystallization from distilled water. The melting points of the purified samples were 103.8 and 111.0', respectively. Kinetic Study of the Solid-state Reaction. The procedure employed for studying the kinetics of the solidstate reaction between (i) picric acid and acenaphthene, (ii) picric acid and P-naphthylamine, and (iii) picric acid and pyrocatechol was the same as described earlier.lbI2 The kinetics were also studied when the reactants were separated by a known distance. Such a study could not be made for &naphthylamine, since a negligible reaction occurred under such conditions. Six to seven runs were made for kinetic studies at each temperature and for a definite particle size. Equation 1 fits the kinetic data when the reactants are in contact. On plotting log ( 4 2 / t ) against 4, a straight line is obtained. The parameters of eq 1 for different temperatures and for different particle size are
given in Tables I and 11, respectively. These are the mean parameters obtained from six runs. Table 11: Influence of Particle Size on ki (45 i l o )
Reactants
Acenaphthenea
Pyrocatechola
Particle size, mesh
ki, cml/hr
2.23 X 1.51 X 1.14 X 4.77 x 1.51 X 1.34 x 1.02 x 4.35 x
120-150 170-200 200-240 240-270 100-120 120-150 170-200 200-240
P*
om-'
10-3
10-4 10-8 10-8 10-8 10-4
13 f 1 13 f 1 16 f 1 12 i 1 14 f 2 21 i 2 20 f 2 18 f 2
The higher values of ki aa compared with those reported in Table I are due to the fact that since in the latter case the particle size waa above 150 mesh the material contained large numbers of particles finer than 270 mesh.
Table 111: Kinetic Parameters When the Reactants are Kept Apart (Partizle Size, above 150 mesh) Temp (*I), Reactants
OC
Acenaphthene
45
d, om
5.6 X 2.8 x 6.2 x 1.5 x 3.0 x 5.7 x 1.1 x 2.2 x 1.5 X 1.7 x 2.6 x 3.8 x 2.5 X 3.3 x 6.1 X 9.6 X 4.9 X 8.3 x 10.6 X 12.5 X
1.401 0.825 0.467 0.218 1.283 0.835 0.567 0.253 1.252 0.909 0.617 0.335 0.810 0.763 0.446 0.256 1.496 1.226 1.006 0.815
55
65
Pyrocatechol
P',
cmE/hr
45
65
10-8 10-6 10-6 10-4 10-5 10-6 10-4 10-4
om-1
2.5
2.0
1.3 10-4 10-4 10-4 10-6
2.3
10-6
10-6 10-6 1.5 10-6 10-6 10-6
Table I: Influence of Temperature on ki (Particle Size, above 150 mesh)
When the reactants are separated by a distance d, the kinetic data are fitted by the equation
Temp
(*I), Reactants
Acenaphthene
p-Naphthylamine Pyrocatechol
O C
25 35 45 55 35 55 65 45 55 65
P,
ki, cmp/hr
(2.50 f 0.00) X (3.33 i 0.14) X (7.92 f 0.00) X (1.47 f 0.06) X (2.44 f 0.07) X (7.92 f 0.00) x (1.25 f 0.02) X (1.54 f 0.28) x (2.34 i 0.06) X (5.47 f 0.13) X
cm-1
lo-' 10-6 10-6 10-4 10-8
35 i 8 22 f 8 14f8 14 f 8 55 f 1 57i1 57f 1 19f2 14 f 2 15 f 2
+
t2 = kt c (3) where k and c are constants. k is found to depend on d in the following manner
k
=
Afe-P'd
(4)
where A' and p' are constants and d is the length of the air gap. When log k is plotted against d, a straight line (2) R. P. Rastogi, 66,2707 (1962).
P.8. Bassi, and S.L. Chaddha, J . Phf48. Chem., Volume 79, Number IS December I968
R. P. RASTOG~ AND N. B. SINGH
4448 is obtained. The parameters of eq 4 are given in Table 111. When log kt is plotted against 1/T, a straight line is obtained. The values of the energy of activation ( E ) , the free energy of activation for diffusion (AG*),the entropy of activation for diffusion (AS*),and the enthalpy of activation for diffusion (AH*) are given in Table IV. From Table IV, it appears that except for anaphthol, the entropy of activation for diffusion in all cases is negative. This means that the entropy in the activated state is less than that in the initial state. I n other words, the activated state is more ordered. It is evident that the vapor-phase diffusion would involve a disordered state and AS* would then be positive, This means that vapor-phase diffusion is not significant in the above reactions. This is also confirmed by the lower values of energy of activation as compared with the heat of sublimation. ~~~
~~
AS*, cal/ mol deg
Particle
E,
AH*,
A@,
sire,
kcal/ mol
koal/ mol
11 10 9 18 9 10 8 5
12 14 13
-6 -13 -13
18
+18
14 17 23 23
-14 -23 -49 -58
Reactants
mesh
kcal/ mol
Acenaphthene 8-Naphthylamine Pyrocatechol a-Naphthola @-Naphthol0 Naphthaleneb Phenanthrene* Anthraceneb
Above 150 Above 150 Above 150 Above 150 Above 150 100 100 100
11 11 10 19 10 11 8 6
Ir
ki,
Reaotants
cmP/hr
Ref
1.51 X 10-8
a
x
10-4
b
4.80 X 10-6
b
2.39 X 10-8
b
4.68
a
This work.
R. P. Rastogi, P. S. Bassi, and S. L. Chaddha,
J. Phys. Chem., 67, 2569 (1963).
~
Table IV: Energy of Activation, Enthalpy of Activation, Free Energy of Activation, and Entropy of Activation for Diffusion
See ref lb.
Table V : Influence of Molecular Size on k , (Particle Size, 100 mesh; 45 & l o )
Table VI: Dependence of ICd on Dipole Moment (Particle Size, above 150 mesh; 35 f l o ) Dipole moment,d D
Reactants
03
his
cml/hr
Ref
0.00
4.22
x 10-4
a
0.79
3.35
x
10-4
b
1.91
1-84 x 10-4
C
HIC-CHp
cb OH
R. P. Rastogi, P. S. Bassi, and S. L. Chaddha,
J. Phys. Chem., 67, 2569 (1963).
We will now examine the dependence of k, on particle size. If temperature is kept constant, it follows from eq 2 that
kt = er2
(5)
where e = 4nlrDoe-E/RT. It is found that kt varies directly with the square of the radius of particle, since when ki is plotted against r2 a straight line is obtained. This further confirms the fact that surface migration plays an important role in solid-state diffusion in the present case, in agreement with our earlier finding.’b Table V shows how IC, depends on the size of reactant molecules. It appears that surface migration of bulky molecules is more difficult as compared with simpler molecules. This is expected. In order to understand the nature of surface migration, it is interesting to compare the values of k, for molecules having different degrees of asymmetry. It would be easier for a flat molecule to drift on the surface, The asymmetry would depend on the dipole moment, The Journal of Physical Chemistry
a R. P. Rastogi, P. S. Bassi, and S. L. Chaddha, J. Phys. Chem., 67,2569 (1963). b This work. See ref lb. d See ref 3.
and hence the values of k, should decrease with an increase in the values of the dipole moment.s The trend of values recorded in Table VI justifies this conclusion. I n order to ascertain the extent of asymmetry in a molecule, the coordinates of the center of gravity of acenaph thene, a-naph tol, /3-naphthol, and /3-naphthylamine with respect to the center of gravity of naphthalene as the origin were estimated. The line joining the carbon nuclei in 9 and 10 positions was taken as the axis, whereas the plane of the naphthalene molecule was taken as the z-y plane. The coordinates of the center of gravity are given in Table VII. It is clear from Table VI1 that as the asymmetry increases (3) A. L. McClellan, “Tables of Experimental Dipole Moments,” W. A. Freeman and Co., San Francisco, Calif., 1963.
SOLID-STATE REACTIVITY OF PICRIC ACID
4449
Table VII: Coordinates of the Center of Gravity Moleculesa
Naphthalene Acenaphthene a-Naphthol @-Naphthol @-Naphthylamine
X
1/
0.00 0.00
0.089 0.397 0.403
0.00 0.550 0.371 0.115 0.150
z
0.00 0.00 0.00 0.00 BO.00
5 The data for bond distances and bond angles were taken from structure reports (N. V. A. Oosthoek’s Uitgevers Mij, Utrecht, 1948-1957). For the purpose of calculation the first four molecules are considered to be planar.
the value of ICl decreases. I n the case of a-naphthol, @-naphthol, and /%naphthylamine the shift of the center of gravity r (r = d z 2 y2 z2) is 0.381,0.413,
+ +
and 0.432, respectively. The values of kt also show this sequence, showing thereby that the asymmetry of the molecules plays an important role in the solid-state reaction where surface migration plays a predominant role. From the above study, surface migration may be pictured as follows. The surface of the reactant which diffuses into the other is in a state of disturbance. The molecules at the surface have a tendency t o vaporize. However, they sometimes find it easier to drift on the surface. The tendency of surface migration is affected by the asymmetry of the molecules. I n a similar manner, bulky molecules have a smaller tendency for surface migration. Acknowledgment. N. B. S . is thankful to the Council of Scientific and Industrial Research for supporting the investigation.
