144 HYDROSTATIC PRESSURE ON REACTION VELOCITY

THE INFLUENCE OF HYDROSTATIC PRESSURE ON REACTION VELOCITY.

BY M. W. PERRIN.

Received 15th July , 1937.

In the development of the theory of the mechanism and kinetics of chemical reactions, a study of the two variables, temperature and con- centration, has played the most important part. The large effects pro- duced by changes in the former have led to the concept of reaction be- tween molecules having an energy greater than the critical " activation

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M. W. PERRIN I 4 5

energy,” while the quantitative effects produced by changes in concen- tration are necessary in determining the order of a reaction and in calcu- lation of the collision rate between reacting molecules. This second variable has been mainly studied in gas reactions taking place at , or below atmospheric pressure, where relatively large changes in concen- tration can easily be obtained and where the simple gas laws may be applied with considerable accuracy.

Very little attention has so far been given to the possible effects of high hydrostatic pressure on chemical reactions. I t is, of course, well known that important effects can be produced in gas reactions, such as the synthesis of ammonia, by the application of pressures of several hundred atmospheres, and that they can be accounted for satisfactorily by the increase in concentration and by the reduction in volume taking place during the reaction. But it is likely that the application of con- siderably higher pressures may produce results of more fundamental importance and may contribute to a closer understanding of some of the outstanding problems in reaction kinetics.

The technical difficulties involved may have been responsible for the small amount of such work that has been done. Cohen and his col- laborators have studied the influence of pressures up to I 500 atmospheres on the kinetics of various reactions in dilute solution, and Conant has made a more general survey of the effect of pressure, up to 12,000 atmo- spheres, on organic reactions in the liquid phase, using the technique developed by P. W. Bridgman.3

An examination, along similar lines, of some 50 organic reactions of various types has been carried out in the Research Department of I.C.I. (Alkali) Limited, using pressures up to 3000 atmospheres and the results have been published by Fawcett and Gibson.* It was con- cluded that the rates of nearly all the reactions, which proceeded slowly at atmospheric pressure, were increased some 5-10 times at a pressure of 3000 atmospheres, and that those reactions which did not take place a t atmospheric pressure (in the absence of catalysts) could not be made to do so at 3000 atmospheres.

have shown that the rates of hydrolysis of esters and esterification of acids show increases up to 50 times under a pressure of 5000 atmospheres, and that various condensation reactions which do not normally occur in the absence of catalysts can be made to do so under this pressure.

I t was considered to be of interest to study the effect of pressure in greater detail in an attempt to obtain a clearer picture of the mechanism involved, and work has been carried out along these lines with various reactions taking place in dilute solution. Under such conditions changes in concentration, produced by the pressure, are relatively small, since the compressibility of most liquids is only of the order of 20-25 per cent. at a pressure of 12,000 atmospheres. Other effects must, however, be considered, such as those due to changes in the degree of solvation and in the degree of dissociation of the solvent. has shown that pressures up to 3000 atmospheres influence the electrical conductivity of aqueous and non-aqueous solutions of electrolytes to a

More recently, Newitt and his collaborators

Tammann

Cf. 2. physik. Chem., 1928, 138, 169. Proc. Nut. Acad. Sci., 1929, 15,680 ; J.A.C.S., 1930,52,1659 ; I932,54,629. The Physics of High Pressure, G. Bell & Sons, 1931. J . Chem. Soc., 1934, 386, 396. Ibid., 1937, 876. 2. anorg. Chem., 1929, 182, 353 ; 183, I.

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146 HYDROSTATIC PRESSURE ON REACTION VELOCITY

greater degree than can be accounted for by the volume changes and the effect on the mobility of the ions.

The work of Cohen and Moesveld was primarily concerned with the hydrolysis of esters and special attention was given to the nature of the solvent. They found tha t the increase in reaction velocity due to pressure was always greater when the ester was dissolved in a mixture of water and some organic solvent, and tha t the maximum effect was obtained when just sufficent of the latter was added to keep the ester in solution. The results were discussed in terms of the forces acting be- tween the molecules of the mixed solvent and the two parts of the ester and their disturbance by the hydrostatic pressure which will alter the intermolecular distances.

In the present work, single solvents only have been used and the rate of reaction has been measured as a function of pressure a t different temperatures. In this way sufficient data have been obtained for a calculation of the numerical constants A and E in the Arrhenius equation for reaction velocity, k = Ae-EIRT, and for a study of the variation of k, A and E with pressure.

Experimental Method. The initial experiments were carried out in a simple type of steel

reaction vessel, shown diagrammatically in Fig. Ia. The solution of the reactants, of known concentration, was placed

in a glass vessel (I) the open end of which was inverted under mercury PRESSURE

GAUGE

PRESSURE GAUGE a

OIL SUPPLY

a & FIG. I.

C

in a lining tube (2). Pressure was applied by means of a screw press and transmitted by a light mineral oil with which the whole system was filled. The steel reaction vessel was immersed in a thermostat, the temperature of which could be kept constant, at any desired value, to 0.1' C . The

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M. W. PERRIN I47

pressure was measured by a Bourdon type of spring gauge which was calibrated from time to time against a dead weight pressure balance. This method was used for work up to 3000 atmospheres. The technique was later somewhat elaborated so that samples of the solution could be with- drawn at intervals during the reaction without taking the vessel out of the thermostat or releasing the pressure. This apparatus is shown in Fig. ~ b . At the start of an experiment the solution was forced into the glass bell (I), through the valve (2), which was built into the head of the steel reaction vessel, displacing the mercury (3) in the vessel. The valve (2) was then closed and oil pressure applied through the tube (4) by the same method as before. From time to time the valve (2) was opened and a sufficient quantity of the solution for analysis forced out of the glass liner while the pressure was kept up by forcing more oil in through (4).

For pressures above 3000 atmospheres, this direct method of applica- tion was no longer suitable and another type of apparatus was used, which is shown diagrammatically in Fig. IG. A relatively low pressure was applied by oil, from a mechanically driven pump, to the top of a piston (I). The lower end of this transmits the pressure, which is increased in the ratio of the areas of the large and small ends of the piston, to oil filling the high pressure cylinder and the reaction vessel which is coupled directly to it. The solution of reactants was again enclosed in an inverted glass tube opening under mercury, and the steel reaction vessel was immersed in a thermostat.

The high pressure was calculated from the known ratio of the areas of the piston and the measured pressure in the top half of the apparatus. A correction was made for the friction of the piston in the cylinder by observing the low pressure readings at the end of the compression stroke and at the time when the tell-tale rod (2), attached to the piston, was seen to begin to move upwards when the pressure was released. In the low pressure range the results obtained in this way were compared with readings on a calibrated gauge which was attached to the high pressure cylinder, and it is estimated that the pressure readings are correct to better than 5 per cent. More detailed descriptions of the various types of apparatus used have already been published.’

Results. A summary of the reactions which have been examined, and of the

results is given in Table I. In the majority of cases the materials used were obtained from British Drug Houses Ltd., and they were always sub- j ected to a purification process by drying and fractional distillation before use. Details of the analytical methods used in following the various re- actions have been given in the original papers with Williams, Fawcett and Gibson,* together with the full results for the velocity constants a t different temperatures. The measured velocity constants have been corrected for the changes in concentration due to the compressibility and thermal expansion of the solvent, and are all expressed in terms of gram mols./litre/min.

The values of the constants A and E in the Arrhenius equation k = Ae-WRT (where R = 1.985 cals./gram. mol. and T is the absolute temperature) have been calculated, from the variation of the velocity constant with temperature, by the method of least squares.

In the table, the first and second columns give the reaction and the solvent in which it was studied. The third column gives the value of the velocity constant at atmospheric pressure and one temperature. The fourth and fifth columns give the values of the constants A and E a t atmospheric pressure. The sixth column gives the pressure in Kg./cm.2, (I Kg./cm.2 = 0.968 atmospheres). The seventh, eighth and ninth

Proc. Roy. SOC. A , 1935, 150, 223 ; Engineering, 1933, 136, 32. Proc. Roy. Soc., A , 1935, 150, 223 ; 1936, 154, 684 ; 1937, 159, 162.

In nearly all cases 0-1 normal solutions were used.

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148 HYDROSTATIC PRESSURE ON REACTION VELOCITY

columns show the changes in the velocity constant and in the values of A and E at the different pressures.

TABLE I.

k at I kg./cm2 and

T O .

7.73 x I O - ~

at 25' C.

4-12 x 1 0 - 3

a t 60" C.

3.24 x I O - ~

at 20' C.

2.90 x I O - ~

a t 40' C.

130'3 X 10-3

a t 60' C.

kp. k0

'ressure (g./cm.:

Reaction. Solvent.

Ethyl Alcohol

Water

A,.

1-28 x 1d3

3'5 x 10'2

3'85 x 109

1.3 x IO*

1-96 x 107

%--EL3

+ 60 - 400 - -

- 290

- 1400 -

- -2010

- 1650 -2150

-3550

+ 350 - -

f 830

+ 960 + I120 + 1990 + 910 -

+ 1400

Sodium ethoxide and ethyl iodide

1-60 2.06

2-41 2'22

1-89 2-64 4.22

4-70 6.38

Hydrol~& of SO-

dium rnono- chloracetate by NaOH

1.16

0.5 I

0.29

0.119

0'01 8

-

-

0'102

6.53 - -

26.9

Esterification of acetic anhydridc with ethyl al- cohol

Ethyl Alcohol

Toluene

Acetone

1.89 3'95 7'37

3'79 7'25 44'8

6.78

6.85 14'7 48.0

Pyridine and methyl iodide

Acetone 33'6 92'4 1170

Pyridine and ethyl iodide

1.93 x I O - ~

a t 40" C.

2-66 x I O - ~

a t 60" C.

2-13 x 107

266 x 107

14,390

16,740 Acetone Pyridine and n- butyl iodide

6-16

8.14

9-60

16.4

24.6

68.8

16.7

32.0

111'0

- - - -

0.661 x I O - ~

a t 60" C.

0.466 x I O - ~

at 60" C.

1'33 x 107

79.1 x 107

Acetone

Acetone

Acetone

Acetone

Acetone

Chlorofom

Pyridine and n- butyl bromide

Pyridine and iso- propyl iodide

18,610

Trimethyl amine and iso-propyl iodide

1.87 x 107 3,000 25-7 x I O - ~

a t 60" C.

0.307 X 10-3 at 60' C.

0.04 x I O - ~

a t 60' C. (Calcd. from

results at 80" C.)

3.76 X 107 16,880 I 6.0 Triethylamine and iso-propyl iodidc

Dimethylaniline and iso-propyl iodide

25'5 80

493 200

~~

3'23 x 10'~ at 25" C.

18.6 x 10'' 0.67 0.322 Decomposition of phenyl - benzyl- methyl-allyl-am. monium bromidt

29,600

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M. W. PERRIN I49

Discussion.

The reactions which have been examined fall into three main classes according to their kinetic behaviour. The reaction between sodium ethoxide and ethyl iodide and the hydrolysis of sodium monochlorace- tate by sodium hydroxide are examples of so-called “ normal ” bimole- cular reactions which take place at a rate approximately equal to the calculated rate of collision between molecules having the necessary activation energy. The esterification of acetic anhydride with ethyl alcohol and the formation of quaternary salts from amines and alkyl halides, on the other hand, are examples of “ slow ” reactions. These are characterised by the fact that the velocity constant is several powers of ten smaller than that calculated from the rate of collision and the measured activation energy. Finally, in the decomposition of phenyl- benzyl-methyl-ally1 ammonium bromide, an example has been studied of a uni-molecular reaction.

One generalisation can be drawn directly from the results in Table I, where it can be seen that the rates of these three types of reaction are very differently affected by the application of pressure. The rates of the two “ normal ” reactions are increased with increasing pressure, but to a relatively small extent. This increase is roughly linear with pressure, although it shows a tendency to fall off a t the higher pressures. The rates of the I ‘ slow ” reactions are also all increased with increasing pressure, but to a much greater extent. An increase of the order of ten times is produced by a pressure of 3000 Kg./cm.2and the acceleration continues to increase with increasing pressure. In contrast with these results, the rate of the uni-molecular decomposition reaction is decreased by a pressure of 3000 Kg./cm.2. This difference in behaviour is clearly shown in Fig. z where the values of jzp/ko are plotted as a function of pressure for the hydrolysis of sodium monochloracetate, the reaction between pyridine and ethyl iodide and for the uni-molecular decom- position.

Examination of the change in the values of A and E with pressure shows again a difference for the different classes of reaction. In the I ‘ normal ” reactions the value of A is not greatly affected by pressure, but shows a tendency to decrease with increasing pressure and the increase in rate is apparently caused by a decrease in the value of the activation energy. In the “ slow ” reactions, increasing pressure causes a large increase in the numerical value of A , which more than com- pensates for an increase in E. This does not hold, however, for the case of the esterification of acetic anhydride by ethyl alcohol in excess of the latter as solvent, where both A and E decrease with in- creasing pressure, the change in the latter being particularly large. Both A and E again decrease with increasing pressure in the case of the uni-molecular decomposition, but here the decrease in A is predominant and accounts for the decrease in rate.

have treated the effect of hydrostatic pressure on reaction velocity by the “ transition state ” method, and used the

Evans and Polanyi

equation * = g’ where AV is the difference in volume between dij RT the solutionLof the reactants and that of the complex in the transition state. The calculated value of AV for the reaction H, + I, -+ 2HI

Trans. Faraday SOC., 1935, 31, 875 ; 1936, 32, 1333.

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I 5 0 HYDROSTATIC PRESSURE ON REACTION VELOCITY

d l n k leads to a value of - - 0.8 x I O - ~ per atmosphere. This is of the

same order as the values found for the acceleration of the " slow" reactions. It has been suggested that the volume of the transition complex in these reactions is intermediate between that of the re- actants and that of the products, but closer to the latter. The change in density between the solution of the products and the solution of the reactants in acetone has been measured for the reactions of pyridine with ethyl iodide, and with iso-propyl iodide and values of 54.3 C.C. and 55.1 C.C. respectively obtained for the decrease involume per gram. mol.

dP

'"I

2

0 8C COMPOSITIC L

30 ioooo 12000 PRESSURE (KG/CWI~).

FIG. 2.

The corresponding values of vreactanta - vproducte are 2 - 2 2 x I O - ~ RT dlnk and 2.25 x IO-~ , while the values of -at 3000 Kg./cm.2 are 0.69 x I O - ~

and 0.75 x I O - ~ respectively. Evans and Polanyi have also pointed out the general agreement of the results on the uni-molecular decom- position reaction with this treatment. A pressure of 3000 Kg./cm.2 causes a decrease in rate of about 1-5 times, while i t has been calculated from the change in equilibrium constant that the rate of the reverse reaction between methyl-benzyl-aniline and ammonium bromide is acclerated about 6.5 times by the same pressure.

dP

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M. W. PERRIN 151

With the assumption that the value of AV is constant, the equation d l n k AV - = - can be integrated to give :

d b RT L

k = k,e so that a linear relationship should exist between log k J k , and the pressure. In Fig. 3 the results for the three reactions between acetic anhydride and ethyl alcohol in toluene, pyridine and ethyl iodide in acetone, and dimethylaniline and iso-propyl iodide in acetone are plotted in this way. A satisfactorily linear relationship is shown by the first reaction, but the agreement is not so good for the other two. This may be accounted for by the nature of the solvent, the effect of which is discussed later.

This same method of treatment leads to the expectation that the " normal " reaction between sodium ethoxide and ethyl iodide would take place a t a slower rate under pressure through the calculated in-

2000 4ooo 6000 8000 loo00 12000 PRESSURE. (Kc/cm2).

FIG. 3. @ Acetic anhydride and ethyl alcohol in toluene. x Pyridine and ethyl iodide in acetone. A Dimethylaniline and isopropyliodide in acetone.

crease in volume on formation of the transition complex froin the re- actants. The relatively small observed increase in rate may, however, be due to other changes in degree of dissociation or of solvation under pressure.

Turning from the quasi-thermodynamical to the kinetic interpre- tation of the results, it must be remembered that a high pressure will have a relatively small effect on the rate of collision between molecules of the reactants in dilute solution. The decrease in the free volume of the solution will have the effect of increasing the number of collisions between two reactant molecules which are close together, but this will be compensated by the increased time between collisions of those mole- cules which are widely separated.

The very large increase in the temperature independent term A, in the Arrhenius equation for the " slow " reactions, cannot, therefore, be accounted for by changes in the collision frequency and is presumably due to an increase in the " probability factor " which for these reactions,

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I 52 HYDROSTATIC PRESSURE ON REACTICN VELOCITY

is very much smaller than unity. In the case of the “normal ” re- actions, the probability factor is approximately unity, and here pressure has only a small effect on the temperature independent term. It has been suggested that the very low reaction efficiency of collisions between molecules having the necessary activation energy in the “ slow ” bi- molecular reactions may be due to the time that is necessary for this energy to be localised in those bonds in the molecule where reaction actually occurs. I t is possible that under a hydrostatic pressure the reactant molecules may be held together, when a collision takes place, for a longer time than otherwise, and there will be a correspondingly greater chance for the correct distribution of energy in the molecules which will, in turn, be followed by a greater chance of reaction due to an increase in the “ probability factor.”

In the case of the uni-molecular decomposition, the rate will ob- viously be unaffected by such considerations, but there would be a smaller rate for the two product molecules to separate from each other after their formation.

The results in Table I. for the formation of a similar series of quater- nary salts show no obvious connection between the numerical values of the temperature independent term or the activation energy and the value of k,/k, . While the latter figure is always of the same order, it does appear to be modified by the geometrical complexity of the reacting molecules. In the series of reactions of pyridine with methyl, ethyl and n-butyl iodides, the value of k, /k , a t 3000 Kg./cm.2 is very little different, although the actual rates vary largely. The introduction of a branched chain halide, however, increases the value of k,/k, , and in the series of reactions of iso-propyl iodide with pyridine, tri-methylamine and di- methylaniline, the value of k, /k , again increases with increasing com- plexity of the amine, and reaches, in the last example, a value of 500 at 12,000 Kg./cm.2.

This effect, which may be superimposed on the one previously dis- cussed, is capable of explanation in the same way owing to the closer approach of the reacting molecules under a hydrostatic pressure.

I t is known that the nature of the solvent may have a large influence on the rates of “ slow ” reactions, and it is of interest to see how the acceleration due to pressure is affected in different solvents. The velocity constant of the esterification of acetic anhydride with ethyl alcohol was measured, at one temperature, in amyl ether, acetone and hexane solutions a t atmospheric pressure and at 3000 Kg./cm.Z. The values of k, /ko did not vary greatly from that given in Table I. for toluene solution. Amy1 ether was chosen as being a liquid of which the vis- cosity is abnormally increased by hydrostatic p r e s ~ u r e . ~ Evans and Polanyig have argued that the viscosity of the solvent can have no appreciable effect on the reaction rate until an almost vitreous state is reached. More recently the reaction between pyridine and ethyl iodide has been studied a t atmospheric pressure and at 3000 Kg./cm.2 at various temperatures in a series of solvents. The values of k,/ko, A,/A,, and E , - E, have been calculated and will be published in detail later. I t can, however, be stated that, in the series of solvents, the value of kJk0 increases as the value of the velocity constant a t atmospheric pressure decreases. The only exception to this rule occurs with acetone, where a high value of k, /ko is obtained, although the reaction takes place a t a relatively fast rate in this solvent. This abnormal behaviour may ac- count for the deviation from the linear relationship between log k,/k0 and

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M. W. PERRIN I 5 3

pressure which has already been mentioned, and it is proposed to follow the pyridine-ethyl iodide reaction over the whole range of pressure in some other solvent.

Although much more experimental data is clearly needed, it can be seen already tha t hydrostatic pressure has an important influence on the kinetics of reactions taking pIace in dilute solution ; and i t appears that this effect is most pronounced in the case of those reactions which involve large and complex organic molecules and which take place, a t atmospheric pressure, at a rate very much slower than would be expected from simple considerations of collision frequency and energy relation- ships.

Imperial Chemical Industries Ltd., Northwich, Cheshire.

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