GEORGE C. PIMENTEL
li2
and the heat content, and free energy functions of l i y d r ~ g e nnaphthalenelo ,~ and cis- and trans-decalins, ((11 I;. D. Rnssini, ~t d.,"Selected Values uf Physical a n d Thermodynamic ProiJerties of Hydrocarbons a n d Related Comr>ounds," Carnegie Press, Pittsburgh, 1953. (10) A . L. lIcClellan and G . C Pimentel, J Chein. Phys , 23, 215 ~lEl5).
[CONTRIBUTIOS FROM THE
DEPARTMEST OF
Vol.
so
the heat, free energy and equilibrium constants of various decalin reactions have been calculated as shown in Table Iv. We did not f i ~ l dany ])ublishcd values of experiinental measurements of these eq& libria for comparison with our results. BERKELEYCALIFORNIA
CHEMISTRY, ~ N I V E R S I T IOF C.4LIFORXl.4,
BERKELEY]
Reaction Kinetics by the Matrix Isolation Method : Diffusion in Argon ; cis-trans Isomerization of Nitrous Acid BY GEORGE C. PIMENTEL KECEIVED J U N E 3, 1957 The use of the matrix isolation technique for the study of reaction rates of cliernic~tlreactions with heats of activatioii as low as one or two kcal. is described. Reactions which might be studied include isomerization, bond rupture, bond formation reactions and the process of diffusion in the solid matrix. A crude estimate of the rate of diffusion of ammonia in solid :irgon is presented. The heat of activation of t h e isomerization of cl's-I-INO2 to trens-HNO~was measured a t 20'K. i n solid nitrogen and found to be much lower than current estimates.
The matrix isolation method, as proposed by V7hittle, Dows and Pimentel, involves the deliberate suspension of reactive molecules in a rigid and inert solid matrix for the purpose of spectroscopic study of these molecules. It is the purpose of this paper to note that the technique not only provides a means of keeping reactive molecules apart but also a method of bringing them together under unusual environmental conditions. In particular, two reactive molecules can be formed together ( ~ g . by , photolysis) or brought together (e.g., by diffusion in the solid) a t extremely low temperatures where measurable reaction rates will be observed even for free energies of activation of the order of one or two kilocalories, a range relatively inaccessible to measurement by other methods. In this paper the experimental technique is described, examples are cited, and difXculties of interpretation are discussed. Proposed Experimental Procedure.-In this Laboratory, the process of diffusion of a molecule A suspended in a matrix AI2 has been studied. The temperature a t which such a diffusion process becomes rapid seems t o be around three to five tenths of the melting point of the pure matrix. Thus a molecule such as KO2,H 2 0 or NH? diffuses rapidly in solid argon ( T , = S3.S°K.) a t temperatures above 3 3 O K Hence reactive molecules can be brought together in solid argon in a period of a few seconds a t 40-50°K. and thereafter their fates can be studied spectroscopically as a function of tinie. Other matrix materials can be used t o obtain either higher or lower diffusional temperatures. Reaction Processes in the Matrix.-Of the possible reactions which might take place under the proposed conditions, the simplest type would be the first-order deactivation of a n excited state, e.g., a state involk ing conformational or tautoineric cxcitation. I n the former case, the rate of fonnatinn of the most stable isomer would be determined by the potential function which governs the intra(11 I3 Whittle D A D o n s and G C Pimentel, J Cheiit P h y s , 22, 1941 ( 1 c ) 3 4 ) ( 3 ) E D Becker and G C Plrnentel, rbtd , 26, 224 ( I D & )
niolecu1,ir niox enient, for example, a potential barrier hindering internal rotation. (Entropy effects will be discussed later.) I n the case of tautomers, the process would be governed by the properties of the transition state in intramolecular rearrangement. If the confines of the matrix impede intramolecular movements, the measured heat of activation probably will exceed that of the gaseous niolecule. Bond rupture reactions would also be of first order. The effect of the matrix cage on AI€= would depend upon the dimension along the reaction coordinate of the activated state, &AB, conipared to the size of the matrix cage. If the cagc is small compared to Y*.AB, then AII* will be influenced by the heat of activation of diffusion, AII*u, the heat of activation for reaction in the gas phdse, . l I I ~ o and . the heat of reaction, AIIK. Situations which are readily interpreted are the special cases' (1) A I P >> A H * D ; ( 2 ) AII*n >> A f S o and r = A B comparable to the cage size; and ( 3 ) of Y*AR sinall compared to the cage size. In case (1) the value of AII* measured is little influenced by the matrix arid in case ( 2 ) the measured A H + is approximately AII*D. I n case ( 3 ) the potential curve applicable to thc gas phase, curve a in Fig. 1, may be influenced somewhat by the matrix cage, as suggested by curves b and c in Fig 1 . Again the measured activation enthalpy should exceed the gas phase A I G 0 Reactions involving bond formation are also illfluenced by cage size. However, in either case (1 ! or (2) the reaction kinetics become of second order. I n case (3) i t is possible for the reaction to occur within the cage and a t a temperature a t which diifusion cannot take place. If a potential curve such as curve b of Fig. 2 mere applicable, the kinetics would he first order because the reactive species are held together by the matrix. In a favorable cdse, where the c'ige iy very large compared to A I I g would provide an estimate of AII*". fourth type of reaction, diffusion, can be studied. The rate can be determined by observing the disappearance of a suitable suspended species which reacts with low AFT.
63
cis-trans ISOMERIZATION OF NITROUS ACID
Jan. 5, 105s
Experimental
A
V.
r. Fig. 1.-Potential curve for bond rupture within the matrix cage: r = reaction coordinate; ( a ) possible potential curve applicable t o a gas phase reaction; (b, c) possible potential curves as modified by constraints of the matrix.
Entropy of Activation.-The matrix isolation technique has been used effectively a t temperatures below 100°K. and, in these laboratories, mainly in the range 4 4 0 ° K . At these low temperatures the entropy of activation in first-order reactions is undoubtedly very close to zero.
The studies reported here were conducted as described in reference 2 except for the photolysis, which was conducted as described in reference 3. Two specific experiments provide interesting examples. The first experiment, A, involved a mixture of NH3 gas in argon a t a mole ratio of argon/ammonia of 195. The mixture was frozen at 20°K. and the infrared spectrum indicated that a fraction of the ammonia was in the form of monomeric NH3. The temperature was allowed to rise a t a rate of about 0.1 degree/second. Two spectra taken 75 seconds apart revealed the disappearance of about 88 3= 6% of the monomer (with the growth of the spectral features of hydrogen bonded polymers). During this 75-second period, the temperature varied from 40 to 47'K. In experiment B, nitrogen gas containing both HS3 and oxygen was frozen at 20'K. The mole ratios were K2: HK3:Oz = 50O:l:x where x was in one experiment 0.5 and other experiments at least 2. After a n infrared spectrum was recorded, the mixture was photolyzed for 13-30 minutes. The spectrum was then recorded as a function of time at a recorded window temperature of 20°K. A welldefined spectral feature at 868 cm.-1 which appeared during photolysis was observed to disappear, while the absorption at an adjacent spectral feature at 818 cm.? increased somewhat, as shown in Fig. 3. Two experiments form the basis of
0.1
%
tl
G
M M
0.2
-t=0
V. 0.3
min .
900 800 900 800 Fig. 3.-Spectra of photolysis products of H S I in argon; T = 20'K.; oxygen present.
r. Fig. 2.-Potential curve for bond formation within the matrix cage: r = reaction coordinate; (a) possible potential curve applicable to a gas phase reaction; (b) possible potential curve as modified by constraints of the matrix.
In second-order reactions the concentration units selected for the standard state will influence the value of ASo*, mole fraction units being convenient. The form of the standard state appropriate to the experiment is, no doubt, the glassy state. Hence ASo* will not approach zero as the temperature approaches zero (as it would, by the third law of thermodynamics, if the standard states were perfect crystals). Nevertheless ASa* is expected to be low a t temperatures below 50OK. and possibly negligible. Heat of Activation.-The familiar reaction rate expression for the rate constant kl or kz applies in most cases. kl,z = kT - eASO*/Re-AHO*/RT h
!. = 2 5
(1)
For rotational isomerization reactions the activated state involves rotational movement rather than a translation. Hence the k T / h factor may require modification.
the estimate t h a t 42 zk 570 of the feature at 868 cm.-l was lost in 25 minutes. The temperature was measured by a copper-constantan thermocouple embedded in the salt window bearing the sample. It is believed that the sample temperature was in the range 20-23°K. A. Diffusion of Ammonia in Solid Argon.-In this experiment the rate of disappearance of ammonia was measured over a temperature interval of 40 t o 47°K. Assuming equation 1 is applicable, t h a t the temperature was 43.5'K., and that the polymer concentration was large enough to be effectively constant, we calculate AF* N 2 kcal./mole. This crude estimate is considered t o apply to the diffusional process since it is expected that AH* of hydrogen bond formation is zero. It is possibly fortuitous that the calculated AF* is only about 500 calories below the AH* of self-diffusion predicted from the melting point of argon and the empirical relation AH* = c T , (c = 28-32) observed for selfdiffusion in cubic close packed metals4v5 (argon crystallizes in a cubic close packed structure). B. The Rotational Isomerization of HNO*.--In this experiment a species was produced by photolysis and its rate of disappearance was examined spectroscopically at a constant matrix temperature near 20°K. At this temperature, diffusion of even diatomic species has been found to be negligible.2 Hence the process is presumed to be governed (3) E. D. Becker, G. C. Pimentel a n d hl. Van Thiel, J. Chcm. P h y s . , 26, 145 (1957). (4) J. Van Liempt, Z . Physik, 96, 534 (1935). ( 5 ) N. H. Nachtrieb, J. A. Weil, E. Catalan0 and A. a'.Lawson. J . Chcm. P h y s . , 20, 1180 (1952).
S. L. ~ I I L L E AND K D. KITTENBEKG
04
by first-order kiiictics. The temperature is taken to be 21.5 f 1.5'K. If equation 1 is applicable and if A S o * = 0,
then the disappearance of the band at 865 cm.-I is governed by a process with a heat of activation of 1500 k 130 cal. The two features which vary with time, 868 and 818 a n . - ] , are assigned, respectively, t o the cis and trans forms of niThis species is presumed t o form in the trous acid, " 0 2 . reactions 2, 3 and 4, followed by 5. Hh'3
+ hv = hTH +
+ NH +
NH
0 2 = 0 9
HONO
(2)
1-2
(31
(~YUTZX)
= HONO (Cis)
(4)
HOXO (cis) = H O S O (tvans)
(5)
Tile idciitification is supported by the vibratioiial assignment proposed by earlier worker^.^^^ They assign the intense absorptions at 856 and 794 c m - ' to the 0-N stretching modes of the gaseous cis and trans isomers, respectively. The energy of the cis form is 506 zt 250 cal./mole above the trans Jones, et al., estimate the barrier t o internal rotation to be about 12 k ~ a l . / m o l e . ~More recently but without new d a t a Palm8 has expressed agreement with this estimate. It is not possible t o rationalize a 12 kcal. barrier with the measured rate either by adjustment of 'Parte, U d . SOL.Roy. S c i . , LiBne, 478 (1951). (71 L. H. Jones, R. M. Badger and G. E. Moore J . Chem. Phys., 19, 15'3'3 (1951). (8) A. Palm, ibid., 26, 855 (lCl.57). (i;) I,. D'or a n d .'1
[ CONTRIUCTIOS FROX
THE
1'01. 80
AS"* or of the ( k T / h ) factor. It is posible but unlikcly t h a t the reaction under study is not the cis-trans isonicrization of HXOz. More detailed studies of this system are in progress, both to corroborate the assignment and tu measure A S o +.
Conclusion It is clear that the matrix isolation technique offers unique possibilities in the study of reaction kinetics. There are limitations and difficulties of interpretation whose importance cannot be evaluated without more experience. The most serious of these is probably that the matrix may influence the activation thermodynamics of the reactions studied. Nevertheless it seems likely that the method will prove to be a valuable tool for the study of extremely fast reactions, including the rcactions of free radicals. Acknowledgment.9 ---The author wishes to thank Professor Robert E. Connick for many helpful and critical discussions. (9) T h e research described was supported i n part by t h e Ainericali Petroleum Institute, Research Project 50, a n d b y t h e United S t a t e s .4ir Force through t h e AFOSR of t h e 4ir Research a n d Development Command, under Contract No. 49(638)-1. Reproduction in whole or in p a r t is permitted for a n y purpose of t h e U. S. Government.
BERKELEY, CALIF.
DEPARTMEST OF BIOCIIEMISTRY, COLLEGEOF PHYSICIAXS XSD SURGEONS, COLUMBIA USIVERSITY]
The Catalysis of the H2-D20Exchange by Aqueous Buffer Solutions' BY S. L. MILLERAND D. RITTENBERG RECEIVEDAUGCST 9, 1957 The exchange between molecular hydrogen and DzO is known to be catalyzed by hydroxide ion and follows the rate la!+ ' r l ( P ~ n ) / d t = ~ ( P H , ) ( O H - ) . T h e exchange has been investigated a t lower pH values in the temperature range 110-190" using borate, phosphate, glycine, succinate and acetate buffers. T h e same rate law is obeyed provided the O H - concentration measured a t 25' is corrected for the change in the pK of the acid and the pK of the water at the higher temperatures The heat of activation is 28 f 3 kcal. Seither dilute nor concentrated acids catalyze the exchange.
'Hic exclimgc reactions were carried out in Pyrex tubcs of ,tl)ouC 3-ml. capacity with a break seal at one end. 0.5 1111. o f buffer and 0.5 nil. of DzO were placed in the tube, and the gas pliasc replaced by hydrogen. The reaction tubes I\ ere kept at a constant temperature (k 1") in an oven which was rockcd about 10 times per minute. After various time intervals the deuterium concentration of the gas phase was
Consider a system in which the gas phase initially coliand the aqueous phase contains D20 of mole fractains Hz, tion YD, If the exchange is catalyzed only by hydroxide ion, the rate law is d(HD)i:/dt = kLVD(OH-)(H2)1 (1) n-liere k is expressed in liters mole-' hr.-l, (HD!i and (H2'81 are the molar concentrations of these gas species in solution. This equation ignores the isotope effect between Hz0 and D,O, b u t i t can be included in the constant A'D. Let VI be tlie volume of solution, V, the volume of gas, K , the conStdnt of Henry's law, PH*the partial pressure Of Hz. Ive will consider the case where the reaction proceeds only to ;t small extent. The number of moles of H D , n m , produced after t hours in VI liters of solution is obtained by iiitegrating cq. 1 to give 11111> = kLvJ> (OI~-)KsI-'fi$ Vlt T h e €11) produced in solution is mixed with tllc 1 ' ~ Lrc/li7' ~ inoles of HQin the gas phase, therefore, tlie ratio of H1) to 1-32 in the gas phase after t hours is (HD:/Hz)* = k,VnK,(OH-)Rr(Vl/V~)i
determined by mass spectrometric analysis.
or
During an investigation of the catalysis by various compounds of the Hz-DzO exchange reaction, it was necessary to correct for the exchange reaction which occurs in the absence of added catalysts. It is known that hydroxide ion will catalyze the exchange. X o r e recently3 an investigation of the mechanism has shown that the rate of exchange is proportional to the pressure of hydrogen gas and the OH- concentration in the range 0.1 to 1 Ad. ,111extension of the exchange experiments to lower values of fiH is reported in this paper. Experimental
The average
of the initial and final P H values was taken as the PH of the
system.
T h e d a t a were reproducible within k5%.
(1) This research was supported b y Atomic Energy Commission Contract #AT(30-1)1803 t o Columbia University. (2) I
