(io
TATSCO SIIYXZAW~\ A N D KENNETH S.PITZEK [ C O S T R I B U T I O N FROM THE
DEPARTMENT O F CHEMISTRY,
\'of.
NJ
U N I V E R S I T Y O F CALIFORNIA, BERKELEY]
Thermodynamic Functions for Gaseous cis- and trans-Decalins from 298 to 1000OK.' BY
s. PITZER
TATSUO h ~ I Y A Z A W AAND KENNETH RECEIVED AUGUST8, 1957
T h e values of the heat content function, free energy function, heat capacity and entropy of cis- and tvans-decalins have been calculated by the use of molecular and thermal data. The functions are tabulated from 298 to 1000°K. The heat, free energy and equilibrium constants of the reactions, C I ~ H S 5Hz = CZ'S-CIOHLB, C W H ~ 5H2 = tvans-CloHla, have been also calculated and tabulated.
+
Experimental thermodynamic data are available for liquid cis- and trans-decalins. It was our purpose t o calculate functions for the gaseous state over a range of temperature. I n either case the data for the heat capacity and entropy of the liquid2 a t temperatures up to 350'K. and precise vapor pressure measurements3 in the range 370-160'K. are available. Therefore, a short extrapolation must be made if one is to obtain thermodynamic functions for these substances in the gaseous state in the range 400-I5OoK. I n the absence of other information, the equations for the heat capacity of the liquid as a function of temperature were obtained by best fitting a straight line to the experimental values available in the range 300-350'K. The equations are C, C,,
= =
12.68
+ 0.1434T (cis-decalin)
10.95 $. 0.1464T (tmns-decalin)
observed infrared5and Raman6frequencies. Those are: 2890(18),7 144-1(8jj71384, 1350, 1342, 1327, 1312, 1300, 1292, 1270, 1258, 12-11, 1216, 1210, 1171, 1165, 1143, 1125> 1114, 1089, 1073, 1069, 10-11,1011, 978, 969, 929, 888, 877, SIR, 853, 833, 800, 793, 752, 742, 706, 661, 594, 538, 489, 4lfi, 375, 348, 317, 191 and 148. I n addition to the incompletely resolved groups of frequencies near 2900 and 1450 cm.-', there are seven unobserved vibrations of lower frequency. The contributions of these unobserved fundamentals to the heat capacity and entropy were calculated by subtracting the contributions of translation, rotation and observed vibrations from the thermal values of heat TABLE
(2)
(1) This research was p a r t of the program of Research Project 50 of t h e American Petroleum I n s t i t u t e
( 2 ) Private communication f r o m D r . G. Waddington, U. S. Bureau AIines, Bartles:ville, Oklahoma. (3) D . I,. Camin a n d F. 33. Rossini, J . Phys. Cheric , 69, 1173
(1!)5,5). (41 Kamez, Groes, T r a p p e , quoted b y I-. Kiedel, Chein. l u g . ZIfch.. 24, 358 (l!l&).
I
C A L C C L A T I O N O F THE E N T R O P Y O F
Cis-
A S D tYnnS-UECALlXS
(ISCAL./DEG. MOLE) cis-Decalin
(1)
These equations were used for the extrapolation of the liquid heat capacity and the calculation of the entropy of the liquid in the range 400-450'K. The values of the heat capacity and entropy of vaporization a t several temperatures were calculated from the vapor pressure equations of Camin and Rossini3 on the assumption that the vapor volume follows the Berthelot equation of state with critical constants Tc = 691.7"K. and P , = 27 atm. for cis-decalin and Tc = 681.5'K. and P, = 27 atm. for trans-decalin.4 The correction of the heat capacity and entropy to the ideal gas state was made with the aid of the Berthelot equation, and the entropy of compression was then added. The heat capacity and entropy values for the ideal gases a t the standard pressure of one atmosphere are shown in Tables I and IT. The contribution of the molecular rotation to the entropy was calcylated by using the bond distances 1.54 and 1.09 A. for c-C and C-H bond, respectively, and tetrahedral angles for all the bond angles. The symmetry number for either case is two; however, in the case of cis-decalin R In 2 = 1.3s cal. 'deg. mole must be added on account of the presence of two equivalent inversion isomers (or conformations). The contributions of molecular vibration to the heat capacity and entropy of cis-decalin were calculated by the use of the
of
+
Temp., '1;. Entropb- of liquid Vaporization Gas imperfection Compression to 1 a t m .
lruiis-Uecalin
4;io 400 450 4ou 81.67 90.34 8 1 . 4 3 90.04 36.44 21.88 2 5 . 4 3 21.01 0.14 u.0ti 0.17 0.05 -:3.82 -0.91 -3.30 -0.X __ __ lU4,:34 111.45 103.63 110.72 ~
Entropy (3rd law! Trans. and rot. I-ibration
i2.0ii 38.il _ ~ _ 111.49 103.61 110.77
2.27 73.20 3%.0ounds," 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.
