1668
0. J. KLEPPA
T'ol. 66
CALORIRIETRTC INVESTIGATIONS OF LIQUID SOLUTIONS OF THE ALK9LINE EARTH NITRATES IS THE ALKALI KITRATES B Y 0. J. KLEPPA Institute for the Study of Metals and Department of Chemistry, University of Chicago, Chicago 37, Illznots Received March I & 1962
Some new calorimetric data are presented for the solutions of strontium and barium nitrate in liquid sodium, potassium, rubidium, and cesium nitrates. It is shown that the limiting heats of solution of the-alkaline earth nitrates in the alkali nitrates obey semi-empirical relations of the type already found for calcium nitrate: A H Y ~ ( NG o ~A) ~- 225 [ ( T + + , ~ - T+ ,,)/ ( d l $- &)I2 kcal./mole. In this expression r++ and r+ are the ionic radii of the two cations (which have charges $ 2 and $l), while dl and dz are the sums of the ionic radii in each of the two solution partners. The parameter A depends on the choice of reference state, and varies from solute to solute. For undercooled, liquid calcium nitrate a t 350" A 0.3 kral./ mole. The corresponding values for strontium and barium nitrates a t 450' are approximately +0.6 and $0.8 kcal./mole, respectively.
I n recent communications we have reported some new thermochemical information on the various binary liquid systems formed among the alkali metal nitrates,lr2 silver i ~ i t r a t e , and ~ thallium nitrate.4 Since all cations have the same charge in these salts, there probabljT is no profound structural change associated with the formation of the mixture from the two pure components. In the liquid mixtures considered in the present work, on the other hand, there is an asymmetry in the charge structure of the two solution partners. This introduces an element of complexity which is absent in the simpler systems explored prelTiously. It is an unfortunate fact that the nitrates of the divalent metals usually decompose more readily a t elevated temperatures than do the corresponding monovalent nitrates. For example, we have noted that in calcium nitrate, which melts at about 560", significant thermal decomposition already sets in between 350 and 400". I n strontium and barium nitrates, with nominal melting points of 645 and 590°, respectively, decomposition start-s betmeen 46Q and 500". In view of these complications, we have been unable to study the complete liquid range from pure monovalent nitrate to pure divalent nitrates, and we have confined our attention to liquid solutions which contain up to 30-50 mole % of the alkaline earth nitrates. Recently we gave a first report on some of this This covered the solutions of calcium nitrate in lithium, sodium, potassium, and rubidium nitrates at 350". I n the present paper we consider the solutions of strontium and barium nitrates in sodium , potassium, rubidium, and cesium nitrates at 450". The higher operating temperature was chosen because of the lower solubility and higher stability of the strontium and barium salts. Unfortunately, lithium nitrate is thermally unstable at 460". Therefore, we have no information on the solutions of barium and strontium nitrates in this salt. Experimental and Chemicals In the course of the present investigation we carried out two types of calorimetric measurements. (1) 0. J. Kleppa, J . Phys. Chem., 64, 1937 (1960). (2) 0. J. Kleppa and 2. S.Hersh, J . Chem. Phys., 3 4 , 351 (1961). (3) 0. J. Iileppa, R. B. Clarke, and L. S. Hersh, i b i d . , 35, 176 (1961). (4) 0. J. Kleppa and L. S. Hersh, ibid., 3 6 , 544 (1962). (5) 0. 3. Kleppa and L. S, Hersh, Discussions Faradnu Soc., 32, 99 (1961).
( 1) Solid-Liquid Mixing Experiments.-In these we measured the heats of formation of various liquid mixtures from liquid monovalent nitrate plus solid divalent nitrate. (2) Dilution Experiments.-After a more concentrated mixture had been formed in the preceding solid-liquid experiment, the solution was diluted in the calorimeter with a known amount of the pure liquid monovalent nitrate. These experiments provide direct information on the heats of dilution for a moderately wide range of compositions. Due to a lack of adequate experimental precision we were unable to extend these experiments into the very dilute range. Details of experimental equipment and procedures have been reported e1sewhere.l The monovalent nitrates used were obtained from the same sources and were of the same quality as the salts used in our earlier work. The strontium and barium nitrates were Mallinckrodt Analytical Reagents. They were used without further purification after appropriate drying. The calorimetric data reported helow are based on calibration by the "drop method," L e . , on the heat content equation for gold as given by Kel1ey.G
Results Our experimental results are presented in graphical form in Fig. 1 and 2. In these graphs we have plotted the mole fraction of the alkaline earth nitrate along the abscissa, and the quantity A P / X along the ordinate axis. AH" is the molar enthalpy change associated with formation of a liquid mixture of mole fraction X from pure liquid alkali nitrate and solid alkaline earth nitrate. The function, f ( X ) = AHM/X, and its derivative are particularly useful for calculating partial molal heat q ~ a n t i t i e s . ~Direct experimental iiiformation on df/dz (actually 011 AflAX) is provided by the dilution experiments. These data are given in separate inserts in the figures. The two limiting values of AHn4/X at X = Q and a t X = 1 are of special interest. The value at X = 0 is the partial molal enthalpy associated with the transfer of one mole of alkaline earth nitrate from the pure crystalline state into the pure liquid alkali nitrate a t the considered temperature. The (extrapolated) value at X = 1 represents the heat of fusion of the salt at 450". Although all our experimental results refer t o solutions with solute mole fractions X 2 0.5, the data for the binaries involving a single alkaline earth nitrate permit us to extrapolate our several curves for AHMIX to X = 1 with reasonable confidence. I n this manner we have obtained the values 10.65 and 9.95 kcal./mole for the heats of fusion of strontium and barium nitrates at 450". (6) K. K. Kelley, "Contributions to the Data on TheoieBcal Netallurgy," Bureau of Mines Bull No. 584, 1960.
Sept., 1962 CALORIMETRIC STUDYOF AIXALINEEARTH NITRATESOLUTIONS IN ALKALI NITRATES1669 These figures should be compared with our earIier value of 5.7 kcal. for calcium nitrate 3 5 O O . j The significance of these results is discussed e l s e ~ h e r e . ~
Discussion Our e d i e r work on the binary alkali nitrates showed that the following approximate relation holds for the dependence of the heat of mixing on the size of the two cations AH" S --14OX(1 - X ) S Zkcal./niole
i
(I)
Here X and (1 - X)are the mole fractions of the two components. The size parameter 6 = (dl d e ) / ( d l 4-d2), where dl and d z are the sums of the Pauling ionic radii in tjhe two salts. Since the ionic radius 01' the anion cancels in the numerator, we may also write 6 = (rl - n ) / ( d l dz), where rl and r2 arc the ionic radii of the two cations. In our study of the alkali nitrate-calcium nitrate solutions we found an empirical expression for the limiting heats of solution of calcium nitrate in the alkali nitrates
+
- 225612kcal./mole ( 2 ) Here the parameter 6' = (r++/2 - ~ + / l ) / ( &
AI?ca(NOi)z(~, 3.50')
1 OSolid-Liquid
Mixing From o And Dilutions I
= 6.0
+
dz); r++ are T+ and the ionic radii of the two cations (which have charges of + 2 and + I , respectively). Correcting for the heat of fusion of calcium nitrate (5.7' kcal.) we obtained for the limiting heats of solution of undercooled, liquid calcium nitrate in the considered salts Af&a(N03)2 (1, 350')
5.0
=
0.1
,
'
.
0.3 Mole Fraction
Fig. 1.-Heat
1
0.5
, X,,
1-
---;;
o
0.1
,;NO3
+ p,,
1
0 2 ( i n i i i a w x,,
1
0.7
,
0.3(ttnatij l
4 ,
m
1 i
0.9
(N03)z.
data for solutions of strontium nitrate in the allcali nitrates a t 450".
0.3 - 2 2 5 P kcal./mole (3)
Figures 1and 2 contain the experimental information which is required in order to check whether relations similar to (2) and (3) hold also for the considereid strontium and barium nitrate systems, For this purpose we have in Fig. 3 plotted the observed limiting heats of solution of calcium, strontiurn, andl barium nitrates us. the square of the sizecharge parameter 6'. These Lhree salts have different heats of fusion. Therefore the curves plotted in Fig. 3 cannot superpose. However, it is apparent that the three curves have very similar slopes. Thus, we find that all the data contained in Fig. 3 can be represented to a good approximation by a general empirical expression
ARM~(No~)~ = A - 2256'2 kcal./mole (4) The parameter A varies from system to system, and depends on the reference state adopted for the solute. When the reference state is the pure, undercooled liquid solute (at the considered temperatures) the experimental values of A are $0.3, +0.6, and +0.8 kcal /mole for calcium, strontium, and barium nitrates, respectively. So far we have been unable to give any really satisfactory theoretical justification for this relation. Its principal merit rests in the fact that for the special case where the charge on the two cations is the samcx, the size-charge parameter 6' reduces to the pure size parameter 6 of eq. 1. This latter parameter occurs in several different theoretical ap(7) 0. J. Kieppa, J . Phys. Chem. Solzds, 23, 819 (1962).
1
1
6
OSolid-Liquid Mixing From 0 And Dilutions
I 0.I
Fig. 2.-Heat
0.3 0.5 0.7 Mole Fraction, X B . ( N ~ ~ ) ~ .
0.9
data for solutions of barium nitrate in the alkali nitrates a t 450".
proaches to the problem of the heat of mixing in simple fused salt systems.2A9 As a result of recent theoretical and experimental work on simple fused salt mixtures, it is believed that the follovcling three factors make the most significant contributions to the enthalpy of mixin g. (a) There is a negative contribution arising to a large extent from the reduction in second nearest neighbor Coulomb repulsion.2 (b) Similarly, there is a negative contribution which is due to the polarization of the common anion. This polarization is in the main ca,used by (8) H. Reiss, J. L. Xat5, and 0. J. Kleppa, J . Chem. Phus., 36, 144 (1962). (9) J. Lumsden, Discussions Faraday Soc.. 32, 138 (1961).
0 . J. KLEPPA
1670
E
J
O
05
I O
I5
20
2 5
Fig. 3.-The dependence of the magnitude of the limiting heat of solution (of calcium, strontium, and barium nitrates in the alkali nitrates) on the parameter ( r + / l r++/2)/ (dl dn).
-
+
the unsymmetrical field produced by the neighboring cation^.^ (c) Finally, there is a positive contribution which is related t o the change in van der Waals energy on mixing. This term probably is largely caused by changes in the second nearest neighbor population^.^^^^ All the binary alkali nitrate systems exhibit negative enthalpies of mixing. Thus, the contributions from (a) and (b) outweigh those of (c). On the other hand, in mixtures of monovalent nitrates involving the more highly polarizable cations Ag+ and Tl+, one sometimes finds positive and sometimes negative enthalpies of mixing. Positive values are common for systems with relatively small values of 6, i.e., in the cases where (c) outweighs the combined negative effects of (a) and (b). So far our discussion has completely neglected possible structural factors. This perhaps may be justified in mixtures of salts of similar charge structure which have a common anion. However, it seems obvious that in the type of solution system covered in the present work we must consider, in addition to the interionic forces, the possible influence of the charge asymmetry on the mixing enthalpy. Here our results demonstrate that for systems with large negative enthalpies of mixing, the magnitude of the limiting heat of solution is determined largely by the square of the difference ( ~ + /1 r + + / 2 ) . This quantity is simply related to the difference between the “ionic potentials” (Zi/q) of the two cations. In a qualitative sense we believe that the negative term in eq. 4 may be given the following tentative interpretation. When we mix two fused salts which have a common anion, a certain structural rearrangement must occur unless the two cations happen to be identical. In the first approximation, (10) M. Blander,
J. Chem. Phys., 36, 1092 (1962).
Vol. 66
this structural rearrangement presumably involves the local organization of the anions around the cation with the higher ionic potential. If this view is correct, we might expect the structural organization of the mixture to be dominated by the high field cation, and this should be the case even in mixtures where the two salts have the same charge structure. I n all the systems considered in the present work, the higher ionic potential of the divalent ion is believed to represent the organizing force. When the difference in ionic potential becomes sufficiently large, the structural organization centered on the high field ion may be considered to take on the character of “complex” formation. It is noteworthy that the heat of solution rapidly becomes more exothermic with increasing size of the lower charged ion. This is consistent with similar trends frequently observed in the inorganic chemistry of ionic salts, e.g., in the stability of double salts. Associated with the structural reorganization there will be a negative change in enthalpy. Due to the long range nature of the Coulombic forces, it is difficult to attribute this enthalpy change to a particular mode of interaction, such as nearest neighbor, second nearest neighbor, polarization, etc. We turn next to the positive term A in eq. 4. It will be noted that when the solutes are in the undercooled, liquid state, the magnitude of this term increases in a regular manner as the size of the divalent cation increases. I n fact, there is a reasonable correlation between this term and the polarizability of the divalent cation.ll This suggests that the term A may be related to the change in van der Waals energy on mixing. I n view of the structural difference between the solution partners it is difficult to make quantitative numerical estimates. This difficulty is compounded by the fact that this energy contribution, due t o the r-6 dependence on distance, is extremely sensitive to the proper choice of interionic separation. However, the magnitude of A is consistent with estimates of the contribution of the van der Waals energy to the heat of mixing in structurally simpler ~ y s t e m s . ~ ~ l ~ It remains to consider briefly the heat of dilution data. The most striking feature of these data is the pronounced maximum in AHMIXfound in all systems which exhibit strong interaction. This maximum is particularly evident for the solutions of strontium and barium nitrates in rubidium and cesium nitrates. Previously, we found similar maxima in the calcium-potassium and calciumrubidium nitrate system^.^ It should be recognized that the maximum in AHMIX corresponds to a maximum in the second derivative of AHM, Le., in the curvature of the aHi”’-X curve. This suggests that the mixture at this composition has a special stability compared to mixtures of other compositions. Frequently such a curvature maximum occurs at or near the composition of the enthalpy minimum for the homogeneous (11) J. H. Van Vleok, “The Theory of Eleotrio and Magnetic SUBoeptibilities,” Oxford University Press, 1932.
Sept., 1962
THERMAL ISOMERIZATION OF VINYLCYCLOPROPANE
(i.e.> liquid-liquid) mixing process. However, this does not scem to be the case for the mixtures considered in the present work. Thus, we see from Fig. 1 and 2 that the curvature maximum appears to fall at solute moJe fractions of the order of 0.2 t,o 0.3. 'I'here is some doubt about the location of the enthalpy minima. However, they probably all occur a t Pignificantly higher solute concentrations. It should be noted also that for a given solute (e.g., strontium nitrate) the curvature maximum tends to shift to a higher solute concentration as the liquidl-liquid mixing enthalpy becomes more negative. Previously we attempted to relate the location of this maximum to the existence of a solid state double salt at the same cornposjiti~n.~In the light
1671
of the information now available we have some doubts about this relation. On the other hand, all t>hesystems with heat of dilution maxima appear to have solid sta,te double salts at some composition. Finally, we should like to mention that the magnitude of the heat of dilution of course is related to the limiting heat of solution and to the sizecharge parameter 6'. However, the extent and quantitative character of these correlations are very sensitive to the actual choice of solute concentration. Acknowledgments.-This work has been supported by the Office of Naval Research under Contract No. Nonr 2121(11) with the University of Chicago, and by the National Science Foundation under grant No. G 19513.
THE THERMAL ISQ&IERTZATIONOF VINYLCY CLOPROPANE BY C. A. WELLINGTON~ Department of Chemistry, University of Rochester, Rochester, N . Y. Received March 19. 1968
The gas phase thermal isomerization of vinylcyclopropane has been studied in a static system between 324.7 and 390.2'. It has been Found to be a first-order unimolecular process a t pressures above 8 mm., giving cyclopentene as the mx'or product (-96%) with small amounts (-1% each) of 1,4-pentadiene, cis- and trans-lJ3-pentadiene, but no isoprene. +he effect of small additions of nitric oxide and the effect of increasing the surface/volume ratio by a factor of 27 are discussed, the former having no significant effect while the latter increased the rate of reaction by a small extent. From experiments with initial pressures of 10-11 5 mm., the two most important processes, the over-all reaction and the formation of cyclopentene, were found to have activation energies of 50.0 f 0.3 and 49.7 f 0.3 Bcal./mole, respectively, and the rate constants (sec.-.l) could be expressed by k(over-all) = (5.3 f 0.1) X 10'8 exp( - 50,00O/RT) and k(cyc1opentene) = (4.09 f 0.05) X 1 0 1 8 exp( - 4 , 7 0 0 / R T ) . Under the same conditions, the activation energies (l;cal./mole) and rate constants (sec,-l) for the formation of the minor products were: lJ4-pentadiene, 57.3 f 1.0, k = (2.7 f 0.2) x 1014 exp( -57,300/RT). trans-l,S-pentadiene, 53.6 f 0.8, k = (1.01 i: 0.06) X 1018exp( -53,60O/ET); and cis-1,3-pentadiene1 56.2 & 0.8, k =' exp( -56,20O/RT). (8.0 f 0 5) X
Introduction Previou1.J work on the pyrolysis of vinylcyclopropane had indicated that the main product was cyclopentene. Vogel2 has stated that vinylcyclopropane and l-phenyl-l-vinylcyclopropane isomerize thermally into the corresponding cyclopentenes. He discusses the similarity between a double bond and a cyclopropane ring and he draws an analogy between the vinylcyclopropane isomerization and the reversible isomerization of cyclopropanecarboxaldehyde to 2,3-dihydrofuran. Furthermore, the pyrolysis in a flow system a t 500520' of a solution of 3 g. of a mixture of 68% vinylcyclopropane, 31% cyclopentene, and 0.3% 1,4pentadienc in 15 ml. of acetic acid gave 70% cyclopentene, 28% vinylcyclopropane, and 3% 1,4pentadiene. This indicated that the vinylcyclopropane had been converted to cyclopentene and perhaps to a little ll4-pentadiene. However, passage of vinylcyclopropane over kieselguhr a t 120-150 O produced piperylene, the catalyst IoRing its activity after one pass.4 Since in this latter experiment the reaction took place on the surface, it probably would not be of great signifi(1) Shell Foiindation Postdoctoral Research Fellow. ('2) E. Vogel, Angem. Chzm., 72, 4 (1960). (3) C . G. Overberger and A. E. Borohert,
J. Am. Chem. Soc., 82, 4896 (1960). (4) B. A. Kazanskii, M. P u . Lukina, and L. G. Cherkashine, Izvrst. Akad. Nnuk S.J.S.R. Ofdel. Khzm. N a u k , 553 (1959); Chena. Abstr., 63, 21701d (1959).
cance in the decomposition in the gas phase. Thus an investigation of the gas phase reaction was undertaken with a view to determining if the ring expansion reaction was a homogeneous gas phase process and determining the kinetic parameters of all the processes that occur. While this work was in progress, Flowers and Freys reported that vinylcyclopropane undergoes a first-order thermal isomerization to cyclopentene. Investigation a t four temperatures in the range 339391' gave a good Arrhenius plot from which they obtain k = exp(-49,600/RT) sec.-l. At 390.5' they report that 1% of the product was a mixture of 1,4-pentadiene, isoprene, and cis- and truns-ll3-pentadiene. Experimental Materials.-Vinylcyclopropane was obtained from the National Bureau of Standards, Washington 25, D.C., and the physical properties quoted for the sample were: m.p. -109.82'; n Z o1.4138; ~ dZo0.72105 g./ml. The purity of the sample was tested by gas chromatography using two different columns, diisodecyl phthalate on celite, and dimethyl sulfolane on firebrick. In both cases no peak other than that due to vinylcyclopropane could be detected, showing that the sample contained less than 1 part in 10,000 of impurity. Cyclopentene and 1,4-pentadiene were obtained from the Sational Bureau of Standards and were used without further purification. The impurity of each was checked by gas chromatography and found to conform to the quoted values of 0.034 f 0.021 and 0.07 f 0.05 mole %, respectively. (5)
PI.C. Flowers end H. M. Frey, J .
Chena. floc., 3547
11961).
