THOMAS F. REDMOND AND BRADFORD B. WAYLAND
1626
Dimerization of Nitrogen Dioxide in Solution: a Comparison of Solution Thermodynamics with the Gas Phase' by Thomas F. Redmond and Bradford B. Wayland John Harrison Laboratory of Chemistry and Laboratory for Research o n the Structure of Matter, University of Pennsylvania, Philadelphia, Pennsylvania 19104 (Received October 63,1967)
The equilibrium of N204 with NO, has been determined in cyclohexane, carbon tetrachloride, and acetonitrile The equilibrium constants and enthalpies for N204 dissociation at 298°K have been determined and are respectively, 1.77 X and 14.6 kcal in cyclohexane and carbon tetrachloride and 0.30 x and 16 kca in acetonitrile. These data are compared with the gas-phase values of 1.51 X 10-1 and 13.64 kcal for N 2 0 dissociation. The differences in gas and solution thermodynamics are discussed.
Introduction There has recently been increased interest in the relationship of gas-phase equilibrium to the corresponding process in s o l ~ t i o n . ~ -There ~ remains a need for further investigations which permit comparison of simple equilibria in the gas phase with that in solution. Because of the extensive gas-phase equilibrium data for and the capability of studying the dissociation of Nz04e77 this reaction in solution, this equilibrium offers an unusual opportunity for investigating the difference between the gas and solution processes. Since the early work of CundalP as interpreted by later a u t h o r ~ , very ~ J ~ little work has appeared pertaining to solvent effects on the thermodynamics for Nz04 dissociation. This paper reports the measurement of equilibrium constants and enthalpies for the dissociation in the noncoordinating solvents, cyclohexane and carbon tetrachloride, and in the coordinating solvent, acetonitrile. The resulting data are discussed with reference to the corresponding gas-phase values. The equilibrium constants were determined by taking advantage of the paramagnetism of NOz. The nmr technique has been applied to the measurement of solution susceptibility and these data have been utilized to determine the concentrations of NOZ and K204 present in solution. The magnetic technique is a convenient direct method for studying this equilibrium, in contrast with electronic spectral measurements which can yield only relative equilibrium constants, owing to the uncertainty of medium effects on extinction c~eficients.~ Experimental Section Materials and Sample Preparation. Fisher Spectroanalyzed cyclohexane and carbon tetrachloride were used without further purification. Fisher reagent grade acetonitrile was shaken with barium oxide, allowed to stand for several days, and then redistilled, bp 81.7" (uncor). Nitrogen dioxide was obtained 99% The Journal of Physical Chemistry
pure from Matheson Scientific Co. On freezing samples of the dioxide to liquid nitrogen temperatures, blue and green colors were often detected, indicating the presence of other oxides of nitrogen. Samples were fractionally distilled until a pure white solid melting at approximately - 11" was obtained. Cyclohexane and carbon tetrachloride were selected as representative noncoordinating solvents on the basis of positive deviations from ideality in vapor pressure" and additivity of volumes12 for solutions of K204 in these solvents. Acetonitrile solutions of N204 show negative deviations in vapor pressure, which is taken to imply complex formation. Magnetic resonance samples were prepared by vacuum distillation of purified oxide and solvent into nmr tubes from reservoir bulbs which were weighed before and after transfer. Bulbs with Teflon stopcocks were used to eliminate the need for grease. The bulbs were tested and proved capable of holding vacuum and constant weight for considerably longer periods of time than required for weighing, transfer, and reweighing. Since N204 is a powerful oxidizing agent, samples were stored at liquid nitrogen temperature until immediately before use. The equilibrium measurements (1) Abstracted in part from the Ph.D. Thesis of Thomas F. Itedmond, University of Pennsylvania, Philadelphia, Pa., 1968. Inquiries should be addressed t o B. B. Wayland. (2) J. Prochorow and A. Tramer, J. Chem. Phys., 44, 4545 (1966). (3) P.Trotter, J . Amer. Chem. Soc., 88, 5721 (1966). (4) J. M. Goodenow and M. Tamres, J . Chem. Phys., 43, 3393
(1965). (5) F. T. Lang and R. L. Strong, J . Amer. Chem. Soe., 87, 2345 (1965). (6) W.F. Giauque and J. D. Kemp, J . Chem. Phys., 6,40 (1938). (7) I. C.Hisatsune, J . Phys. Chem., 65, 2249 (1961). (8) J. T. Cundall, J . Chem. Soc., 67,794 (1895). (9) P. Gray and H. Joffe, Chem. Rev., 55, 1077 (1955). (10) P. Gray and P. Rathbone, J . Chem. SOC.,3550 (1958). (11) C. C. Addison and J. C. Sheldon, ibid., 1937 (1957). (12) C.C.Addison and B. C. Smith, ibid., 3664 (1958).
DIMERIZATION OF NITROGEN DIOXIDEI N SOLUTION
1627
were found to be reversible with changing temperatures, which precludes significant irreversible reactions during the time required for the magnetic measurements. Procedure. By analogy with the theory of atomic dipoles, the shift of the nmr position of a sample due to a change in volume magnetic susceptibility can be expressed in terms of a ratio of geometric factor^,'^ such that for a capillary tube containing pure solvent inside an nmr tube containing solution
carbon tetrachloride were taken from the International Critical Tables while a value calculated from the data of Wickenden and Krause15 was used for acetonitrile. The diamagnetic susceptibility of Nz04 was taken as as the commonly accepted value of 0.276 X determined by Sone, and the diamagnetic susceptibility of NO2 was assumed to be one half that of the dimer. Deviation of the diamagnetic susceptibility of NO2 from this value would have little effect on the calculation, owing to the small contribution this term makes to the susceptibility of paramagnetic NOz. The paramagnetic susceptibility of NOz was calculated from the g value, as determined by esr in CC14 solution. l7 An experimental value of the susceptibility was determined directly by Havens'* in 1933 which would lower the equilibrium constants by 15% while leaving the enthalpies unchanged. The esr value is very close to the free-electron value and undoubtedly is the more accurate measurement of the susceptibility. The solution composition was corrected for the presence of vapor above the solution. Deviations of the vapor pressure from ideality as expressed by Raoult's law were corrected for by extrapolation of data reported by Addison. l 1 The corrections increased the equilibrium constant by as much as 5% in the case of cyclohexane but were unimportant with the other solvents. Several runs were made with rimr tubes sealed close to the surface of the solvents and the results supported the accuracy of the correction. The solutions were also corrected for deviations from ideality in terms of volume additivity by extrapolation of Addison's data.12 The method is particularly sensitive to volume corrections, since the magnitude of the diamagnetic correction term in the susceptibility is large when compared to the susceptibility of the dissociated NO2 species. The densities of the solvents were taken from Lange's Handbook of Chemistry, as were the coefficients of volume expansion for CC1, and CH,CN. The volume expansion of cyclohexane over the temperature range employed was determined previously in this laboratory. The density of N204as a function of temperature was taken from the work of Mittasch et al.19
AxV
36 2n
= -
where Axv is the total change in susceptibility from capillary to nmr tube and 6 is the shift in ppm. A x v can also be expressed in the NOz case as AxV
XVNOi
+
xVNi01
+
XVs
-
XVo
(2)
where xvois the volume susceptibility of pure solvent and xv, is the volume susceptibility of the solvent in the solution equal to ( V o / V , ) x V , , where V , represents the total volume of the solution and V orepresents the volume contribution of the pure solvent. Combining eq 1 and 2 and rearranging we have
This can be readily converted into gram susceptibilities
where m is the total grams of NO2 and K204per milliliter of solution. From a knowledge of the magnetic susceptibilities for NOz and N204the concentrations of these species can be calculated. This is essentially the method of Evans, and eq 4 can be readily converted into his original expression.14 For the cyclohexane measurements, the shift of the solvent peak itself was measured. I n the case of carbon tetrachloride and acetonitrile, the solvent both in the tube and capillary contained approximately 5% cyclohexane as a standard. Most measurements were carried out on a Varian A60A spectrometer with a few made on an HR-60. Temperature was controlled by a Varian temperaturecontrol accessory using nitrogen gas and was measured by peak separation in ethylene glycol and methanol samples. Samples were scanned an average of six times on a 100-cycle scale. Shifts were on the order of 2-10 sec-' and were reproducible within a t least f0.03 sec-'. Spinning problems were encountered occasionally due to the capillary tube. Attempts to overcome this problem by use of separate tubes for samples and standard led to nonreproducible results due to field drift and small differences in tube characteristics. The diamagnetic susceptibilities of cyclohexane and
Results Representative data for the determination of equilibrium constants by the nmr method are shown in Table I for several temperatures and concentrations. The (13) G. Dickinson, Phys. Rev., 81, 717 (1951). (14) D . F. Evans, J. Chem. Soc., 2003 (1959). (15) A. E. Wickenden and R. A. Krause, Inorg. Chem., 4 , 404 (1965). (16) T. Sone, Science Repts. Tbholcu Imp. Uniu., 11, 139 (1922). (17) M. Bersohn and J. C. Baird, J . Chem. Phys., 28, 738 (1958). (18) G. G . Havens, Phys. Rev., 41, 337 (1932). (19) Mittasch, Kuss, and Schlueter, 2.Anorg. Chem., 159, 1 (1927). Volume 72, Number 6
May 1968
THOMAS F. REDMOND AND BRADFORD B. WAYLAKD
1628 Table I : Representative Data for Nz04 Dissociation W t of NzO4 NO%,
Wt of
+
vo,
V N Z O I+ NO,
g
ml
ml
26.7 26.7 34.3 34.3 42.0 42.0 50.0 50.0
0.06196 0.04768 0.06196 0.04768 0.06196 0.04768 0.06196 0.04768
0.7577 0.4408 0.7661 0.4457 0.7748 0.4507 0.7840 0.4561
0.0433 0.0333 0.0439 0.0338 0.0445 0.0343 0.0452 0.0348
Cyclohexane 0.8068 0.0663 0.4784 0.0823 0.8161 0.0765 0.4841 0.0937 0.8257 0.0926 0.4898 0.1104 0.8359 0.1067 0.4960 0.1290
-0.00635 -0.00982 -0.00133 -0,00428 0.00655 0.00393 0.01345 0.01300
26.5 35.0 35.3 50.0 53.0
0.05553 0.04120 0.05553 0.05553 0.04120
0.4707 0.6130 0.4756 0.4841 0.6264
0.0388 0.0292 0.0394 0.0405 0.0302
35.0 44.8 53.0
0.06189 0.06189 0.06189
0.6123 0.6201 0.6268
0.0439 0.0447 0.0454
Temp, =C
vata
+ NaO4,
1 0 e X g NO?+ NZO48 ml g-1
g
104~,, mol I,-1
- 0.08268 -0.09850 -0.01752 - 0.04345 - 0.08733 0.04039 0.1815 0.1353
4.442 3 134 6.091 4.217 8.772 5.881 11.331 7.838
1.74 1.90 3.25 3.40 6.73 6.60 11.19 11.63
Carbon Tetrachloride 0.5116 0.0913 -0.01085 0.6439 0.0720 0,00199 0.5171 0.1067 - 0.00322 0.5268 0.1364 0.01245 0.6583 0.1092 0.02016
- 0.10000 0.03109 - 0.02998 0.1181 0.3220
3.620 4.821 5.210 8.749 9.939
2.03 3.90 4.19 11.74 16.6A
Acetonitrile 0.6562 0.0275 0.6648 0.0368 0.6722 0.0477
-0.1647 -0.1136 - 0.05841
0.571 0.889 1.181
0.75 1.67 3.14
ml
1O'XNOz
ml
b m ,
g-1
-0.01533 -0.01074 - 0.00538
104~0*,
a Cyclohexane and carbon tetrachloride solutions corrected for deviation from additivity of volumes by assumption of linear dependence of density on temperature and of validity of Biron relationship. n
Table I1 : Thermodynamic Values for Nz04 Dissociation
Cyclohexane Carbon tetrachloride Acetonitrile Gas phase'
1.77 f:0.1x 10-4 1 . 7 8 2C 0 . 1 X 0.30 0.1 1 . 5 1 X lo-'
x
10-4
4FaS8disan,
4 H z88dissn,
koa1 mol-1
kcal mol-'
5.1 5.1
14.6 dz 0.5" 14.6 f: l . O b
31.8 2C 1 . 0 31.8 f: 1 . 5
6.1 1.12
16 2Cl.5 13.64d
33.0 i 2 . 5 42.8
'
Least-squares analysis of thirteen points with 80% confidence limits. Least-squares analysis of eight points with 80% confidence AHo' = 12.69 kcal mol-', AHoZQ8 - APV = 13.0. limits. Reference 7.
thermodynamic values calculated from these data are shown in Table 11.
Discussion Noncoordinating Solvent E f e c t s . The Nz04 dissociation constant in CCl, and CsHlz determined in this mol L-l) compares study (KC2O0= 1.1 f 0.1 X reasonably well with the value calculated from the data mol l.-l)lO in CCL. of Cundall (Kczoo= 0.8 X The temperature dependence of K , ( A H = - 14.6 kcal mol-') is, however, found to be significantly smaller than the value calculated from Cundall's data (AH = -18.8 kcal mol-') and the value for liquid Nz04 ( A H = -17.8 kcal mol-l).lO The enthalpy value reported here is fairly close to the gas-phase enthalpy and thus consistent with many other experimental observations on related systems, such as NzF420 and various molecular addition compounds.21~2*Since the enthalpy The Journal of Physical Chemistry
of dissociation is increased only slightly in going from the vapor phase to a noncoordinating solvent environ: ment, the drastic decrease in N204dissociation in a solvent is primarily the result of a decreased entropy change (32 eu in solution us. 43 eu in gas phase). This is in direct contrast to analysis of Cundali's data which predict an increase in the entropy of dissociation on going from the gas to the solution phase. A decrease in dissociation entropy in solution compared to the gas phase is to be expected in terms of several simple models for noncoordinating solvent systems. Consideration of the solute molecules as (20) (a) F. A. Johnson and C. B. Colburn, J . Amer. Chem. Soc., 83, 3043 (1961); (b) H. E. Doorenbos and B. R. Loy, J . Chem. Phys., 39, 2393 (1964). (21) F. G. A. Stone, Chem. Rev., 58, 101 (1958). (22) C. H. Henrickson and D. P. Eyman, Inorg. Chem., 6, 1461 (1967).
DIMERIZATION OF NITROQEN DIOXIDEIN SOLUTION being subjected to a sharply decreased free volume when passing from the gas to the solution phase leads to a significant decrease in entropy for all solute species to approximately the same extent. A similar result would be expected for solute molecules in terms of very large internal or mechanical pressures exerted by the solvent on the solute. Thus in general, when the entropy change in going from the gas to the solution phase is dominated by the solvent structure and not by chemical interaction, a dissociative process will be less entropy favored in the solution compared to the vapor phase. This is shown to be true in many systems, such as the molecular addition compounds of boron and aluminum acceptors.21,22 Similar results are predicted from application of a crystalline model of solution in which the translational motions of the solute molecules are converted into low-frequency vibrations in the solvent lattice. This general statement does not, however, account for some recently reported charge-transfer equilibria2 involving highly complex molecules such as tetracyanoethylene-xylene adducts.2a I n these cases, dissociation occurs more extensively in solution than in the vapor phase. These data are difficult to understand within the framework of current knowledge of the properties of liquids. The translational entropies of the solute molecules must be considerably smaller in the solution than the gas phase. This effect should favor higher association in solution. Deviations from ideality in the gas phase, solvation effects, and restriction of rotational motions for the large, unsymmetrical adducts may be responsible for the observed behavior. 14,5
1629 Coordinating Solvent &$'e&. The dissociation of Nz04 in the coordinating solvent acetonitrile is even smaller than in noncoordinating solvents (Table 11). The increase in the association of K204results from the increase in the apparent enthalpy of Nz04dissociation to 16 f 1.5 kcal. This suggests that N204is a better Lewis acid than NOZ and thus is more highly associated with acetonitrile. These data may be compared with values (KcZ9* = 1.0 X lou4mol l.--I, AH = 17.8 kcal) lo for dissociation in the coordinating solvent liquid N&. The apparent entropy of dissociation is approximately the same as in the noncoordinating solvents suggesting that even when a weak specific interaction is involved in the system, the solvent structure may be the dominant factor in entropy reduction. It is difficult to rigorously assess the significance of equilibrium data in coordinating solvents due to the probability of competitive equilibria involving species of varying degrees of complexation and solvation. It is most likely that the dominant equilibrium involves a simple process such as 2?JO2.B 8 NzO4-2B. The temperature dependence of the apparent equilibrium constant is consistent with a simple equilibrium but cannot be used to rule out the possibility of other competing equilibria such as Nz04 B Nz04.B,N 2 0 4 - B B F? N204.2B, and NO2 B 8 NOz.B.
+
+
+
Acknowledgment. We wish to thank the Advanced Research Projects Agency for its support of this research through Contract No. SD-69. (23) M.Kroll and M. L. Ginter,
J. Phys. Chem., 69, 3671 (1965).
Volume 72, Number 6 M a y 1968
