3633
NOTES
There are various reaction steps which, together with step 10, could conceivably consume O2 by a chain mechanism, for instance5
H
+
0 2
+HOz
+ SO2 + + OH OH + SO2 +HSOa HS06 + SO2 +2SO3 + OH HO2
so3
Acknowledgments. We are grateful to Professors G. Ackermann, S. Herzog (Freiberg), and L. Kevan (Wayne State University) for their suggestions and helpful comments.
(11) (12)
Thermodynamic Data for the
(13)
Water-Hexamethylenetetramine System
(14)
We have observed, as displayed by the data in Figure 3, that this is indeed the case. However, the chain mechanism involves, as is evident from the low chain yield, rather short chains. After an initial rise, G(SO8) soon drops to a value close to that in the corresponding anhydrous liquid sulfur dioxide-oxygen system (see Figure 1). It is useful to remark here that the yield of SO3in this system is too high to arise by direct interaction with oxidizing species from the radiolysis of water (the water absorbs about 0.3% of the total dose). Nor does it turn out that the product formation in wet liquid SO2is simply a superposition of that of the anhydrous substance and that derived from the aqueous system-even taking the highest (initial) yield of H2S04 formation reported. l7 We find that various observations in the water-containing systems are difficult to describe quantitatively or to explain at all on the basis of our simple mechanisms. For instance, we have measured that the yield of HzSz06formation is 1.6 at -40.8’ (see Figure 2) but 2.5 at -23.7’. We see no way to rationalize this temperature dependence, which is outside the experimental error (and shows a consistent trend), with the help of the above reaction steps. Furthermore, we unexpectedly find some initial shortchain oxidation of SO2to SO3in wet, air-free liquid SO2 a t 16” (vapor pressure 2.9 atm). In fact, the G value of this short-chain oxidation process (-17), as well as its duration, were the greatest observed in our experiments. We are therefore led to the conclusion that the radiation-induced products in anhydrous liquid sulfur dioxide systems can be explained satisfactorily on the basis of a few radical steps involving 0 and SO, the “primary” decomposition products. On the other hand, in the presence of water the mechanism no longer accounts quantitatively for the reaction products nor (even qualitatively) predicts the observed temperature dependence.
+
(J7) For instance, consider formation of HzSOa in wet, 02-saturated liquid SOZ a t a dose of 0.25 X lozoeV cm-8. The observed yield amounts to 0.4 mg/cma (see Figure 3). Regarding the aqueous “part system” (0.42 vol %) as O r and SOz-saturated water, we compute a maximum yield of 0.062 mg/cma HzSOa, based on G(HzSO4) = 510 (see ref 7), for it. For the anhydrous liquid SOz, we compute a yield of 0.10 mg/cm3 SOS, based on G(S0s) = 2.6, for this dose. These individual contributions do not add up to the observed H z S O ~ yield.
by F. Quadrifoglio, V. Crescenzi,” A. Cesho, and F. Delben Istituto d i Chimica, UniversitQd i Trieste, Trieste, Italy (Received February 3, 1971) Publication costs assisted by the Consiglio Nazionale delle Recerche
The physicochemical properties of hexamethylenetetramine (HMT) aqueous solutions have attracted considerable attention. 1-4 In terms of certain features exhibited by these solutions, HMT has been considered as a “structure-maker” solute in water.6 The results reported here should help to gain a more complete physicochemical picture of the water-HMT system and hence also to provide additional, though indirect, information on the influence of HMT on the structural organization of the solvent. Our work has been concerned with measurements of Table I: Heat of Dilution of HMT Solutions a t 25’a Pobsdv 111.2
0.1809 0.3118 0.3277 0.5625 0.8509 0.9671 1.3447 1.6824 2.0680 2,6044 2.8076 4.4004
0.1708 0.2984 0.3120 0,5457 0.8029 0.9078 1,2534 1.5551 1,9486 2,4125 2.6828 4.0973
crtl
x
10-1
2.012 4.602 5.311 8.644 39.84 56.71 117.2 207.0 242.2 457.7 333.1 1252.0
AH7 cal/mol
AH/Am
2.655 3,888 4.426 4,886 13.86 16,998 28.36 40.91 38.63 64.65 42.02 113.3
262.2 290.1 281.9 290.8 288.7 286.6 310.6 321.4 323.6 336.9 336 7 373.8 I
=All measurements have been carried out using a LKB batch-type microcalorimeter. The purification of HMT has been made as already described.28
(1) J. F. Walker, “Formaldehyde,” Reinhold, New York, N. Y., 1944.
(2) (a) V. Crescenai, F. Quadrifoglio, and V. Vitagliano, J. Phys. Chem., 71, 2313 (1967); (b) Ric. Sci., 37, 529 (1967); (c) L. Costantino, V. Crescenzi, and V. Vitagliano, J. Phys. Chem., 72, 2588 (1968).
(3) J. L. Neal and D. A. I. Goring, ibid., 74, 658 (1970). (4) 0 . Nomoto and H. Endo, Bull. Chem. SOC.Jap., 43, 2718 (1970). (5) G. Barone, V. Crescenai, A. M. Liquori, and F. Quadrifoglio, J. Phys. Chem., 71, 984 (1967).
The Journal of Physical Chemistry, Vol. 76,No. 23,1971
NOTES
3634 Table I1 : Thermodynamic Characterization of the HzO-HMT System 4 OC
ms.ta
Vb
25 30 35
6.470 6.326 6,150
+ 0.220m ... 1 + 0.196m 1
-
AH/Amc
273 272 278
Lz
+LI
+ 24m + 24m + 21m
273m 272m 278m
+ 12m2 + 12m2 + lOma
546m 544m 556m
+ 36m2 + 36m2 + 31m2
L1
-(4.9m2 -(4.9m2 -(5.0m2
+ 0.43ma) + 0.43ma) + 0.38m3)
Integral heat of H M T solutiond (30'): AH, = - 5 . 1 kcal/mol ( m = 0.110) Differential heat of HMT solutione (30"): AR = -3.2 kcal/mol (msat = 6.326) Heat of dilution; msat-+ 0 . llOm (30'): AH = -2.2 kcal/mol (from AH/Am) Enthalpy of melting of the water-HMT clathrate: (Elemental analysis: HPIIT. 6H20)
AHm = 9.51 kcal/mol (at 13")
a The concentration of H M T in the saturated solutions was determined oia HMT decomposition with HzSOa as reported in the literature.' b Isopiestic gravimetric measurements.2 c Measurements with a LKB batch-type microcalorimeter. Standard deviation from fit, u ; at 25", u = 2.1; at 30", u = 4.7; at 35", u = 4 . 1 , d Measurements with an isothermal calorimeter of the type described by Schreiber and Wa1dman.B E From solubility and activity coefficient data (see text).
(1) the enthalpy of dilution of HMT in a rather wide range of concentrations at three temperatures; (2) the osmotic coefficient of HMT aqueous solutions at 35"; and (3) the differential and the integral heat of solution of HRIT in water at 30". Measurements have been also carried out of the heat of fusion of the crystalline clathrate, HRIT .6Hz0. Only the results of the heat of dilution experiments a t 25" are reported in Table I, data for 30 and 35" being in fact very close to those for 25". In Table I1 a summary is given of some relevant thermodynamic quantities derived from the experimental heat of dilution data, as well as of other data useful for a physicochemical characterization of the system examined. These data permit a direct evaluation of the dependence of the excess partial molal entropy of water, (Sl XI"), upon HMT concentration. The excess entropy values mere calculated according to the equation'
(S1 - X1o)
= L1/RT
- R In (al/N1)
(1)
where al is the activity of water at the solute mole fraction N z = 1 - N 1 , on the basis of the L1-m and cp-m ( p = - (55.51/m) In al) relationships reported in Table 11, for 30". For low m values (m 5 2, moles/kilogram of water) the correlation A& = -0.010m2 is easily verified. From the magnitude and sign of the relative partial molal heat content of solute and of solvent, i.e., LZ and El, respectively, and of the excess partial molal entropy of water, the hypothesis that HhlT interacts with water in a way typical of "structure-maker" solutes gains further support. I n Table 11, data on the integral and on the differential heat of HMT dissolution in water are also reported. The differential heat of solution, AR, at 30" was calculated from HMT solubility data (for illustrative purposes rounded off solubility values at only three temperatures have been reported) and the osmotic coefficient data, with the equation The Journal of Physical Chemistry, Vol. 76, N o . 28, 1071
where y is the activity coefficient of HMT. The approximate relationship: In y = 0.413m, immediately derivable from the p-m data at 25 and 35", was assumed. Taking into account the important contribution of the heat of dilution (from the AH/Am data at 30") it is seen that the experimental integral heat of solution value is reproduced with reasonable accuracy (Table 11). I t is worth recalling, finally, that the ability of HMT of interacting with water molecules giving rise to ordered solvent structures is also very clearly demonstrated by the facile formation of a clathrate H M T 6 H z 0 of well-defined crystal structure* and dielectric properties.9 In our experiments the heat of melting of the HMT clathrate (AH, = 9.5 kcal/mol at 13", the melting temperature) was determined using small crystals of the clathrate with the aid of a differential scanning calorimeter (Perkin-Elmer, DSC-1B). A detailed theoretical evaluation of AH, for the (CH2)6N4-6HZOspecies, as it has been made in the case of simple gas hydrates,1° is hampered by various difficulties. I t is nevertheless worth pointing out that a rough calculation based on the simple equation
AH,
=
6(AHi,,
+ AC,AT)
(3)
where AHi,, = 1.436 kcal/mol is the heat of melting of pure ice I at 0" and 1 atm, and ATAC, is the heat capacity term for water (ACp = 8.91 cal/(mol deg) for the transition ice + water, with AT = 13")) yields a limit(6) H. P. Schreiber and M. H. Waldman, J . Polym. Sci., Part A-8, 5, 555 (1967).
(7) H. S. Frank and A. L. Robinson, J . Chem. Phys., 8 , 933 (1940). (8) T. C. W. Mak, ibid., 43, 2799 (1965). (9) D. W. Davidson, Can. J . Chem., 46, 1024 (1968). (10) D. Turnbull, J . Phys. Chem., 66, 609 (1962).
NOTES ing value of ca. 9.3 kcal/mol for AHm,which happens t o be very close to our experimental figure. I n view of the oversimplified model underlying eq 3 in our case, this coincidence may be somewhat fortuitous. I t is conceivable that a t temperatures higher than 13’ and at slightly lower concentrations, HMT molecules may induce in water a local order reminiscent of that of the clathrate. I n our opinion, speaking of solvent structure around solute particles would thus mean, in the case of HMT, building of a sphere of solvation whose geometry is strongly influenced by the fourfold symmetry of donating +IT groups of the solute. Acknowledgments. This work has been sponsored by the Consiglio Nazionale delle Ricerche, through the “Istituto di Chimica delle Macromolecole” Milan. We wish to thank Dr. lf.Pillin of this institute for the measurements of the integral heat of solution of HMT.
Analysis of Broadly Overlapping Absorption Bands According to a Two-Absorber Model
3635 may easily be modified to accommodate other possibilities. Suppose that a measured absorption band with a shape function F ( v ) 5 1 a t a fixed temperature consists of two overlapping components corresponding to two distinct chemical species. The shape of the composite band may be written as
F(v)
=
sfl(Y)
+ YfdV)
in which fi(v) andfz(v) are the characteristic shape functions for the two components and thus depend only on frequency v, and x and y are coefficients which depend only on composition. Each shape function is normalized so that its maximum value is unity. F ( v ) is thus a function of metal concentration as determined by the magnitudes of the coefficients x: and y. I t is easy to show t h a t s = Al(V1m)/A(Ym) and y = A 2 ( ~ 2 m ) / A ( ~ m )in which Al(vlm) and AZ(vZm) are the absorbances due to species 1 and species 2, respectively, at the positions of the maxima of fi(v) and fi(v), respectively, and A ( v m ) is the total absorbance at the position of the maximum of F( v) . Because Al(v1m)
+ Az(vzm)
2
Al(vm)
+ Az(vm)
Department of Chemistry, Brandeis University, Waltham, Massachusetts 02154 (Received April 1, 1971) Publication costs assisted by the National Science Foundation
The optical absorption of alkali metal solutions in liquid ammonia consists of a single broad band under a variety of experimental conditions. l-6 The dependence of the spectrum on composition of the solution is slight.1~2~6~6 This fact has been cited in support of a one-absorber model of the optical spectra of these solut i o n ~ . ’ ~ ~n’evertheless, ~’ the fact that the spectra do depend on composition at all suggests that the observed band may be a composite of broadly overlapping absorbances from two or more distinct absorbers.* To test this possibility we have developed a method of analyzing a composite band into two components whose behavior as a function of solution composition provides a test of the validity of the txo-absorber model. In addition, possible equilibria between the absorbers may be tested under certain circumstances. Although the method of analysis was developed with metal-ammonia solutions in mind, it mag be applied to any case in which two absorption bands overlap. To suit our purpose it has been assumed in the development which follours that the overlap between the components is great enough so that only one maximum in the spectrum occurs at each composition. The analysis
= A(vm)
(2)
it follows that x + y l l
by T. R. Tuttle, Jr.,*Gabriel Rubinstein, and Sidney Golden
(1)
(3)
The equal sign applies when vim = VZm. When the bands are close together and have comparable widths the sum(3) will be close to unity. To apply eq 1 to separate F ( v ) into components it is necessary to know a t least one of the shape functions fi(Y) or f z ( v ) . Suppose fi(v) has been determined by extrapolation to infinite dilution.6 Then if s is also known yfz(v) and hence f z ( v ) may be determined through an application of eq 1. If there is a region in the spectrum wheref2(v) = 0, then s = F(v)/fl(v) for frequencies in this region. When no such region exists, as is the case for metal-ammonia solutions, x: cannot be determined directly. However, a useful analysis can still be made which under certain circumstances leads to a value of c. Let F(v)
+ YOfi”(V)
(4) in which 1 2 fz’(v) 2 0 and yo 2 0; Le., za is chosen = ZOfi(Y)
(1) R. C. Douthit and J. L. Dye, J . A m e r . Chem. Soc., 82, 4472 (1960). (2) M. Gold and W. L. Jolly, Inorg. Chem., 1,818 (1962). (3) D. F. Burow and J. J. Lagowski, Advan. Chem. Ser., 50, 125 (1965). (4) R.K.Quinn and J. J. Lagowski, J . Phys. Chem., 72, 1374 (1968). (5) W . H.Koehler and J. J. Lagowski, ibid., 73, 2329 (1969). (6) I. Hurley, T. R. Tuttle, Jr., and S. Golden, “Metal Ammonia Solutions,” Butterworths, London, 1969, p 503. (7) iM.Gold, W. L. Jolly, and K. S. Pitser, J . Amer. Chem. Soc., 41, 3089 (1964). (8) S. Golden, C. Guttman, and T. R. Tuttle, Jr., J. Chem. Phys., 44, 3791 (1966).
The Journal of Phgsical Chemistry, Vol. 76, No. dS, 1971
