NOTES
297
these studies, however, were carried out at or above room temperature, whereas the formation of nitrous oxide by the direct reaction of hydrogen atoms with nitric oxide21Khas been directly observed only at low temperature. In view of this, we have carried out a brief investigation of the catalytic reduction of nitric oxide between -80 and 100".
Results and Discussion The catalyst used for this study was prepared by impregnation of alumina (from the hydrolysis of aluminum isopropoxide) with chloroplatinic acid followed by drying and air calcination at 400". A 0.25-g. sample was used in these runs. Prior to each series of runs, it was reduced in hydrogen for 2 hr. at 400". The surface area was 110 m.2/g. In the studies with nitric oxide, the reactant stream was hydrogen at 1 atm. passed through a saturator containing nitric oxide at -183" to give a nominal 250:l H2:NO composition. I n the studies with nitrous oxide, the reactant stream was hydrogen at 1 atm. passed through a saturator at -132" to give a nominal 1OO:l H2:N20 composition. Temperature control at or below room temperature was achieved by liquid baths manually controlled. Above room temperature an oven was used. Products collected in a trap at - 195" were analyzed mass spectroscopically with a few check runs by gas chromatography. Figure 1 shows the analysis of condensables (except for water) found in the effluent stream as a function of catalyst temperature. Points for ammonia, and nitrous oxide very near 0% are shown only when these products were detected. The solid symbols indicate points obtained on increasing the temperature; the open-circle point indicates the result of a check run performed after the above sequence; the triangular points show results obtained after the catalyst was reduced at 400" for 2 hr. The results definitely show that nitrous oxide is the product formed first as the temperature is increased. The occurrence of a maximum is consistent with the initial formation of HNO followed by one of the subsequent steps 2HNO -+
H20
+ N20 -% 2NH3 + 2H20
or
TEMPERATURE
"K
Figure 1. Composition of the exit gas (water excluded) as a function of temperature in the catalytic hydrogenation of nitric oxide.
nitrous oxide over the same catalyst yielded no detectable ammonia. (Nitrogen would not be detected by our method of analysis, but since reduction did occur, as evidenced by water formation, it is likely that the sole product is nitrogen and water as reported by other 12)
Acknowledgment. Acknowledgment is made to the donors of the Petroleum Research Fund, administered by the American Chemical Society, for support of this research. (12) See ref. 9, pp. 135, 181.
On the Refractive Indices of
Aqueous Solutions of Urea by John R. Warren' and Julius A. Gordon Biochemistry 8&ion, Depart& of Pathology, University of Colorado Medical Center, Denver, Colorado 80220 (Received August I , 1966)
11[1 NHs + H20
Recently, it has been reported28that the refractive index, viscosity, and density of aqueous urea solutions undergo identical sharp transitions below 1 M ; the refractive index becomes completely linear with con-
The first possibility is unlikely for two reasons. First, variation of the flow rate by a factor of 10 caused only slight variation in the composition of products. Second, at room temperature and at 125O, hydrogenation of
(1) Trainee under U. S. Public Health Services Grant GM-97703. (2) (a) V. K. Venkateaan and C. V. Suryanrtrayana, J . Phys. Cbm., 60, 776 (1956); (b) these authors report their data, in terms of normality. They apparently assume the equivalent weight of urea to be half the gram molecular weight for reasons unclear to us.
HNO +H20
+ N20
Volume 7'0,Number 1
January 1066
NOTES
298
butyl alcohol,6 and acetone.’ Viscosities were determined in Cannon-Manning semimicroviscometers having water flow times of around 250 sec. at 20”. Viscosities are given as relative viscosities, q/qo = (t/to)(p/po), for which 9/90 is the relative viscosity, t and to the flow times of solution and water, respectively, and p and POthe density of solution and water.8 The densities of urea solutions at 20” were determined by linear extrapolation from known densitiesBJ0 at 30 and 25O, and that of water1’ was taken as 0.988.
Results and Discussion I
1
’I
2
t
I
t
t
I
3
4
6
6
7
Concentration (M)
Figure 1. Refractive indices of aqueous urea solutions a t 35’ plotted against concentration: 0, data from this study; A, data of Venkatesan and Suryanarayana, ref. 2a; the authors report intensification of the plot between 1 and 2.5 M , but no experimental points are given.
Venkatesan and Suryanarayana, 2a considering urea solutions to be solutions of a weak electrolyte, studied the physical properties of these solutions up t o a concentration of 10 M . These investigators observed abrupt breaks in the plots of refractive index, vis-
These surprising obcentration only above 2.5 servations suggest notable concentration-dependent intermolecular rearrangements of aqueous urea solutions below 2.5 M . Our interest was aroused by the significance such rearrangements might have for the unusual ability of urea to denature proteins as it is yet unclear whether denaturation depends upon specific interaction between urea and protein molecules or some general alteration in the physical structure of the water ~ o l v e n t . ~This paper presents data showing, in fact, a linearity without any detectable transition in the physical properties of aqueous urea solutions with concentration and draws attention to the discrepancies in older, widely used values of the refractive indices of urea solutions with those obtained in this laboratory. Experimental Section Refractive indices and viscosities were determined for urea solutions using deionized, double-distilled water and reagent grade urea (Mallinckrodt, Lot 8648) purified by double recrystallization from 75% ethanol followed by drying under vacuum at room temperature. For comparison purposes, two other brands of reagent grade urea (Baker, Lot 4204; Merck, Lot 53061) were used. Refractive indices relative to air were read to an accuracy of =!=0.00004 on a Bellingham and Stanley Abbe 60 High Accuracy refractometer thermostated at the desired temperature within h0.05” by a largevolume water bath. The refractometer was calibrated daily against the known refractive index of water4 and tested intermittently utilizing the reported refractive indices of N,N-dimethylformamide,5 n-
Concentration (M)
Figure 2. The Viscosities of aqueous urea solutions a t 20” plotted against concentration: 0, data from this study; A, ref. 5, Vol. v, p. 22. ~
(3) F. M. Richards, Ann. Rev. Bwchem., 32, 269, 282 (1963). (4) L. W. Tilton and J. K. Taylor, J. Res. Nail. Bur. Std., 20, 419 (1938). (5) E. W. Washburn, Ed., “International Critical Tables,” Vol. VII, McGraw-Hill Book Go., Inc., New York, N. Y., 1930, p. 35. (6) Sea ref. 6, p. 36. (7) E. Pahlavorini, Bull. 8oc. chim. Belges, 36, 533 (1927). (8)8. Glaaetone, “Textbook of Physical Chemistry,” D. Van Nostrand Go., Inc., New York, N. y., 1946, p. 498. (9) F. T. Gucker, Jr., F. W. Gage, and C. E. Moser, J . Am. Chem. Soc., 60, 2589 (1938). (10)A. N. Campbell and E. M. Kartsma~k,Can. J. Res., 28B, 161 (1960). (11) R. C. Weast, Ed., “Handbook of Chemistry and Physics,” Chemical Rubber Publishing Go., Cleveland, Ohio, 1964, p. F-4.
299
NOTES
Table I: bfractive Indices and Viscosities of Urea Solutions
9.00 8.00 7.26 6.00 5.73 5.00 4.00 3.50 2.58 2.00 1.75 1.30 1.25 1.10 0.90 0.50 0.20 Water
1.40794 1.39908 1.3935" 1.38322 1.3810' 1.37488 1.36665 1.36256 1.3547" 1.34998 1.34790 1.34397 1.3435" 1.34222 1.34062 1.33728 1.33409 1. 3330d
1.41013 1.4020"
1.41886 1.4103"
1.40482
1.37684
1.38381
1.37211
1.36432
1.37123
1.36005
1.35528 1.35122
1.34788 1 .34583 1.34214
1.823 1,4073' 1.4000 1.3855 1.299
1.3560 1.35188 1.34950 1.34557
1.098 1.085 1.3442
1,34394 1.33871
1.34958 1.34809 1.34473
1 . 3345d
1 . 3403d
'
See ref. 19c. Viscosity relative to water (density corrected). See ref. 19a. e See ref. 11, p. E105.
cosity, and density against concentration in the region of 0.09 to 2.5 M at 35" (for refractive index data, see Figure 1). This sudden arrest of the increase in these physical properties with concentration is interpreted by them as a reorientation of the molecules in solution arising from some change in solutesolvent dipole interactions. For comparison our refraction data for urea solutions at 35" are similarly plotted, there is no suggestion of n break in linearity with concentration, and, except for two deviant points, the two sets of data closely approximate each other. Within experimental error, both sets of data are then linear for solutions from 2.5 to 10 M . Furthermore, relative viscosities determined for identical solutions used in our refractive index study can best be represented by a smooth curve and are in good agreement with other work (Figure 2). Thus, our observations fail to confirm the Viscosity and refractive index data of Venkatesan and Suryanarayana and therefore suggest that the intermolecular forces of urea-water solutions are either undetectably small and probably weaker in magnitude than those of the hydrogen bond,12 or the forces are insufficiently Merent from those in the pure components and are concentrate independent.l* In either event, the inability to demonstrate a dramatic concentration-dependent urea-water interaction is less favorable to a mechanism of protein denaturation in-
1.34032 1.33876 1.33548 1.33282 1.33122*
" Determined from
1.048 1.039
refractive index vs. concentration graph.
volvhg changes in the general properties of water14 than to mechanisms lnvolving a more direct interaction between proteins and urea.I6 Consistent with the latter concept are the observations that bovine serum albumin retains its native configuration in concentrated dioxane solutions1*whose refractive indices are nonadditive" and recent experiments in this laboratory indicating a small but sigdicant binding of urea to bovine plasma albumin during the denaturing process.la The refractive index data for 0.2 to 9 M urea solutions at 20' taken at the wave lengths 589, 546, and 436 mp are shown in the first three columm of Table I. Linearity exists with urea concentration at all three wave lengths, and the functions intercept the ordinate at known values of the refractive indices of water at 20°.1sa The refractive indices of urea solu-
(12) F.M. Arabid, C. Gilea, E. McClure, A. Ogilvie, and T. J. Rose, J . C M . SOC.,67 (1966). (13) N. Bauer, K. Fajam, and 9. 2. Lewin, "Phyeicd Methods of Organic Chemistry," Vol. I, 3rd Ed., Part 11, Interscience Publishers, Ino., New York, N. Y., 1969,Chapter XVIII. (14) J. A. Rupley, J . Phys. C h . ,68, 2002 (1964). (16) W. P. Jencks, Fed. Proc., 24, Suppl. No. 16,S-60 (1966). (16) J. A. Gordon and W. P. Jencke, B w c h i a t r y , 2,47 (1963). (17) F.Hovorka, R. Schaefer, and P. Preiabach, J . An. C h . SOC., 58, 2264 (1936). (18) J. R.Warren and J. A. Gordon, Boon to be published.
Volume 70,Number 1 JanuayllO66
NOTES
300
tions prepared from three different commercial preparations of urea at several concentrations differed by only *0.0002. Thus, only the more extensive data obtained with the Mallinckrodt preparation are summarized in Table I. The refractive indices of urea solutions are extensively used for the reduction of the optical rotatory power of macromolecules in urea solutions to values they would have under vacuum by means of the Lorenz-Lorents correction.lgb Comparing our refraction data at the sodium D doublet to the older and widely used data,lSo major discrepancies increasing with urea concentration are seen (compare columns 1 and 5 of Table I). At 8.00 M urea the older value of the refractive index is +0.0082 higher than the value obtained in this study, a difference well outside our maximum over-all experimental error of =k0.0002. We are unable to ascribe this deviation to small errors in technique or to extremes in ambient temperature and pressure which usually give rise to differences less than a few units in the fifth decimal place.20 Moreover, Foss, Kang, and Schellman recently obtained data for 8.00 M urea at 20’ as a function of wave length,ledand a comparison of their data with ours a t 436 and 546 mp and an extrapolation of their data to 589 mp reveal positive differences ascribable to minor experimental variations of two units or less in the fourth decimal place; therefore, their data are consistent with the present report. I n view of the refractive index and viscosity data reported in this communication, it seems, therefore, that urea solutions do not undergo a detectable transition in structure a t some critical concentration or concentration range of urea. This is not entirely surprising in view of Gucker, Gage, and Moser’s elegant study on the densities of aqueous urea solutions which showed that the apparent molal volume of urea is a linear function of the first power of the volume concentration up to 4 M , suggesting that urea is very nearly a perfect solute and does not exhibit the large electrostriction of electrolytes and polar nonelectrolyte~.~
Acknowledgment. Support by a grant from the National Institute of General Medical Sciences, U. S. Public Health Service (GM-11345-02), to Julius A. Gordon is acknowledged. ~~~
~
(19) (a) G.Fasman in “Methods in Emymology,” Vol. VI, Academic Press Inc., New York, N. Y.,1963, P. 952; (b) ibid., P. 930; (0) ibid., Table VI; (d) ibid., p. 957. (20) See ref. 13,p. 1141.
The Journal of Physical Chemistry
The Principle of Microscopic Reversibility by Robert L. Burwell, Jr., and Ralph G. Pearson Department of Chemistry, Northwestern University, Evanaton, Illinois (Received August 9, 1966)
The principle of microscopic reversibility, p.m.r., is often invoked to exclude certain postulated reaction mechanisms. This principle states’ that any molecular process and its reverse occur with equal rates at equilibrium. In mechanistic terms it states that, if a certain series of steps constitutes the mechanism of a forward reaction, the mechanism of the reverse reaction (under the same conditions) is given by the same steps traversed backwards.2 Thus, it is certainly valid to exclude all other mechanisms in any case when the reverse mechanism is known. However, the p.m.r. is often used as a basis for exclusion where neither mechanism is known beforehand. The exclusion is usually due to a certain lack of symmetry in the forward and reverse direction^.^ The argument is most easily seen for the case of isotopeexchange reactions, where, if kinetic isotope effects are ignored, the mechanism must be precisely the same in both directions, The purpose of this note is to point out the exact nature of the application of the p.m.r. to such isotope-exchange reactions. This can be simply done by drawing conventional free energy profiles along reaction coordinates. If the exchange reaction proceeds by but one path, then p.m.r. does indeed require a symmetric free energy profile with respect to the reaction path. If the number of intermediates formed is even, including zero, the two isotopic atoms entering and leaving become equivalent in the central transition state; if odd, in the central intermediate. This is illustrated in Figure l a ~ between CHJ3r and *Br- (zero interfor an S Nreaction mediates) and in Figure l b for an SN1 reaction between &butyl bromide and *Br- (one intermediate, (CH3)aCf Br*Br-). Two or more atoms are equivalent if, within an appropriate time period, the environments seen from the nuclei of the two or more atoms are identical or are mirror images of each other. The p.m.r. does not permit a one-path mechanism
+
+
(1) R. C. Tolman, Phys. Rev., 23, 699 (1924); “The Principles of Statistical Mechanics,” Oxford University Press, London, 1938, pp. 163, 165. (2) A. A. Frost and R. G. Pearson, “Kinetics and Mechanism,” John Wiley and Sons, Inc., New York, N. Y.,1961,pp. 211-213. (3) For a recent example see 8. L. Johnson, J. Am. Chem. SOC.,8 6 , 3819 (1964). The author rejects nonsymmetric reaction paths by incorrect application of the p.m.r.
