The Journal of Physical Chemistty, Vol. 82,No. 17, 1978
Self-Association of Gases
parison between IR and dielectric measurements shows that 6, is close to zero for LiSCN. Consequently quadrupoles must be nonpolar in agreement with the result of the present paper.
1947
(7) J. P. Badiaii, H. Cachet, A. Cyrot, and J. C. Lestrade, J. Chem. Soc., Faraday Trans. 2 , 69, 1389 (1973). 18) C. F. J. Bottcher, “Theory of Electrical Polarization”, Elsevier, Amsterdam, 1973. (9) (a) P. Jagodzinski and S. Petrucci, J . Phys. Chem.,78, 917 (1974); (b) H. Farber and S. Petrucci, ibid., 80, 327 (1976); (c) H. C. Wang and P. Hemmes, J . Am. Chem. SOC.,95, 5119 (1973). (10) R. M. Fuoss and M. Accascina, “Electrolytic Conductance”, Interscience, New York, N.Y., 1959, Chapter XVIII, p 254. (11) P. Debye, “Polar Molecules”, Chemical Catalog Co., New Yo&, N.Y., 1929. (12) M. Davies in “Dielectric Properties and Molecular Behaviour”, N. Hill et al.. Ed.. Nostrand-Reinhold. London. 1969. D 298. (13) M. Chabanel, C. Menard, and G. Guiheneuf, C . A. Acad. Sci., Paris, 272, 253 (1971). (14) D. Paoli, M. Lucon, and M. Chabanel, to be submitted for publication.
References and Notes (1) H. Farber and S. Petrucci, J . Phys. Chem., 79, 1221 (1975). (2) H. Farber and S. Petrucci, J . Phys. Chem., 80, 327 (1976). (3) D. Saar, J. Brauner, H. Farber, and S. Petrucci, J . Phys. Chem., 82, 545 (1978). (4) D. Menard and M. Chabanel, J . Phys. Chem., 79, 1081 (1975). (5) S. K. Garg and C. P. Smyth, J. Chem. Phys., 42, 1397 (1965). (6) S. Petrucci, P. Hemrnes, and M. Battistini, J. Am. Chem. Soc., 89, 5552 (1967).
Self-Association of Gases. 1. Theory. Application to the Nitrogen Dioxide-Dinitrogen Tetraoxide Systemt David
R. Powell and E. T. Adams, Jr.”
Department of Chemistry, Texas A&M University, College Station, Texas 77843 (Received March 27, 1978) Publication costs assisted by The Robert A. Welch Foundation
Using the Gibbs-Duhem equation and some simple assumptions about activity coefficients, an equation of state for nonideal gas self-associations can be developed. This equation, which relates total pressure to the total concentration, temperature, and apparent number average molecular weight, is formally identical with an equation developed for osmotic pressure of a self-associating solute. Thus, one can use previously developed procedures in the analysis of gas self-associations. These procedures have been successfully applied to the NO2 data of Verhoek and Daniels.
Introduction Self-association of molecules in the gas phase is a well-known and long-studied phenomenon.l-17 Verhoek and Daniels,l as well as other^,^^^ carried out pressurevolume (P-V) measurements on NO2 gas at several temperatures. The analysis of the data obtained by Verhoek and Daniels1 led them to conclude that their data were best represented as a monomer-dimer association, i.e. 2NO2(g) + N@,(g) (1) Another well-known self-association involves H F gas. Hildebrand and his associate^^^^ believed that H F gas underwent a monomer-hexamer association at temperatures below 80 “C. Others believed this to be the case, but later studies indicated that the association might be more c~mplicated.~-~ The association of vapors of organic acids1°-13 has also been studied. The dimerization of formic acidlOJ1and acetic acid12J3are notable examples of this case. At high temperatures vapors of alkali metals,14 KBr, and other salts16-17 are also reported to self-associate. At present, the theories for the analyses of gas-phase self-associations have been largely based on methods developed by Verhoek and Daniels,l Kreuzer,ls and Rossotti and Rossotti.lg These methods suffer in that they must assume ideal behavior. Usually no attempt has been made to correct for nonideal effects. In addition, none of these methods explicitly takes advantage of the interrelation between the number average (Adnc)and the weight average (MWJmolecular weights, or their apparent values (M, and MwJ when nonideal behavior exists.*22 By using these interrelations it is possible to test for the presence or absence of a variety of self-associations, set up plots or Presented in part at the 32nd Southwest Regional Meeting of the American Chemical Society, Ft. Worth, Tex., Dec 1-3, 1976.
0022-3654/78/2082-1947$01 .OO/O
other tests to choose the best model, and evaluate the equilibrium constant or constants (Ki) and the nonideal term (BMl).21i22This is done using the experimental data and other data derived from it. In addition one can also evaluate the apparent weight fraction of monomer (f,) and use it in the analysis. These advantages were not possible with the other previously developed methods. The purpose of this paper is to show how one’can analyze both ideal and nonideal gas phase self-associations using methods of analysis very similar to those used for studying self-associations in solutions by membrane or vapor pressure osmometry.20B21We will show how one can obtain M,,, Mwa,and fa from measurement of the total gas pressure in a series of experiments at constant temperature. This method will be applied to the self-association of NO2 gas. In a subsequent paper we will discuss its application to the self-association of H F gas and to CH,COOH gas.
Theory At constant temperature the condition for chemical equilibrium for a self-association is npl = p,, (n = 2, 3, ...) (2) Here p, is the molar chemical potential of species i (i = 1, 2, ...). In order to develop a relation between the equilibrium total pressure, P, and the apparent number average molecular weight, M,,, one starts with the Gibbs-Duhem equation. Thus a t constant T V d P = E n , dp,
(3)
1
can be rearranged to give (4)
Here ci is the concentration of species i in g/L. Now 0 1978 American Chemical Society
1940
The Journal of Physical Chemistry, Vol. 82, No. 17, 1978
assume that the natural logarithm of the activity coefficient of species i can be expressed as20-25 In yi = iB*Mlc (i = 1, 2, ...) (5) Here B , is a function of T , M1 is the molecular weight of the monomer, and c is the total concentration of the gas in g/L. The following relations also apply: pb =
+ RT In yici
(6)
D. R. Powell and E. T. Adams
Note that these are proper integrals since
= (-Kz
+ BM1)/2
if dimer is involved in the association
= BM1/2
if no dimer is involved in the association (18) For very strong self-associations it may be more advisable to evaluate In (fa/fa*), which is defined by21
and Mi = iM1 (i = 2, 3, ...) (8) Here is the partial molar volume of species i in L/mol, & is the partial specific volume in mL/g, and Mi is the molecular weight of species i. For simplicity it is assumed that the partial specific volumes of the associating species are equal. In a manner similar to the one used with membrane osmometry,20the above relations (eq 2-8) can be used to obtain
vi
P =- c C + Bc2 - + ... = (9) Mnc 2 Mna Here Mna is the apparent number average molecular weight, Mncis the number average molecular weight and B is the second virial coefficient. They are defined by Mnc = C n i M i / C n i = c / C ( c i / M i ) i
I
(10)
i
ci
B = B * + p 1000M1
-Mi- - -M1
BMlc +Mnc 2
(12) Mna Note that eq 9 is formally identical with the equation developed by Adams20 for osmotic pressure of self-associating solutes, namely
Here R is the gas constant in mL atm deg-I mol-l. It has been shown previously that one can obtain the apparent weight average molecular weight, Mwa,from the relation20
Here Mwc is the weight average molecular weight; it is defined by Mw, = C n i M t / C n i M i = C c i M i / c i
(15)
i
The quantity M l / M w acan be expressed as
Additionally one can obtain the natural logarithm of the apparent weight fraction of monomer, In fa, from 2o In f a = In fl
+ BMlc = X C ( $ - 1 ) $ =
'(M1 Mna
-
1)
The quantities cl, Mna,Mwa,and In fa (or In fa/fa*) can be used to establish the type of self-associationpresent, if that is not known a priori, and to evaluate the equilibrium constant or constants, Ki, and the nonideal term or second virial coefficient, BM1. For instance one can combine Ml/Mna (see eq 12) and M 1 / M w a(see eq 16) in the following way to eliminate BM1, namely21i22 2M1 MI 2M1 M1 [=---(21) Mna Mwa Mnc Mwc The quantity [ is the easiest function to use in the analysis of the self-association. Other quantities can also be used, and the details are given elsewhere.21p22We will show the application of these methods to gas phase self-associations. --I-
and
1
Here Mna, is the value of Mna at c = c*. It should also be noted that the concentration of the gas, c , is related to the ideal pressure, Pid, which is the pressure that would be observed if no self-association occurred. Thus Pid/RT = c/M1 (20)
$ + (Mna M1
- 1)
(17)
The Self-Association of NO2 Gas To illustrate the application of our methods to gas-phase self-associations, we will first examine the self-association of N02(g), using data from the elegant experiments of Verhoek and Danie1s.l They measured the equilibrium pressure of different amounts of N,O4(g) in a thermostatted container of known volume. Their experiments were carried out at 25,35, and 45 "C; more complete details about their experimental procedure will be found in their paper. We have used data from their Table I. The pressures used in their experiments ranged from 0.1566 (25 "C) to 1.0474 (45 " C ) atm, which correspond to values of c/Mm of 6.401 X to 4.012 X mol/L, respectively. The first step in this analysis is to make plots of cM1/Mnavs. c , like the one shown in Figure 1. Since Verhoek and Daniels1 listed the concentration of the gas as moles per liter of Nz04(g),we obtained c in g/L very simply from c = 2M1[NZO,] = 92.02[N204] (22) Note that M 1 = 46.01 g/mol. The quantity cM1/Mnais obtained from eq 9. A variable knot spline function was used to obtain the smooth curve through the data points. The next step is to construct plots of M l / M n avs. c from the smoothed data. Alternatively, one can use a variable knot spline function to smooth the plots of M1/Mnavs. c. Both procedures were tried here, and essentially the same results were obtained in both cases. In some cases, particularly with strong associations, it may be preferable to smooth the plots of cM1/Mnavs. c and use them to obtain
The Journal of Physical Chemistty, Vol. 82,No. 17, 1978
Self-Association of Gases
d
,4___l' j_l
I 20
1949
c
15 3-
5:
i
tB
0 0
0 5
1 1
C
i
2 5
1 1
I
10
5
Figure 1. Plot of cM,/M, vs. cfor NO2 gas at 25 O C . The solid curve through the experimental points was obtained from variable knot 6-splines; the rectangle indicates the position of the knot or spline. o l i 0
,
-L 1 2
I
w
,
I
I
O 0
2.0
1.0 c
(dl)
Flgure 2. Plots of M,/M,, and M1/Mw,vs. c for NOp gas at 25 O C . MIIMwawas obtained from eq 14. The points represent data obtained from spline smoothed data. The curves through the points were obtained for a monomer-dimer association having K2 = 7.79 L/g and BM1 = -5.3 X L/g (see Table I).
smoothed values of Ml/Mnavs. ca21 Figure 2 shows plots of M , / M , and Ml/Mwavs. c at 25 "C; the self-association was strongest at this temperature. Inspection of these plots indicates that the values of M l / M w aremain greater than 0.5 a t the higher concentrations. This supports the possibility that the association is a monomer-dimer association; however, one must still establish which is the best model for this association. The easiest way to do this is to use the quantity 5 (see eq 21). Test for a monomer-n-mer self-association. Here the self-association is described by
nP1 & P, ( n = 2, 3, ...) (23) where P represents the self-association molecule. For a monomer-n-mer self-association the following relations have been shown to apply, whenever eq 5 applies. The total concentration is given by2@24 c = c1
+ Kncln
(24)
Division of both sides by c leads to fl
+fn = 1
(25)
or 1 - fl = c l / c is the weight fraction of monomer, and f, fn =
Here f1
.
L
-
-
-
L
-
-
.
d
3 (c
0.9
-
(nil
5
I"
Figure 3. Tests for monomer-n-mer associations. Here we have tested for the presence of a monomer-dimer ( n = 2), monomer-trimer ( n = 3), and monomer-tetramer ( n = 4) association. For each choice of n, values of f , were calculated from eq 27 and then used in lots based on eq 28. The curvature in the plots of (1 - f l ) / f 1 3 vs. c'for n = 3 indicated a monomer-trimer association was not present: similar resuks were obtained for the corresponding plot with n = 4. The straight line plot going close to the origin with n = 2 indicates that a monomer4mer associatlon was the best of the three choices: K, was obtained from the slope of the plot.
= cn/c is the weight fraction of n-mer. One can obtain f l from 5, since21i22 2M1 Mi 1 [=---- 2 2fl(n- 1) (26) Mna Mwc n n + f l b - 1)
+
and fl
=
1
(n-ii# 5+2-
;)
-
Once f l is known then K , can be obtained from a modification of eq 25, namely (1- f i ) / f i n = Kncn-'
(28)
and BM1 can be obtained from eq 12 since
Using values of n = 2,3, and 4, we solved for f l (see eq 27) and used it to make plots based on eq 28. The results for n = 2 and n = 3 are shown in Figure 3. It is evident that the plot for n = 2 gives a straight line which passes close to the origin, whereas the plot for n = 3 shows curvature. Clearly, the monomer-dimer association is the better choice. Further support for the monomer-dimer model can be obtained by the following procedure. Since the monomer-dimer association (1,2) is a subset of a monomer-dimer-trimer (1,2,3) association, the values of f l and B M , from the (1,2) association can be used to calculate values of M l / M n afrom an equation appropriate to a (1,2,3) association, namely
1950
The Journal of Physical Chemistry, Vol. 82, No. 17, 1978
D. R. Powell and E. T. Adams
TABLE I: Thermodynamic Parameters for 2N0, Z N,O, B M , x 103: Lk -5.3 * 1.1 -6.9 f 2.6 -8.9 * 1.8
t, "C 25 35 45
K,, x 10-2; L/mol 1.79 f 0.02 0.86 * 0.02 0.407 i 0.005
K,? Llg 7.79 f 0.07 3.73 f 0.11 1.77 f 0.02
A S " ,e
A G ",d kJ/mol -12.86 -11.41 -9.80
f
J K-'mol-' -135.7 i 0.1 -136.0 f 0.2 -136.8 * 0.1
0.03
* 0.06 * 0.03
a These are pointwise average values calculated from eq 12 and 29. The errors reported are the respective standard deviations of the means (Le,, urn = U / N " ~ ) .b These are association equilibrium constants calculated from the slope of plots based on eq 28. (See also FEgure 3). K,, is the molar association equilibrium constant. K,, = K,M,/2. A G O = -RT In K,,. e A S " = ( A H " - A G " ) / T . From the van't Hoff plot AH' = -58.41 kJ/mol (or -13.96 kcal/mol).
2.0
c
** *
.
/ I
/ / /
0
2.0
1.U
c kfl)
Figure 4. Deviation plot used to check on the monomer-dimer association. Since a monomer-dimer association is a subset of monomer-dimer-trimer association, values of f , and 6M1 obtained from the monomer-dimer analysis were inserted into eq 30, which was developed for a monomer-dimer-trimer association, and used for the calculation of 6M1/MW.The deviation plot shows the percent difference between calculated and observed values of 6M,/M,. Note that the deviations fall within f 1%, which indicates that the monomer-dimer association is a good choice.
A deviation plot based on differences between calculated and observed values of Ml/Mna as a function of c can be constructed. This is shown in Figure 4;the deviation from zero is less than fl% . We also tested for the possibility of a sequential, indefinite self-association of the first type,21i22p25 mainly to show the versatility of our method. It is assumed for this association that the molar association constants, Ki, for any step such as P(i-l) P1 e Pi (i = 2, 3, ...) (31)
+
are equal, Le., Ki = K. For this case one obtains the following relations. The total gas concentration C (in g/mL) is given by21922,24325 C = Cl/(l - kC1)' if kC1 < 1 (32) Here h = 1000K/M1
(33)
is the intrinsic equilibrium constant. The quantity become~21,2%24,25
4
This equation is quadratic in fl1I2, and fl1I2 = (1/4){(4
+ 3)2- [([ + 3)' - 16{]1/2)
(35) The intrinsic equilibrium constant, h, can be evaluated from (1 - fl"')/fl
= kC
and the second virial coefficient from M1/Mna = f11j2 + BM1C
(36) (37)
/ii,
*
*
* *
,
,
,
,
0' 0
1.0
c
(dl)
2.0
Flgure 5. Test for a sequential indefinite self-association, using a plot based on eq 36. If this model were correct then one should obtain a straight line passing through or close to the origin.
Note that since Ml/Mna is the same whether one uses concentrations in g/L or in g/mL, it follows that BM1 = 1000BM1,since c = 1OOOC. Figure 5 shows a plot based on eq 36. If this model were the correct choice, one should get a straight line plot going through or close to the origin; the curvature of the plot in Figure 5 indicates that this is not the correct choice. Thus, the simplest model that describes the observed self-association of NO2 gas is a monomer-dimer self-association. In Table I we have listed the values of the equilibrium constants (column 2) and nonideal terms (column 3) in L/g obtained at the three temperatures. The values of Kz were converted to molar association constants, Kzm(see column 4),from which values of AGO (see column 5 ) , the standard Gibbs free energy change, were obtained. A van't Hoff plot of In K2, vs. 1/T was constructed. The value of the standard enthalpy change for the association, AH", obtained from the slope of the plot, was AH" = 14.i!j3 kcal/mol. The values of the standard entropy change, AS", were calculated from AS" = (AH"- AG")/T and are listed in column 6.
Discussion Table I1 shows a comparison of our analysis with the Verhoek and Daniels1 results; note the range of their Kp values we calculated. Chao, Wilhoit, and Zwolinski4 have made some statistical mechanical calculations on the NOz-N204 system, They assumed an ideal monomerdimer self-association was present. Their values of Kp (dissociation), also shown in Table 11, are in good agreement with the values we obtained. The virtue of the P-V-T procedure for studying selfassociations in the gas phase compared to other procedures (see ref 4 for references to other procedures), such as infrared spectroscopy or light transmission measurements, is that it avoids the necessity for introducing parameters
The Journal of Physical Chemistry, Vol. 82, No. 17, 1978 1951
Self-Association of Gases
TABLE 11: Comparison of the Verhoek and Daniels: the Chao, Wilhoit, and Zwolinski,b and Our Results for N,O, 2 2 NO, ref 1 ref 4 this work "C 25
Kp, atm 0.1426
range of Kp , atm 0.1121-0.1476
35 45
0.3183 0.6706
0.2644-0.3174 0.5567-0.6771
t,
AH", kcal/mol 14.67 (25-35 "C) 14.53 (35-45 "C)
Kp , atm 0.146
AH", kcal/mol 13.65' (25-45 "C)
0.308 0.621
Kp, atm 0.137 f 0.001
AH", kcal/mol 14.54d (25-45 a C )
0.294 k 0.007 0.642 f 0.008
EvalEvaluated from In Kp vs. 1/T. The values of Kp are taken from their Table 4. a Reference 1. Reference 4. uated from a plot of In Kp vs. 1/T. The value obtained from a plot of In K,, vs. 1 / T is - 13.96 kcal/mol for the association.
(such as extinction coefficients) other than the equilibrium constant or constants and the nonideal term or terms. It is a relatively simple method to use. Its main disadvantage may be that one may have to do measurements out to sufficiently high concentrations in order to distinguish between two different models in some casesaZ5In order to make their elegant statistical mechanical calculatioins, Chao, Wilhoit, and Zwolinski4needed a lot of physical data available to them. Infrared spectroscopy could give some more direct insight into the nature of the structure4 (type of bonding involved, possible structure: cyclic or noncyclic dimer) which P-V-T data do not do. The use of P-V-T data with these other procedures would give a more detailed picture about the nature of the association. The self-association of NOz gas was studied by Harris and Churney26over the temperature range of 299.71-376.52 K and at pressures of 2-5 cm Hg by absorption of visible light (A 546.1 nm). They were forced to assume ideal conditions, and the extinction coefficients were evaluated by an iterative method. A monomer-dimer associations was assumed to be present; no tests were done for other models. They obtained AHO298.16 = 13.6 kcal/mol, whereas our reanalysis of the Verhoek and Daniels1 data gave a AHo = 14.5 kcal/mol. Verhoek and Daniels' did make an attempt to eliminate nonideal effects by calculating Kp*(we will use the symbol Kp*to indicate an apparent value of Kp) a t every point, and then they plotted these values of Kp*against the total gas concentration as mol/L of Nz04,Le., [N204],,. They thought that the intercept of this plot at [N2O4Itotal= 0 would give Kp. We will show that this is not the case, unless the gas undergoes an ideal self-association, in which case the values of Kp should be independent of gas concentration. A further disadvantage of their method is that the data become less precise as zero concentration is approached, and the value of Kp chosen is based on the intercept of their plot. Thus, less precise data in the low concentration (or pressure) region may have an incommensurate effect on the intercept. In order to calculate Kp, Verhoek and Daniels' first calculated a, the fraction of N204 dissociated. For an ideal self-association, a is defined by
However, if the association is nonideal, then one calculates a*, defined by a* =
2M1-
Mna
(0 Ia* I 1)
Mna
(39)
Thus Kp*for the dissociation of N204 (i.e., N204e 2NOZ) is given by Kp* = 4a*'P/(1
- CY*')
(40)
Since P = 0 at c = 0 and a* = 1 a t c = 0, it is necessary to use l'H6pital's rule to find the limiting value of Kpt. Thus one can show that
Here K2 is the association equilibrium constant; its units are L/g. To achieve this result we made recourse to eq 9 and 4 as well as the following relations:
lim Mna= M1
(43)
c-0
and lim da*/dc = lim [-2M1(dMna/dc)/M,,2] = C-O
c-0
-(Kz - BMi) (44) It is apparent from eq 41 that the nonideal term, BM,, does not vanish, even though values of Kp*are extrapolated, using plots of Kp* vs. c, to zero concentration. If the association were ideal, then BM1 = 0 and KP,O = Kp. For the Verhoek and Daniels' experiments, the values of BM1 shown in Table I are quite small, so that the system that they studied underwent a quasi-ideal self-association. However this should not be the case with all gas selfassociations, and our methods have the advantage of allowing one to calculate BM1 from the experimental data, as well as testing for the presence or absence of a variety of self-associations. The analysis of self-associations that approached our methods most closely was that of Kreuzer.le With his method one could analyze a monomer-n-mer association or a sequential indefinite self-association having all molar equilibrium constants equal (see eq 31), but again his procedure was restricted to ideal self-associations. Although Lansing and Kraemer2' had pointed out the existence of various average molecular weights several years before Kreuzer's18 paper, no explicit use of average molecular weights was used by him. Acknowledgment. This work was supported by a grant (A-485) from The Robert A. Welch Foundation. We thank Dr. Jing Chao, Dr. Peter J. Wan, and Mr. Edward F. Crawford for their comments and interest in this work.
References and Notes (1) F. H. Verhoek and F. Daniels, J. Am. Chem. Soc., 53, 1250 (1931). (2) M. Bodenstein and F. Bo&, 2. Phys. Chem., 100, 75 (1922). (3) W. F. Giauque and J. D. Kemp, J. Chem. Phys., 6, 40 (1938). (4) J. Chao, R. C. Wiihoit, and B. J . Zwolinski, Thermochim. Acta, 10, 359 (1974). (5) J. Simons and J. H. Hildebrand, J. Am. Chem. Sm., 46,2183 (1924). (6) L. R. Long, J. H. Hildebrand, and W. E. Morrell, J . Am. Chem. Soc., 65, 182 (1943). (7) K. Fredenhagen, 2.Anorg. Ai@. Chem., 218, 161 (1934). (8)W. Strohmeier and G. Briegieb, Z. Electrochem., 57, 8 (1953).
1952
The Journal of Physical Chemistry, Vol. 82, No. 17, 1978
(9) J. N. Maclean, F. J. C. Rossotti, and H. S. Rossotti, J. Inorg. Nuci. Chem., 24, 1549 (1962). (10) J. D. Holford, J . Chem. Phys., 10, 582 (1942). (11) A. S.Coolidge, J . Am. Chem. Soc., 50,2166 (1928). (12) E. Johnson and L. Nash, J . Am. Chem. Soc., 72, 547 (1950). (13) F. H. MacDougal, J . Am. Chem. Soc., 58, 2585 (1936). (14) C. T. Ewing, J. P. Stone, J. R. Spann, and R. R. Miller, J. Phys. Chem., 71, 473 (1967). (15) S. Datz, W. T. Smith, Jr., and E. H. Taylor, J. Chem. Phys., 34, 558 11961). (16) K. Hagenmark, M. Blander, and E. B. Luchsinger, J. Phys. Chem., 70, 276 (1966). (17) K. Hagenmark and D. Hengstenberg, J. Phys. Chem., 71, 3337 (1967). (18) J. Kreuzer, Z. Phys. Chem., 853, 213 (1943).
Communications to the Editor
(19) F. J. C. Rossotti and H. S. Rossotti, J . Phys. Chem., 85, 926,930, 1376 (1961). (20) E. T. Adams, Jr., Biochemistry, 4, 1655 (1965). (21) F. Y.-F. Lo, 6.M. Escott, E. J. Fendler, E. T. Adams, Jr., R. D. Larsen, and P. W. Smith, J . Phys. Chem., 79, 2609 (1975). (22) E. T. Adams, Jr., W. C. Ferguson, P. J. Wan, J. L. Sarquis, and B. M. Escott, Separation Sci., 10, 175 (1975). (23) E. T. Adams, Jr., fractions, No. 3 (1967). (24) J. L. Sarquis and E. T. Adams, Jr., Arch. Biochem. Biophys., 183, 442 (1974). (25) L.-H. Tang, D. R. Powell, B. M. Escott, and E. T. Adams, Jr., Biophys. Chem., 7, 121 (1977). (26) L. Harris and K. L. Churney, J . Chem. Phys., 47, 1703 (1967). (27) W. D. Lansing and E. 0. Kraemer, J . Am. Chem. Soc., 57, 1369 (1935).
COMMUNICATIONS TO THE EDITOR Oscillatory Gas Evolution from the System Formic Acid-Concentrated Sulfuric Acid-Concentrated Nitric Acid
Sir: In 1916,Morgan1 first observed the periodic evolution of carbon monoxide from a mixture of formic acid and concentrated sulfuric acid at temperatures between 40 and 70 "C. Recently, Showalter and Noyes2v3have made a comprehensive study of this oscillatory reaction, and have adduced evidence for the chemical nature of the observed rapid pulses of gas evolution. They have also suggested a mechanism for the reaction based on hydroxyl radical catalysis of formic acid decomposition involving iron salts which are present at the parts per million level in sulfuric acid. We have carried out a preliminary study of oscillatory gas evolution in the Morgan reaction when concentrated nitric acid is present. The three reactants in the system, and formic acid, concentrated H2S04,concentrated "Os, were mixed in the proportions of 5:l:l by volume. Standard analytical grade reagents were used without further purification. To avoid an unduly vigorous reaction, a procedure was adopted in which the formic acid was added slowly to a previously prepared mixture of concentrated sulfuric and nitric acids. The reaction vessel (a large test tube) was immersed in a thermostat maintained a t 50 f 0.5 "C. Periodic foaming of the solution was observed (ashad been noted by Morgan1),the rise and fall of the froth clearly indicating the oscillatory nature of the gas evolution. A manometer connected to the reaction vessel was used in preliminary experiments to observe the stepwise increase in gas pressure in the closed system. These oscillations were made more clearly visible using a gas chromatograph thermal conductivity cell as in the experiments of Showalter and no ye^.^ The evolved gases were mixed with a carrier gas (helium) and then entered the thermal conductivity cell which was connected to a pen recorder. The bursts of gas evolution occurred every 30-40 s, and were preceded by maximum frothing of the solution. Regular oscillations persist for about 0.5 h. The evolved gases were primarily carbon monoxide, carbon dioxide, and nitrogen dioxide. The presence of these product gases was confirmed by gas-phase infrared spectrophotometry using a Perkin-Elmer 457 grating instrument. The absorption bands at 2340 (CO,) and 2140 cm-l (CO) observed at 5-min 0022-3654/78/2082-1952$0 1 .OO/O
intervals during the reaction show that initially carbon monoxide is present in a greater amount than carbon dioxide, but, as the reaction proceeds, the product gases become much richer in carbon dioxide. Further research on these product gases is currently underway in these laboratories. The period of oscillation, as well as the occurrence of oscillations was found to depend critically upon stirring conditions in the reaction vessel as noted by Showalter and no ye^.^ If stirring is too slow, gas evolution is erratic, and, under rapid stirring conditions, the gases are evolved smoothly without oscillations. While this would seem to indicate a physical basis for the oscillatory behavior in a supersaturation effect as suggested by Bowers and Rawji4 in their study of the Morgan reaction, there are nevertheless other observations which point to the chemical nature of these oscillations. We have noted that bubbles are always present in the solution even in quiescent periods which indicates that the observed bursts of gas must be due to a rapidly accelerating reaction. Furthermore, the faint blue color of the reacting solution has been observed to appear and disappear several times before persisting for the duration of the reaction. These observations of color oscillations are difficult to replicate and seem to depend very sensitively on reaction conditions. The final solution is always faintly blue in color. This color was tentatively ascribed by Morgan1 to the presence of N203,but in view of the temperature (50 "C) at which we carried out the reaction and the probable presence of NO+ as an intermediate, we feel that the color may be due to a nitroso compound formed from traces of organic impurities, Considerably more work will be necessary to establish the mechanism of the Morgan reaction including concentrated nitric acid. We feel that oxynitrogen chemistry may play a more important role than in the ShowalterNoyes mechanism for the oscillatory formic acid decomposition in sulfuric acid only. It may be speculated that the additional mechanistic steps will include: (i) the reaction of formic acid and nitric acid to yield nitrous acid and C 0 2 gas: HCOOH + "03 HNOz + COZ + HzO (ii) the formation of N203and its reaction with sulfuric acid to yield nitrosonium ions as well as its decomposition to yield NO2: 2HN02 + N20s(aq)+ H 2 0
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0 1978 American Chemical Society
