J. C. RUSSELL AND G. R. FREEMAN
SO8
for discussion, criticism, and support of this work. Drs. G. Goles, S. Hart, H.C. Urey, and D. Weill read the paper and offered comments. The facilities of the Computer Center of the University of California,
San Diego, Calif., were used for the calculations; I thank Rilrs. J. Hays for advice about the programming. This research was supported by the National Science Foundation, Grants GP-4547 and GP-3347.
Reactions of the Primary Reducing Species in the Radiolysis of Liquid 2-Propanol1 by J. C. Russell and G. R. Freeman Chemistry Depatrment, University of Alberta, Edmonton, Alberta, Canada
(Received June 26, 1967)
A study has been made of the effects of temperature, acid, and nitrous oxide on the yield of hydrogen in the radiolysis of 2-propanol. The yields of free-ion solvated electrons and those that undergo geminate neutralization have been calculated to be G(e-solv)ri= 1.2 (at 25") and G(geminate neutralization) = 2.8 (at 25"). The fate of a portion of the electron yield equivalent to G(es0lv-) = 1.9 is temperature dependent. At low temperatures, there is no hydrogen produced from this portion of the solvated electron yield. At temperatures above 140", all of these electrons give rise to hydrogen. The results of electron scavenging reactions by nitrous oxide have been tested against a nonhomogeneous kinetics mechanism, with moderate success. Secondary reactions involving nitrous oxide produce large yields of nitrogen a t high temperatures and high nitrous oxide concentrations.
Introduction The radiolysis of the higher aliphatic alcohols has not been studied in the Same detail as has that of methanol and ethanol. The radiolysis of ethanol exhibits a number of unusual feature^.^^^ A study of the primary reducing species in the radiolysis of 2propanol should aid in understanding both ethanol radiolysis and alcohol radiolysis in general. Sherman4 has suggested that in 2-propanol at room temperature, G(esolv-) = 2.5 and that the free-ion yield, G(esolv-)fi = 0.9. He reported G(H2) = 4.0. A consequence of the suggested mechanism is that G(H)= 3.1.4 Nitrous oxide in water is known to react with hydrated electrons with a high specific rate @(eaq- f NzO) = 7 X lo9 M-l sec-1).6>6 Sitrous oxide reacts much more slOwly with hydrogen atoms in water (Ic(* N2O) = 2 x lo6M-l 8ec-1)a7 2-Propanol would be so with hydrogen expected to react attack of the atoms on the nitrous oxide is probably of no consequence in propanol solvent. Changing the temperature Over a wide range causes large changes in the properties of a liquid such as 2-
+
The Journal of Phyaical Chemistry
propanol. The dielectric constant is particularly temperature dependent. Thus the Present experiments were conducted over as wide a temperature range as was Practicable-
Experimental Section Most of the experimental methods used were identical with those used in an earlier study of the primary reducing species in ethanola2 All samples were irradiated with 6oCoy radiation. In the present work, some irradiations were performed a t higher temperatures than those used previously.2 Above 150") the vapor pressure of 2-pro(1) This work received financial support from the National Research Council of Canada. (2) J. C. Russell and G. R. Freeman, J . Phys. Chem., 71, 755 (1967). (3) J. C. Russell and G. R. Freeman, ibid., 72, 816 (1968). v. Sherman, ibid,, 70, 667 (1966). (4) (5) F. S. Dainton and D. B. Peterson, Proc. Roy. Soc. (London), A267, 433 (196% (6) S. Gordon, E. J. Hart, M. S. Matheson, J. Rabani, and J. K. Thomas, Discussions Faraday SOC.,36, 193 (1983). (7) F.S. Dainton and D. C. Walker, Proc. Roy. SOC.(London), A285,
339 (1965).
RanIoLYsIs OF LIQUID2-PROPANOL panol rapidly exceeds that which may be contained by the glass cells used. The samples irradiated above 150' were placed in the usual glass cells in a steel pressure vessel partially filled with 2-propanol.* The pressure vessel was placed in a small electrically heated oven and warmed to the desired temperature, allowed to equilibrate, and then irradiated. The temperature was measured with an indicating pyrometer which was calibrated against a mercury thermometer. The design of the pressure vessel is shown in Figure 1. The walls were made as thin as practicable to minimize attenuation of the y radiation. The vessel was machined from a bar of SPS-245 steel and heat treated to Rockwell C-30. The estimated bursting pressure of the vessel was approximately 650 atm before heat treatment and 1350 atm after heat treatment. The vessel was pressure tested on a hydraulic pressure system to 300 atm before use. Lead was found to be the most suitable gasket material, as a good seal is formed without the application of a high force through the screws in the head, and lead is not affected by temperature or radiation under the experimental conditions. The 2-propanol which partially fills the pressure vessel exerts its vapor pressure on the glass sample cell, equalizing the interior and exterior pressures. Thus a glass cell may be used at very high over-all pressures. It was found to be necessary to flush the pressure vessel with nitrogen gas before closing it. At high temperatures and pressures, oxygen in the entrapped air oxidizes the alcohol, and the resulting acid rapidly attacks the steel. The vessel could be constructed from stainless steel, but this would require a greater wall thickness for the same strength. The analysis for 2-chloropropane was made using techniques described elsewhere.a Reagent grade 2-propanol from Fisher Scientific Company was treated with 2,4dinitrophenylhydrazine, by a previously described technique,* in order to remove carbonyl impurities. It was then thoroughly degassed and stored under vacunm in a Pyrex vessel. All other materials were as previously described.*
Results The yield of hydrogen from pure 2-propanol as a function of dose at 25O is shown in Figure 2. At a dose of 1.5 X 10'' eV/ml, the yield was G(HJ = 4.5. All other experiments were performed at this dose, and all experiments were performed at a dose rate of 4.5 X 10" eV/ml min. Between -85 and 140", the hydrogen yield increased roughly linearly with temperature from G(H*) = 3.6 to 5.5. Higher temperatures, up to 225", caused no further increase in yield (Figure 3). The addition of hydrogen chloride caused different effects at different temperatures. Addition of aeid at -85" caused G(H,) to increase from 3.6 to 5.1 at [(CHa),CHOH,+] = 0.03 M, and it did not appear to
1
1
\
I
IN SIZE
Figure 1. Steel pressure cell used for high-temperature irradiations. The diagrsm is drawn to scale and the inside diameter of the steel pressure eel1 is 5.1 cm.
't
-1
Figure 2. The yield of hydrogen 84 a function of dose at 2.5' and a dose rate of 4.5 X 10" eV/ml min.
have reached a maximum (Figure 4). At 25", G(H2) increased from 4.5 to 5.3 at 0.03 M (CH8)&HOH2+and also did not appear to have reached a maximum (Figure 5). At 140", G(H3 = 5.5, independent of acid concentration (Figure 6). Above 150", addition of a high concentration of hydrogen chloride caused G(H,) to decrease by as much as 1.1 units at 1.4 M acid and 180" (Figures 7 and 8). At these higher temperatures, addition of a low concentration of hydrogen chloride caused no change in G(H,) (Figures 7 and 8). (8) The authors m indebted t o Dr. T. J. Hsrdwick for ~uggestirg the principle of this technique. Vdutne 73. Number 3 Mwch 1988
J. C.RUSSELLAND G. R. FREEMAN
810
r+ a00
.IO0
?IO0
T
'C
Figure 3. The yield of hydrogen as a function of temperature: dose = 1.5 X 1017 eVjml.
I
I
I
I
[NzO] or [(CHal$HOH;]
I
O L b
I
0
l
l
I
I
I
10IO" Io" [N20] or [(CH3)$HOHi] M
IO"
10-
1
Figure 6. The effect of hydrogen chloride and nitrous oxide concentration a t 140': NZin the presence of nitrous oxide; e, Nz yields which required correction for secondary reaction; 0, (Ns Hz) in the presence of nitrous oxide; 0, HZin the presence of hydrogen chloSde.
+,
I
M
+
:L,! 0
Figure 4. The effect of hydrogen chloride and nitrous oxide N2 in the presence of nitrous concentration a t -85": oxide; e, Nz yields which required correction for secondary reaction: 0, (Nz Hz) in the presence of nitrous oxide; and 0, Hz in the presence of hydrogen chloride (this line has been extrapolated as discussed in the text).
+,
+
10-
I
1
I
I 10''
I
I
I
I IO.@ 10'' ADDED bCiJ,M
io-.
I 1
~
1
_1
Figure 7. The yield of hydrogen a t 180" as a function of added hydrogen chloride.
3 -100
I
I
0
I
,100
I
I
200
T 'C
[NzO] or [(CHj)$HOH;]
M
Figure 5 . The effect of hydrogen chloride and nitrous oxide concentration a t 25': Nz in the presence of nitrous oxide; e, Nz yields which required correction for secondary reaction; 0, (Nz H2) in the presence of nitrous oxide; and 0, Hzin the presence of hydrogen chloride (this line has been extrapolated as discussed in the text).
+,
+
The concentration of hydrogen chloride in the samples was computed assuming that all the hydrogen chloride was dissolved in the propanol. The dissociThe Journal of Physical Chemistry
Figure 8. The yield of hydrogen in the presence of added hydrogen chloride as a function of temperaure: 1.4 M ; and 0, 4 x 10-4 M hydrogen chloride.
+,
ation constant Kdiss = 4 X for hydrogen chloride in 2-propanol was calculated from the value Kdisa = 0.015 in ethan01,~"using an equation that relates the acid dissociation constant to the dielectric constant of (9) (a) I. I. Bezmann and F. H. Nerhock, J . Am. Chem. Soc., 67, 1330 (1946); (b) I. M. Kolthoff and S. Bruckenstdn in "Treatise on Analytical Chemistry," Part I, Vol. 1, I. M. Kolthoff, P. J. Elving, and E. B. Sandell, Ed., Interscience Encyclopedia, Inc., New York, N. Y., 1969, Chapter 13, p 488.
RADIOLYSIS O F LIQUID %PROPANOL
811
-1
4
0
4
-
L
'
I
I
,
I
10"
10-4
lo"
10-E
IO"
I
2
IN,OlM
Figure 9. The yield of hydrogen as a function of nitrous oxide concentration: 0, 140'; 0, 25'; and f,-85".
the medium.Qb The concentrations of (CH&CHOH2+ for the data in Figures 4-6 have been calculated assuming this value of K d i s s . The dissociation constants of weak acids in water and in aqueous-organic mixed solvents do not change rapidly with temperature. Furthermore, some dissociation constants increase and others decrease with increasing temperature.'O It is, therefore, assumed, for lack of anything better, that Kdiss = 4 X for hydrogen chloride in 2-propanol, independent of temperature. Because of the decrease in G(H2) found at high temperatures and high acid concentration, and a similar effect found in ethanol accompanied by formation of ethyl ~ h l o r i d e ,samples ~ were analyzed for 2-chloropropane. A sample containing 1.4 M added hydrogen chloride and treated as for irradiation at 170" was found afterwards to contain 1.1 M 2-chloropropane. The addition of nitrous oxide to the propanol caused nitrogen to be formed (Figures 4-6) and the hydrogen yield to decrease (Figure 9). The sum G(H2 N2) increased with increasing nitrous oxide concentration. At -85 and 26", this increase was very similar to the increase in G(llz) caused by addition of acid (Figures 4 and 5). At 140°, G(H2 S,) did not rise above 5.5 until the concentration of nitrous oxide exceeded M . Above this concentration, G(N2) and G(H2 N2) rose very rapidly to high values (Figure 6). The nitrogen yields are shown in Figures 4-6 both as measured and, in the high-concentration regions, as corrected by a method which will be discussed later. The lines through the nitrogen yields were calculated by the use of nonhomogeneous kinetics. These calculations will be discussed later. All other lines were drawn to suit the experimental points. The lines through the hydrogen yields as a function of acid concentration (Figures 4-6) were extrapolated to 1 M (CH&CHOH2+, as it was not possible to attain this concentration in practice. The extrapolation was made assuming that G(H2) did not exceed 5.5 at the lower temperatures, as it did not at 140". The hydrogen yield decreased with increasing nitrous
+
+
+
oxide concentration at all temperatures. The difference between the yields at -85", 25", and 140" decreased with increasing concentration of nitrous oxide (Figure 9). The hydrogen yield was corrected for the hydrogen from direct radiolysis of the hydrogen chloride in those samples where the acid concentration was high enough to make this significant. The appropriate yield to use in these solutions was not known, so it was assumed that G(H2) = 6.5 for the direct radiolysis of the acid." The solubility of nitrous oxide in 2-propanol is not known. However, the solubility in 2-propanol is not likely to be radically different from that in ethanol, and thus the same values and techniques were used as for ethanoL2,l2 At -85", all the nitrous oxide was assumed to be dissolved in the 2-propanol. A correction was made to the nitrogen yield for the direct radiolysis of nitrous oxide in the high-concentration solutions. It was assumed that the energy absorbed by the nitrous oxide was proportional to its electron fraction in the solution, and that G(N2) = 12.9 for direct radiolysis. l 3 A study was also made of the effect of a high concentration of both hydrogen chloride and nitrous oxide. The results are shown in Table I. Knowledge of the dielectric constant is required for the nonhomogeneous kinetics calculations of scavenging and free-ion solvated electron yields. The dielectric constant, e, was measured over the temperature range -85 to +SO" (Figure 10). An extrapolation of the curve was used to estimate E at 140". The values shown were determined at 1000 cps by a previously described methoda2
Discussion Reaction Mechanism. The present results are consistent with but more detailed than those previously p ~ b l i s h e dand , ~ a more complex mechanism is required to explain them. The yield of hydrogen is quite strongly dose dependent. Doses below 5 X lo1' eV/ml are required in order to be certain of observing initial effects. Sherman4 reported G(H2) = 4.0 at room temperature and a dose of 5.8 X 10ls eV/ml. The present results indicate G(H2)= 3.85 at this dose and 25". The yield of hydrogen increases with increasing temperature between -85 and 140°, and is constant at G(H2) = 5.5 between 140 and 225" (Figure 3). At 140", the addition of as much as 1.4 M hydrogen (10) H. 9. Harned and B. B. Owen, "The Physical Chemistry of Electrolytic Solutions," 3rd ed, Reinhold Publishing Corp., New York, N. Y., 1958, pp 755-757. (11) R. C. Rumfelt and D. A. Armstrong, J . Phys. Chem., 68, 761 (1964). (12) International Critical Tables, McGraw-Hill Book Co., New York, N. Y., 1926. (13) G(Na)= 12.9 for liquid nitrous oxide a t -88': M. G. Robinson and G. R. Freeman, J . Phys. Chem., in press. Volume 73, Number 3 March 1968
J. C. RUSSELLAND G. R. FREEMAN
812 Table I: The Effect of Acid on G(H2) and G(N2) at 25'
a
Na0, M
HC1, M
(CHs)zCHOHz *,
0.16 0.16 0.016 0.016
1.4 0.14 0.14 0.0125
0.024 0.0075 0.0075 0.0023
M
IN201 3.5[H+l
+ [NzOl
U(Ni)o"
Q(Ndos1cd'
U(Ndexpt1
U(Hd
3.45 3.10 2.40 2.15
2.3 2.7
2.7 2.7 0.5 1.2
3.5 3.7 5.0 4.2
0.66 0.86 0.38 0.67
0.91 1.4
See eq i.
+ (CHJzCHOH]
1 [(CHa)2COH+
[(CHJzCO
\..
1
4
10
---t
+ (CH3)zCHOH2+]
(1.5) (5)
The solvated electrons in the spur appear to be involved in a reaction mechanism that is temperature dependent. This mechanism may be reactions 6-8. Reaction 6 must occur rapidly before reaction 4 takes place, and probably involves the less widely separated
I
1
[(CH&CHOH+
+ esolv-l
--+
oo + [(CHa)&HOH*l
T
'C
[(CH3)2CHOH*]+ (CH3)zCOH
Figure 10. The dielectric constant as a function of temperature.
chloride (Figure 6 ) has no effect on G(H2), which remains at 5.5. However, at 25 and -85" the addition of high concentrations of hydrogen chloride causes G(H2) to increase nearly to G(H2) = 5.5. I t thus appears that the temperature-sensitive and acid-sensitive hydrogen precursors are the same. It would also appear that this hydrogen precursor is scavenged by nitrous oxide, as shown by the correspondance between N2) in the presence of nitrous the values of G(H2 oxide and G(H2)in the presence of acid at -85" (Figure 4). It is suggested that this hydrogen precursor is the solvated electron. The mechanism which follows is based upon that proposed for ethanoL3*14 It is also based on consideration of the fate of ionic species in irradiated liquids, following a previously described approach.2i16 The brackets indicate that the species are inside a spur. The yields ( G ) specified in parentheses after each reaction refer to 25" and are based on the experimental yields and theoretical considerations.
+
(CH3)zCHOH ---+ [(CH&CHOH+ --+
+ e-] [(CH3)2COH++ H + e-]
[e-] -+[esolv-l
The Journal of Physical Chemistry
(2.5) (1) (1.5) (2) (4.0)
+ (CHJzCHOH] [(CHa)zCHOHz++ (CH3)zCHOI
[(CHs)zCHOH+
(1.1) (7)
[(CH3)2CHOH*]-+ no hydrogen
*IO0
-I00
(3)
---t
(0.6)
(4)
(1.9) (6)
H
(0.8) (8)
ion-electron pairs.a Reactions 6-8 could account for the observed temperature dependence of G(H2). The balance between reactions 7 and 8 is temperature dependent. At low temperatures reaction 7 is favored, and at 140" and higher temperatures, reaction 8 proceeds to the exclusion of reaction 7. Those solvated electrons which do not undergo reaction 6 will either undergo reaction 9 or escape the spur to become free ions (reaction 10).
+ (C&)ZCHOH~+] [H + (CH3)2CHOHl
[esolv-
-+
+
[esolv- (CH&CHOH2+1 esolv- (CH3)&HOH2+(freeions)
+
(0.9) (9)
+
(1.2) (10)
The yield of free-ion solvated electrons was calculated as previously described,Z assuming G(tota1 ionization) = 4.0. Those electrons which do not escape the spur undergo geminate neutralization (reactions 6 and 9). The same theory indicates that, at times less than 10-lo sec, the majority of the electrons have not yet undergone geminate recombination, and that they are therefore solvated before recombination takes place. The hydrogen atoms attack the propanol.
H
+ (CH3)zCHOH --+ Hz + (CH3)zCOH
(11)
The free-ion solvated electrons decay, giving rise to further hydrogen atoms. (14) J. J. J. Myron and G . R. Freeman, Can. J. Chem., 43, 381 (1986). (16) G. R. Freeman, J. Chem. Phya., 46, 2822 (1967).
RADIOLYSIS OF LIQUID%PROPANOL esoly-
+ (CH&CHOH
--j
H
+ (CH3)&HO-
813 (12)
The product acetone is a good electron scavenger, as the addition of 0.68 M acetone was found to depress G(H2) to 2.0. Reaction 13 is probably responsible for esolv-
+ (CHd2CO
+(CHJZCO-
(13)
the observed dose dependence of G(H2). The experiments, other than the dose study, were conducted at a sufficiently low dose that reaction 13 was negligible. The presence of acid would cause reaction 14 to be esolv-
+ (CH3)2CHOHzf +H + (CH3)zCHOH(14)
substituted for reaction 12. This would not alter the hydrogen yield, as it would not alter the number of hydrogen atoms formed. A high concentration of acid would also cause reaction 14 to interfere with reaction 6. At lower temperatures, this would cause an increase in G(H2) of as much as 1.9 units at -85". A rise of 1.6 units was observed at -85", and it is felt that the full increase of 1.9 units was not observed, due to the low degree of dissociation of hydrogen chloride in 2-propanol. Thus 1.4 M hydrogen chloride gives only approximately 0.09 M (CH3)2CHOH2 +, a concentration which, by comparison with the calculations for nitrous oxide, would not be expected to completely scavenge the electrons in spurs. At temperatures above 150") virtually all the added hydrogen chloride was converted into 2-chloropropane and Figure 7 suggests that this compound scavenges electrons and inhibits hydrogen formation. Reactions 15 and 16 can account for the drop in G(H2) seen at high acid concentrations and high temperatures.
+ esolv- +(CHa)2CHC1(CH3)&HC1(CH3)ZCH + C1-
(CH&CHCI
----t
(15) (16)
A similar pair of reactions appears to occur in ethanol under the same circumstances.a It appears that 2chloropropane is a less efficient electron scavenger than, and is formed at a lower rate than, ethyl chloride in ethanol. Below 150", there is no evidence that 2chloropropane interfered with the acid studies in 2propanol, in contrast to the case of ethan01.~ Nitrous oxide reacts with the free-ion solvated electrons in the bulk of the liquid, and if present in sufficient concentration scavenges electrons within the spurs. esoly[esoly-
+ NzO +NzO-
+ N201 +NzO-
N2O-
--j
Nz
+ 0-
(17) (18) (19)
+
Reactions 17 and 18 increase the gas yield, G(H2 NJ, only to the extent that they interfere with reaction 6. Such increase in G(H2 Nz) should not give a yield greater than G(H2 N2) = 5.5 a t high concentrations of nitrous oxide. At -85", G(H2 Nz) rises to 5.9
+
+
+
at 1 M nitrous oxide, indicating that a small amount of nitrogen is being formed by reactions other than 17 and 18. At 25", G(Hz Nz) = 6.5 on a gently rising curve at 0.8 M nitrous oxide, which was the maximum concentration which could be used. At 140") G(H2 Nz) shows no increase up to 2 X M nitrous oxide, as expected from the previous mechanism, but above this concentration both G(N2) and G(Hz N2) rise rapidly in a manner which suggests the extensive occurrence of a secondary reaction at above 10+ M nitrous oxide. Such a secondary reaction might be reaction 20 in competition with reaction 21 or 22.
+
+
+
0-
0-
+ N20 *Nz +
02-
+ (CH3)tCHOH +OH- + (CHJz*OH +OH
+ (CH3)ZCHO-
(20) (21)
(22)
However, reaction 20 apparently does not occur in ethanol3 and it probably cannot compete with 21 or 22 in propanol. The large nitrogen yields at high temperature and high nitrous oxide concentration might be due to the occurence of a short chain reaction similar to that proposed for nitrous oxide-methylcyclohexane vapor mixtures.16 This would involve reaction 21 or 22, followed by 23 or 24, and then 25. A similar
+ (CH3)zCOH H2O + (CH3)zCOOH + (CHJzCHO- +HzO + (CH3)zCO(CH3)zCO + N2O(CH3)ZCO- + NzO
OH-
--j
(23) (24)
(25) series of reactions including reaction 25 has been proposed by Sherman1' to explain a chain reaction found in alkaline solutions of nitrous oxide in 2-propanol. There is a great need for knowledge of values of electron affinities of molecules and radicals, in the vapor phase and in solvents of various polarities, to help to decide the feasibility of reaction such as 25. Using the values for the rate constants for the re(CH3)zCHOH,4and H Nz0,5,6the actions H expected contribution to the nitrogen yield from the reaction of H NzO was calculated. This was found to be less than G(H) under all experimental conditions. Because of the occurrence of what is most probably a secondary reaction of nitrous oxide, it is necessary to apply a correction to the experimental nitrogen yields in order to obtain a reasonable measure of the number of solvated electrons scavenged. This was done by subtracting from G(N2) the difference between the nitrous oxide vs. G(H2 Nz) and the acid os. G(H2) curves (Figures 4-6). Since the low dissociation constant of the acid made experiments above 0.03 M (CH&CHOH2+impractical, the G(H2) vs. acid curves --j
+
+
+
+
(16) W. H. Holtslander and G. R. Freeman, Can. J . Chem., 45, 1661 (1967). (17) W.V. Sherman, J. Phys. Chem., 71, 1696 (1967).
Volume 72, Number 3 March 1968
J. C. RUSSELL AND G. R. FREEMAN
8 14
were extrapolated. The assumption was made that at the lower temperature, G(H2) did not exceed 5.5, as it did not at 140". The presence of a high concentration of both acid and nitrous oxide would cause a competition of reactions 17 and 18 with reactions 9 and 14. This would cause both G(H2) and G(N2) to be between the values caused by the presence of either solute alone. The value of NzO) has been reported to k(esoly- H+)/k(e,,~,be 3 in water;lsa in methanol, it was 7.9 at zero ionic strength and decreased to 1.3 at an ionic strength of 0.l.lsb Approximate agreement between calculated and experimental values of nitrogen yields from solutions containing both acid and nitrous oxide was obtained by assuming a value of 3.5 for this ratio in 2propanol. The nitrogen yields were calculated using eq i and are reported in Table I.
+
+
[NzOI G(N2) = G(N2)o([N20] 3.5[(CH3)&HOHz+]
+
G(N20)o is the yield of nitrogen at a nitrous oxide con3,5[(CHa)2CHOHz+], centration equal to [NzO ] uncorrected for any secondary reaction. The secondary reactions accounted for only 10% or less of the nitrogen formed at these concentrations of nitrous oxide in the absence of acid. Secondary reactions, such as eq 20-25, would also be inhibited by acid, so the error introduced by neglecting them in these calculations is small. Adjustment of the value of the ratio k(esoly- H+)/k(e,,l,N20) for the different ionic strengths, using a zero ionic-strength value of 14 and eq 1 of ref 19b, gave somewhat closer agreement between the calculated and experimental values of G(SJ. Within the uncertainties of the calculations, the results in Table I support the conclusion of Sherman4 that acid and nitrous oxide compete for the same species, namely solvated electrons. The direct competition of acid and nitrous oxide for the same species in 2-propanol is slightly different from the case in ethanol. I n ethanol, acid competes for all species with which nitrous oxide reacts, but it also reacts with a species with which nitrous oxide does not react.a Nonhomogeneous Kinetics Calculations. The yield of free-ion solvated electrons and the scavenging effect of nitrous oxide were computed using nonhomogeneous kinetics, as previously described.2r16 A spectrum of N(y) vs. y, the number of ion pairs formed with initial separation distance y, was computed for 2propanol at each temperature.'5 Data for the density of 2-propanol required for this computation have been measured by Costells and Bowden.l9 The N(y) spectrum permits calculation of +fi, the probability that a given pair of ions will become free ions, and @-, the probability of reaction of an electron with a scavenger. The equations used for these calculations have been
+
+
+
The Journal of Physical Chemistry
previously described.2 The yield of free-ion solvated electrons and the yield of nitrogen may be calculated by use of eq ii and iii. G(eS,,,,-)fi = ZN(y)'fi G(tota1 ionization) ZN(Y)
(ii)
ZN(y)@G(tota1 ionization) ZNb)
(iii)
G(NJ
=
The calculation of @- involves an adjustable parameter2J5
p- = u+
-+ + u- ["-
(id 6
where D- and D, are the diffusion coefficients of the solvated electron and nitrous oxide, respectively, Aand A, are the respective average diffusive jump distances, b- and b, are the number of new neighbors encountered per jump, and u+and u- are the mobilities of the positive and negative ions. Since these quantities are not known, p- was adjusted to give the best fit with the experimental results. The dielectric constant, E , is required in order to calculate both +fi and @-.lS The values of E were taken from Figure 10. The values of p- used for the present calculations are smaller, by approximately a factor of 4, from those found to be most suitable in a similar calculation for ethanol.3 This difference may be rationalized in terms of differences in the values of the quantities in eq iv. As in ethanol, the most suitable value of p- varied with temperature (p- = 2.3 X 10'2 V/cm2 at -85", 2.4 X 10'8 V/cm2 at 25") and 2.9 X l O l 3 V/cm2 at 140"). This variation may be rationalized in terms of the variation of the quantities in eq iv. M nitrous I n the low-concentration region below oxide, G(N2) was computed using eq v. G(esoiy-)tiwas calculated using equation ii and k17/k12 was adjusted to
give the best fit with the experimental results. G(esoly-)ri was calculated to be 1.5 at -85") 1.2 at 25", and 0.8 at 140". The values of the rate-constant ratio used were 3 X 105 at -85", 1.6 X lo5 at 25") and 3 X lo6at 140". Thus the ratio was essentially independent of the temperature, although the temperature range and hence the variation in viscosity and other factors is very large. The corresponding ratio of rate constants in ethanol was also insensitive to temperature.a The value of k17 = 7 x 109 M-I sec-1 in water at 25" (18) (a) L. M. Dorfman and M. 8. Matheson, Progr. Reaction Kinetics 3, 237 (1966); (b) G.V. Buxt,on, F. 8. Dainton, and M. Hammerli, Trans. Faraday SOC., 63, 1191 (1967). (19) J. M. Costells and S. T. Bowden, Rec. Trav. Chin., 77, 86 (1968).
RADIOLYSIS OF
IJIQUID
2-PROPANOL
suggests that reaction 17 is nearly diffusion controlled. It therefore appears that the effect of temperature on reaction 12 is mainly a viscosity effect or is associated with the breaking of hydrogen bonds in the liquid structure.
Comments on the Yields of Primary Reducing Species Dorfman, et u ~ . , ~ Ohave estimated the yield of free ion solvated electrons in 2-propanol to be G(esoiv-)ri = 1.0 0.3. The temperature to which this estimate refers was not specified, but is presumably about 25”. This measurement is in reasonably good agreement with the present value of G(esoiv-)ri = 1.2 at 25”. The present results agree generally with those of Sherman.4 The variation of the yields with temperature, and the nonhomogeneous kinetics treatment of the scavenging of the solvated electrons, allow a fuller understanding of the radiolysis. Sherman4 estimated the yield of free-ion solvated electrons to be G(esoiv-)ri = 0.9 by the use of homogeneous kinetics. The nonhomogeneous kinetics calculations show that there is no sharp division between free-ion solvated electrons and those which undergo geminate neutralization in propanol. Thus it is not valid to use homogeneous kinetics to describe radiolytic scavenging in this system. Under the circumstances, the agreement between Sherman’s value of G(esolv-)fi= 0.9 and the present value of 1.2 is acceptable. Sherman2 also estimated G(esolv-)T = 2.5 by the use of homogeneous kinetics. In this case, as would be expected, the agreement with the present value of G(esolv-)T= 4.0 is poor. The present results and mechanism may be compared to those for ethanol.3 The yields in ethanol of G(H) = 2.2, G(esolv-)fi= 1.5, and G(geminate neutralization) = 2.5 are similar to thevalues of G(H) = 1.5, G(esoiv-)fi = 1.2, and G(geminate neutralization) = 2.8 found for 2propanol. The somewhat larger value for G(esOlv-)f i in ethanol is to be expected in view of the somewhat larger value of e for ethanol (25 compared to 19 for 2-propano1, at 25”). I n both alcohols, there are temperature- and acid-sensitive hydrogen precursors. However, in 2-propanol these appear to be the same and to be solvated electrons, whereas in ethanol there are two additional species, one acid sensitive, and the other temperature sensitive. The solvated electrons appear to behave similarly in the two alcohols. The total hydrogen yield in ethanol at high temperatures and in the presence of acid is higher than in 2-propanol, because of the influence of the additional species. It does not appear that secondary reactions of nitrous oxide occur in ethanol up to 1 4 5 O S 3 This is in contrast to 2-propanol, where there is a large secondary reaction at this temperature. Comments on the First-Order Decay of esolvThe activation energies for self diffusion in water,
815 ethanol, and 2-propanol are 4.6, 4.6, and 5.3 kcal/mol, respectivelya21 Since reaction 17 appears to be nearly diffusion controlled and the ratio k17/k12 is temperature independent, the activation energy of reaction 12 is also about 5 kcal/mol. If it is assumed that k17 has the same value in 2-propanol as in water, corrected for the difference in viscosity, the value of k12 at 25” would appear to be approximately 104 A 4 - l sec-’. This implies a half-life for the free-ion solvated electron in 2-propanol of approximately 5 psec. This may be compared with a value of 7 psec in ethanol at 250a2 If the decomposition of a solvated electron to form a hydrogen atom and an alkoxide ion is considered to be a unimolecular reaction (reaction 12’), the entropy of esolv- +H
+ (CH3)zCHO-
(12’)
activation may be calculated by use of eq vi.22
ek T k12, = h
_ .
-
e A S + / R e - ~ / ~ ~
10xieAs*/Re-E/RT
(vi)
Substituting the values of klzl = 1 X 106 sec-l and = 5 kcal/mol into eq vi yields AS*121 = -20 cal/deg mol. The entropies of activation for the corresponding decompositions of solvated electrons in ethanol and water (assuming the activation energy to be equal to that of diffusion23)were also calculated and the values are listed in Table 11. The entropies are all negative and large. This seems to indicate that a large amount of structural rearrangement occurs in each of the solvents during the reaction.
Elz!
Table 11: Entropies of Activation of the First-Order Decay of Solvated Electrons E,
Solvent
2-Propanol Ethanol Water
*,
kd,
ked/
Bee-1
moll1
AS cal/deg mol
5 5
- 20 - 20
1 x 106 1 x 106” 1x 103~
Calculated from data in ref 2.
5
- 29
’ Calculated from data by
E. J. Hart, quoted by J. Rabani in “Solvated Electron,” Advances in Chemistry Series, No. 50, American Chemical Society, Washington, D. C., 1965, p 251.
(20) M. C. Sauer, 5. Arai, and L. M. Dorfman, J . Chem. Phya., 42, 705 (1965). (21) H. J. V. Tyrrell, “Diffusion in Heat Flow and Liquids,” Butterworth and Go. Ltd., London, 1961,p 155. (22) A. A. Frost and R. G. Pearson, “Kinetics and Mechanism,” John Wiley and Sons, New York, N. Y.,1953,p 95. (23) (a) It might be better to relate the activation energy of reaction 12’ to that of dielectric relaxation. However, the energies of activation of dielectric relaxation in 1-propanolb and in watefl are also 5 kcal/mol at temperatures in the vicinity of 20°, so the results of the calculations would be the same; (b) S. K. Garg and C. P. Smyth, J . Phya. C h m . , 69, 1294 (1965); (c) calculated from data in NBS Circular 559,p 6.
Volume 76. Number 8 March 1968
