6697
J. Phys. Chem. 1991, 95, 6697-6701
Enthalpy and Entropy of Formatlon of the Hydrated Electron Harold A. Scbwarz Chemistry Department, Brookhaven National Laboratory, Upton, New York 1 1 973 (Received: January 14, 1991; In Final Form: April 1 , 1991) Pulse radiolysis was used to study the equilibrium of the reaction e,- + NH4+ H' + NH3 in aqueous solution between 4 and 87 O C . The rate of equilibration was much larger than the sukquent radical decay. The equilibrium constant (corrected to zero ionic strength) is 2.2 at 25 OC, A P is -2.0 kcal/mol, and Uo is -5.1 cal/(deg mol). When combined with , , these values give AGo,-(e,-) = 66.2 kcal/mol, W,-(e,,-)= 66.3 kcal/mol, thermodynamic data for NH4+q, NH3,, and W and So(e -) = 16 cal/(deg mol). The enthalpy is 1-3.7 kcal/mol lower than recently published values based on kinetic studies. f i e forward and reverse rate constants of the reaction with ammonium ion are 1.0 X lo6 and 0.67 X 10' M-I at 0.05 M ionic strength and 25 OC. The activation energy of the forward reaction is 7.2 kcal/mol.
Recently, there has been renewed interest in the equilibrium between ea; and H' in aqueous s o l u t i ~ n : ~ - ~ Haaq+ OH,
* ea; + H201iq
(1)
Until now, all experimental estimates of the thermodynamics of e,- have been based on this equilibrium and reasonable assumptions for the thermodynamics of H'. The only method of obtaining the equilibrium constant Kl around 25 OC has been by measuring the forward and reverse rate constants of the reaction, which gives' Kl = 2.6 X 10' M-' at 25 OC. Two recent measurements of the activation energy of the forward rate constant kl differ by 2.9 kcaI/m01.~*~ The reverse reaction is more dificult to study, and only one measurement of the temperature coefficient for it has been reported! The usual method of varying concentration to obtain the rate constant is not applicable to the reverse reaction, and so the observed rate must be corrected for all other known reactions based on the composition of the solution. The corrections are large6 and the activation energy is correspondingly doubtful. Consequently, the enthalpy of reaction 1 would seem to be in doubt to 3 kcal/mol or more. Equilibration has not been directly measured for reaction 1 because the rate of equilibration near the pK is too slow, about 2000 s-l at 25 OC. Of course, this very slowness is the reason that ea; is such a useful species. Equilibration can be speeded up by working at elevated temperature (150-250 "C) as was done by Shiraishi? but extrapolation to 25 OC is not reliable. This paper reports an investigation of the reaction e;,
+ NH4+,q
H',
+ NH3,,
(2)
The rate of the forward reaction was first studied by Jortner et ai.' by a competition kinetic method. The absolute value of k2 from their ratios is 1 X IO6 M-I s-', which is large enough to be useful for equilibrating e,; and H'. Furthermore, and most important, the pK, of NH4+ is8 9.244 at 25 OC which, with K1, suggests that K2 should be about 2. This means that the reverse rate constant will also be usually large and that the temperature coefficient of the equilibrium might be expected to be small, which would facilitate accurate measurements. Experimental Section A 2.7 M stock solution of NH4Cl was prepared by neutralizing Mallinckrodt hydrochloric acid with Mallinckrodt ammonium (1) Baxendale, J. H. Rudfar. Res. 1964 (Suppl. 4), 139. (2) Jortner, J.; Noyea, R. M. J. Phys. Chem. 1966, 70, 770. (3) Hickel, B.; Sehated, K. J . Phys. Chem. 1985,89, 5271. (4) Han. P.; Bartela, D. M.J . Phys. Chem. 1990, 91, 7294. (5) Shiraishi, H. Private communication. (6) (a) Fielden, E. M.; Hart, E. J. Truns. Furuday Soc. 1%7,63, 2975. (b) Ibid. 1968. 61, 3158. (7) Jortner, J.; Ottolenghi, M.;Rabani, J.; Stein, 0.1.Chem. Phys. 1962, 37. 2488. (8) Smith, R. M.;Martell, A. E. Criricul Srubiliry Consrunrs; Plenum Press: New York, 1976; Vol. 4, p 40.
0022-3654/91/2095-6697$02.50/0
hydroxide. The ammonium ion concentration was determined by potentiometric titration with NaOH. Several other sources of NH4+ (3 times recrystallized NH'Cl, 3 times recrystallized NH4CI04,and Aldrich 99.999%(NH4)$04) were tried, but e,lifetimes were shorter than in the stock solution when the solutions were made basic. Apache 99.999%NaOH was used to prepare [e, -1. basic solutions for measurement of total initial [H'] Reaction 2 was studied by preparing 50 mL of 0.027,0.034, and 0.108 M NH4CI and removing the air by bubbling with argon in the reservoir of the pulse radiolysis cell. A concentrated ammonium hydroxide solution containing the same NH4Cl concentration as in the reservoir was separately degassed, and small aliquots (0.03-0.3 mL) were added to the solution. Data were collected, and then a 2-mL aliquot was analyzed for NHo by potentiometric titration with 0.05 M HCI with a reproducibility of 1% or better. Tests ensured that there was no loss of NH3 from the solution before titration even when the sample was at 85 OC when collected, though at the higher temperatures the precaution was taken of using chilled beakers and pipettes in handling the solution. The pulse radiolysis was performed with a 2-MeV Van de Graaff electron accelerator, a 6 c m light path, and a 150-W xenon arc. The radiation dose was low (about 15 rad per pulse). Dosimetry was based on the ea; absorption itself (extinction coefficient9 = 19 OOO M-'cm-l at 700 nm and 25 "C) and a G value of 2.70 per 100 eV as the initial yield in 0.05 M NH4+containing about 0.01 M NH3 or a G value of 3.30 as the yield after equilibration at 25 OC in 0.004 M NaOH solutions. The actual extinction coefficient does not affect either the kinetics or the equilibrium constants.
+
Results Transient absorption signals were averaged over many pulses for each run,usually 40,because the initial absorbances were about 0.003, which is too small to measure accurately in a single pulse. The first five or ten pulses were used to "clean up" the solution and then up to six runs (several hundred pulses) were made on the sample, but the total radicals produced in all pulses added up to about 15 pM. There was never any significant difference between the first and last runs and indeed, within the reduced precision of smaller averaging, between the second five pulses and the rest. An example run is shown in Figure 1 . There is a fast decay of absorbance to a near-equilibrium level at 1.54 x lo5s-I followed by a slow decay, eventually to zero, at 3400 s-l. Kinetic Treatment. The pulse radiolysis of water produces 2.7 e,-, 0.6 H, 2.8 OH, 0.7 H202, and 0.45 H1 per 100 eV absorbed in the water.1° No net product is seen in the y-radiolysis of ammonia solutions." The OH radicals all react with a m m ~ n i a : ~ OH' + NH3 NH2' + H 2 0 k = 9 X IO7 M-I s-I
-
(9) Buxton, G.V.; Grccnstcck, C. L.;Helman, W. P.; Ross, A. B. 1.Phys. Chem. Re/. Duru 1988, 17 (2). (IO) Schwarz, H. A. J. Chem. Educ. 1981,58, 101.
0 199 1 American Chemical Society
Schwarz
6698 The Journal of Physical Chemistry, Vol. 95, No. 17, 1991 4 c
.;
of the rather complicated relationshipd3 are possible. In kinetic terms f, is k-2[NH3]/ko.
1
kO
Af
f,=-+
- kslow - ( l - 2fe)(k3e - k3h) kslow k 3 f e + k3h(l - f e ) ( k 3 e - kslow)Af + ( k l o w - k3h)(A0 - Af)
kfast
(5) (6)
(7) kdT This method of data analysis requires separate estimates of k3h and k3,. Below 35 OC the separation of kslw into k3eand k3hwas accomplished by varyingf, through additions of several aliquots of NH3 to the solution and analyzing the resulting kllowvalues using eq 6. It was separately determined that neither the NH3 nor its associated impurities contributed directly to the radical decay. At 25 O C k3h was 1600 PI,which is very close to the value of 1500 s-I calculated at this dose from known reactions in the Appendix. The sample-tesample variation of kk was larger, from 4000 to 1 X lo4 s-). Above 35 OC ksiOw was less reproducible but also less important as it was smaller relative to kfSdt'In this range k3h was estimated from the 25 OC value assuming an E, of 3.5 kcal/mol, and k3, was then calculated from eq 6. Temperature and Concentration dependence^ of A T and A 0 AT was measured in 0.004 M NaOH solutions containing about 0.02 M NH3. In these solutions H atoms are converted into e,, at 1 X lo5 s-l, largely by reaction 1, and so the absorbance at the end of this step is a measure of the total H + e,; yield. Radiation yields depend slightly on concentrations and temperature, and the absorption spectrum of ea, is temperature dependent.14 The concentration effects are attributed to interference with reactions between species in the spurs in which they are formed (small groups of 1-3 or so radical pairs). NH4+and NH3 do not react rapidly with the radicals, and so changes in their concentrations are not expected to influence the total H and e,, yield, though the presence of NH3 should (and did) increase the initial ratio of e,, to H by removing H+ from the spur. The absorbance produced in 0.003 M NaOH solutions decreased by 1% when NH3 was increased from 0.015 to 0.11 M, a negligible effect. A 3% increase in AT was observed upon increasing [OH-] to 0.016 M. This change is likely due to the conversion of some OH' to 0-which is much less reactive toward eap-. In the rest of the studies the OH- was less than 1 X lo-' M, so all concentration effects on AT were ignored. The variation of AT with temperature was more pronounced. It is due to a combination of the change in extinction coefficient, change in yield, and change in density of the solution with temperature. The dose-normalized AT at 700 nm decreased nonlinearly with temperature between 5 and 85 OC by 16%. Equilibrium Constant. The ionic strength of the solutions came solely from the NH4CI, which varied between 0.027and 0,108 M, so the equilibrium constants were corrected for ionic strength. K 2 was expressed as AT
Figure 1. Absorbance change before and after a 100-ns pulse of 2-MeV electrons in a deaerated solution containing 0.054 M NH,+ and 0.044 M NH3 at 40 OC. The locations of the initial absorbance, Ao, and the absorbance after the fast decay step, Al, are indicated.
The reducing species, e, and H, undergo equilibration by reaction 2 and also disappear from the reducing radical pool by a number of reactions which will be represented here simply as
-
eaqand H
-
products
products
(34
(3h)
The known reactions and how they relate to k , and k3h are discussed in the Appendix. Reactions 3e and 3h should have appreciable components which are second order in the radical concentration. For this reason the reaction was only followed until the first 20-30% of the H and e,; pool had disappeared, during which time the distinction between first- and second-order kinetics has negligible effect. The absorbance of the sample did go to zero at longer times as it should since e,, is the only species present with appreciable absorbance at 700 nm. The solution of the rate equations that describe reactions 2, 3e, and 3h is that the absorbance A can be represented by the sum of two exponentialsI2 A = (Ao- 4) exp(-kf,,t) + 4 exp(-ksIowt)
(4)
where A. is the initial absorbance and Af is the absorbance at the completion of the first step but corrected to zero time by the second step. The two steps were well separated in time. The ratio kt,,t/k,i, varied from 20 at low NH4+ concentration and low temperature (5 "C) to 100 at high NH4+and high temperature (86 "C). The average was about 40, and Figure 1 is an example of such data. if kllowwere entirely negligible, then kfastwould be the equilibrium rate, ko, defined as
ko = k2[NH4+] + k-,[NH3]
+
and the fraction of ea, in the H' ea; pool at equilibrium,f,, would be Af/AT where AT is the total initial absorbance that would be observed if all reducing radicals were present as eaq-. The equilibrium constant is given by [NH3](l/f, - 1)/[NH4+]. This is not the method finally chosen for analysis, because the magnitude of kSh was large enough to introduce corrections of 1-10%, which are not completely negligible. In the general case kfartand krloware combinations of the four rate constants k2, k-2, k3,, and k3h, and Af does not directly give the equilibrium absorbance of ea
