J. Phys. Chem. 1981, 85, 1977-1983
1977
ARTICLES Initial Thermoelectric Power of the Sliver-Silver Chloride Electrode from 30 to 90 OC. An Ionic Scale for of Aqueous Electrolytest
e,,,'
Peter
R. Tremalne,' N. H. Sagert; and 0. J. Wallace
Research Chemistty Branch, Whiteshell Nuclear Research Establishment, Atomic Energy of Canada Limited, Pinawa, Manitoba, Canada ROE 1LO (Received: August 27, 1980; In Final Form: Merch 27, 1981)
The initial thermoelectric power, €0, of the cell Ag/AgCl/KCl/AgCl/Ag has been measured from 30 to 90 "C at KCl molalities of 0.01,0.005, and 0.001 m. The temperature dependence of to is consistent with other workers' results, obtained at lower temperatures or higher concentrations, and can be used to establish an absolute or single-ion heat capacity scale, providing the indeterminate single-ion Eastman entropy and heat capacity of transport, S0(C1-,25 "C) and Cpo(C1-),can be estimated. qpplication of the Eastman-Agar expression for the concentratipn dependence of to suggests that Cpo(Cl-)2 Cpo(KC1)/2. Our €0 data, combined with literature values for S"(KC1) and Cpo(KCl),yield a self-consistent ionic scale, s0(H+,25"C) = -19.4 f 2.5 J K-! mol-' and cp0(H+,25"C) 2 -57 J K-' mol-'. A more speculative argument, based on the assumption that So(Cl-) = &'(K+) at high temperature due to similarities in the secondary waters of hydration and Stokes radii of each ion, suggests that cp0(H+,25"C) 5 13 J K-' mol-'.
Introduction The contribution of individual ions to the properties of electrolyte solutions cannot be derived by thermodynamic measurements due to the need to preserve electroneutrality. Extrathermodynamic methods have been devised to circumvent this and several "absolute" or single-ion properties have now been estimated by two or more independent techniques.' Absolute values for the Gibbs energy and entropy of ionic hydration at 25 "C are generally accepted and are widely used by theoreticians interested in developing physicochemical models for solvated
ion^.^-^
An absolute heat capacity scale for single aquo ions is of particular interest in this context because Cpo is very sensitive to ion-induced changes in solvent structure. A second, more pragmatic area of interest is in recent attemptsM to extrapolate thermodynamic data for aqueous electrolytes to high temperatures. These require single-ion values for the change in partial molal entropy and enthalpy with temperature, both of which are defined by an ionic cpo scale: ( S S " / S T ) ~ = c p 0 / Tand (Sh0/Sr),= cpo. Here, we use Agar's notationg in which absolute and conventional partial molal properties are noted by lower case and capital letters, respectively. Nonelectrochemical attempts to estimate an absolute cpo scale have been reviewed by Conway' and by Mercier and Jolicoeur.lo These yield results for cP0(H+,25"C) in the range 126 J K-' mol-' 1 cp0(H+,25"C) 2 -61 J K-' mol-'. The most detailed of these, a recent study by Mercier'O using analogous neutral and ionic quaternary compounds, places cp0(H+,25"C) = 13 f 15 J K-' mol-'. An alternative approach is to use thermoelectric power measurements on simple galvanic cells to estimate the variation of s"(H+) with temperature and, hence, c p o . Although values for s"(H+) at 25 "C based on thermocell measurements are among the most widely accepted, only 'Issued as AECL-6990. QQ22-3654f81f2Q85-1977$Q1.25f Q
a few w~rkers''-'~have reported results obtained over a wide enough temperature range to be of use in calculating cpo. Here, we report measurements of the initial thermoelectric power of the Ag/AgCl/KCl/AgCl/Ag cell from 30 to 90 "C. The results are used to estimate the partial molal entropy of the isolated chloride ion at finite concentrations, s(Cl-), and, hence, the standard partial molal entropy of the ion in the hypothetical 1m reference state, so (Cl-). We recognize that the thermodynamic properties of single ions cannot be measured in any totally unambiguous, rigorous experiment, since their determination requires nonthermodynamic assumptions.
Experimental Section Water for these experiments was triple distilled from Pyrex and had a conductivity of 0.8 pS cm-'. Washed Pyrex glassware was freed from organics by heating overnight to 530 "C, before use. All chemicals were reagent grade (Fisher HC1 and NaOH, Anachemia KC1 and AgNOJ. Silver oxide for the electrodes was prepared from (1) B. E. Conway, J. Solution Chem., 7, 721 (1978). (2) J. E. Desnoyers and C. Jolicoeur, Mod. Aspects Electrochem., 5, l(1969). (3) G. W. Schnuelle and D. L. Beveridge, J. Phys. Chem., 79, 2566 (1975). (4) S. Goldman and R. G. Bates, J. Am. Chem. Soc., 94,1476 (1972). (5) J. W. Cobble and R. C. Murray, Jr., Faraday Discuss., Chem. Soc., 64, 144 (1978). (6) P. R. Tremaine and S.Goldman, J. Phys. Chem., 82,2317 (1978). (7) H. C. Helgeson and D. H. Kirkham, Am. J. Sci., 276, 97 (1976). (8) C. M. Criss and J. W. Cobble, J.Am. Chem. SOC., 86,5385 (1964). (9) J. N. Agar, Adu. Electrochem. Electrochem. Eng., 3, 31 (1963). (10) (a) C. Jolicoeur and J. C. Mercier, J.Phys. Chem., 81,1119 (1977). (b) J. C. Mercier, Ph.D. Thesis, Universit6 de Sherbrooke, 1979. (11) R. Haase and H.Schonert, 2. Phys. Chem. (Frankfurt am Main), 25, 193 (1960). (12) (a) A. J. de Bethune, H. 0. Daley, Jr., N. A. S. Loud, and G. R. Salvi, J.Electrochem. Soc., 114, 578 (1967). (b) Ibid., 116, 1395 (1969). (13) D. D. Macdonald, A. C. Scott, and P. Wentrcek, J.Electrochem. SOC., 126, 1618 (1979).
0 1981 American Chemical Society
1978
Tremaine et al.
The Journal of Physical Chemistry. Vol. 85, No. 14, 1987
Pt WIRE
TEFLON TOP
--@%lh/ \
an amplifier circuit to control these very low temperature differences to k0.05 "C. Ambient temperature was controlled to *O.l "C by enclosing both cells in a Blue M POM-206B-1 forced-convection oven. Changes in the solution concentrations were monitored by measuring the specific conductance at 25 0.1 "C with a Beckman Model RC-18 conductivity bridge. The cell and thermocouple emfs were measured on a Dana Model 5900 high-impedance (>lolo ohm) digital voltmeter, which had been calibrated against a Hewlett-Packard Model 740B d.c. standard cell. The procedure for making the thermoelectric power measurements was as follows. First, the cell was brought to the temperature of measurement, T, then a differential temperature, AT = 10 "C, was applied to one of the compartments. After thermal equilibrium was reached, the valve separating the compartments was opened for 16 min while the thermoelectric power of the two pairs of electrodes was monitored. Constant readings were generally obtained after -5 min. The procedure was then reversed, heating the second compartment rather than the first and, afterward, reversed again to ensure that the emf from the first thermal configuration was unchanged. Conductance measurements were made on the cooled solutions from each compartment and on a sample of the initial starting solution to determine changes in concentration caused by thermal diffusion or evaporation. The initial thermal emf, eo, was assumed to correspond to the mean cell temperature, T + AT/2, and was calculated by averaging the results from the two cell configurations, which differed by up to 100 pV K-l. These bias potentials were usually consistent with the Nernstian potentials corresponding to the ratio of the final compartment concentrations, which differed from unity by as much as 2%.
*
HEATING COILS-
0 0 0
0 0 0
Figure 1. The AglAgCIIKCIIAgCIIAg thermogalvanic cell. Heating coils maintain one cell 10 "C above the ambient temperature which is controlled by the surrounding oven.
AgNU3 by the method of Bates"+" and washed at least YU times with triple-distilled water until the conductivity of the washings was 35 pS cm-' or less. Emission spectra of the final product showed Mg, Ca, Al, and Si as the major metallic impurities, all less than 30 pg g-l. The silver-silver chloride electrodes were prepared by the thermal electric method, following exactly the procedure of Janz.15 The chloridization step was done in preelectrolyzed 1m HC1, using a current of 10 mA, until 15 f 3% of the Ag (total mass -400 mg) was converted to AgCl assuming 100% current efficiency. The resulting light grey electrodes were stored in 0.1 m KCl solutions. The electrode potentials agreed with one another to *50 pV and, after a few days initial aging, agreed to within 300 p V with the potentials of electrodes prepared several months previously. The potential of silver-silver chloride electrodes is The Br content particularly sensitive to Br impurities.'"" of the KC1 was analyzed by X-ray fluorescence, using standard additions made by evaporating known volumes of a standard KBr solution onto weighed portions of the KC1. The result, 40 10 pg g-' of Br (manufacturer's lot analysis, 10 pg g-l), lay within the accepted limit'"" of 50 pg g-l. X-ray photoelectron spectra of the electrode surfaces, taken after the high-temperature experiments were complete, showed no detectable Br or I and we therefore judge the atomic detection limits on the surface to be I/C1 5 0.02 and Br/C1 50.2. These limits are based on longterm scans in the I(3d) and Br(3d) regions and the known photoelectron cross sections of the elements. A schematic drawing of the cell assembly is shown in Figure 1. Briefly, each cell compartment contained two parallel silver-silver chloride electrodes whose glass-jacketed Pt leads projected through the tight-fitting Teflon top via an O-ring seal. The compartments were separated by a Teflon stopcock. The temperatures of each, and the differential temperature between them, were monitored by stainless steel jacketed, chromel-alumel thermocouples, calibrated to *O.l "C against a thermometer tracable to NBS. The thermocouples passed through tight-fitting holes in the Teflon tops but were not sealed. Each compartment was surrounded by heating tape so that the temperature of one could be maintained a t 10 "C above the other by means of a Thermo Electric Co. Model 400 proportional temperature controller, modified by adding
-
*
~~~
(14) R. G. Bates, "Electrometric pH Determinations", Wiley, New York, 1954, p 206. (15) G. J. Janz in "Reference Electrodes-Theory and Practice", D. J. G. Ives and G. J. Janz,Ed.,Academic Press, New York, 1961, Chapter
Analysis of Data From Agar? the thermoelectric power, to, of a silversilver chloride thermocell which uses aqueous KC1 as the electrolyte may be expressed as
Fco = S(Cl-) - tKS(KCl) + so(Ag) - sO(AgC1) - &e) (1) where F is the Faraday constant, s"(Ag) and s"(AgC1) are standard values for the entropy of metallic silver and solid silver chloride, respectively, and tK is the transport number for K+ ions. The Eastman entropy of transport for KC1, S(KCl), is given by s(KC1) = 2uRT[1 + 6 In y/6 In m] (2) where m is the solution molality, y is the mean molal ion activity coefficient, and u is the Soret coefficient (a -6 In m/6T) at the steady @ate whenthe Soret equilibrium is achieved? The terms S(C1-) and S(e) are the transported entropies of the C1- ion in the cell and of the electron in the metal wire where the temperature drop in the ezternal electrical cirguit occurs. Since accurate values for S(e) are available,18S(Cl-) can be calculated from values of t o by using eq 1 if Soret coefficient data are available. The single-ion entropy is the difference between the transported entropy and the Eastman entropy of transport s(Cl-) = S(Cl-) - &Cl-)
(3)
4.
S(Cl-) cannot yet be rigorously de_terminedgand, hence, must be estimated, usually from S(KCl), in order to determine s(C1-) via this method.
(16) G.D.Pinching and R. G. Bates, J.Res. Nut. Bur. Stand., 37,311 (1946). 104, 123 (17) H. Taniguchi and G. J. Janz, J. Electrochem. SOC., (1957).
(18) R.D.Barnard, "Thermoelectricityin Metals and Alloys", Wiley, New York, 1972, p 49.
Thermoelectric Power of the Ag-AgCI Electrode
The Journal of Physical Chemistry, Vol. 85, No. 14, 1981
1979
T A B L E I : Physical Parameters for Ag/AgCl/Cl- Thermocellsa
a
tl" c
D
103 x ( a In D / a T )
s(Ag)
s(AgC1)
s=( e,Pt )
tK
r(K')
r(C1-)
20 25 30 40 50 60 70 80 90 100
80.27 78.47 76.70 73.26 69.96 66.79 63.77 60.87 58.11 55.47
-4.53 -4.55 -4.57 -4.60 -4.62 -4.63 -4.64 -4.65 -4.65 -4.66
42.26 42.68 43.10 43.93 44.73 45.52 46.28 46.99 47.70 48.41
94.98 96.23 97.44 99.79 102.09 104.26 106.36 108.41 110.37 112.26
0.50 0.50 0.50 0.54 0.59 0.59 0.63 0.67 0.67 0.71
0.492 0.491 0.490 0.488 0.486 0.485 0.484 0.483 0.481 0.479
1.222 1.244 1.265 1.303 1.337 1.368 1.396 1.422 1.448 1.477
1.183 1.198 1.213 1.241 1.266 1.289 1.309 1.327 1.343 1.358
Entropies i n J K - ' m o l - ' , radii in A .
From equilibrium thermodynamics, the concentration dependence of the entropy may be expressed in terms of standard state and excess entropies, so(Cl-) and s'(Cl-) s(C1-) = so(Cl-) - R In m
+ s'(Cl-)
(4)
Agarg has shown that, by analogy with eq 4
S(C~-) = SO(C~-) - R In m
+ Slcl-)
(5)
with
+ S"(Cl-) = s'(Cl-) + S'(Cl-)
9"(Cl-) = s"(Cl-) 9'(Cl-)
(6) (7)
Now, using the limiting law Debye-Huckel theory,lg the single-ion activity coefficient, y,is given as In y = -(e2/2Dkr)~ K
(8)
= [(8~Ne2do)'~2/(1000Dkr)'/2]m1~ (8a) 2
where K is the Debye reciprocal distance; do, the density of water; D, the dielectric constant; N, Avogadro's number; and the other terms have their usual significan~e.~J~ The excess partial molal entropy is defined as s'(Cl-) = -R(6 T In y / 6 T ) ,
an ion as it moves through a solvent has been deyeloped by Agar.n The result is given as eq 12, where the So terms
(9)
On carrying out this differential for a 1:l electrolyte, the result is -e2NK s'(Cl-) = -[ l 36 In D / 6 In T + c y T ] 4 TD where cy is the coefficient of thermal expansion of water. Agarg has considered two available theoretical approaches for calculating the excess transported entropies. The more rigorous approach was developed by Helfand and Kirkwood.20 For 1:l electrolytes
are the entropies of transport of the individual ions corresponding to eq 6. While the derivation of eq 12 is generally conceded to be less rigorous than that of eq 11, it is important for our purposes in that the similarity between the two equations relates the Helfand-Kirkwood B integrals to the difference in the individual ionic entropies of transport. Comparing eq 11 and 12 yields the result [B(Cl-) - B(K+)] i= T[B"(Cl-) - Bo(K+)]
(13)
bearing in mind the approximations in the Agar treatment. Using the Helfand-Kirkwood approach and the results from eq 7,10, and 11,we can calculate the nonideal contribution to the entropy of transport, S'(Cl-), with &(Cl-) =
*[I4TD
3
6lnT
+ aT + 1 / 3 1 +
For data-fitting purposes, eq 1,3-7, and 14 were combined to yield Fto = (so(cl-)+ (1 - 2tK)@(C1-) + tK[S"(Cl-) so(K+)])- R In m + s'(Cl-) + [s"(Ag) - s"(AgC1) &e)] (1 - 2 t K ) ~ [63In D/6 In T + cyT + 1/31 +
+
+
The first term in eq 15 contains the standard-state single-ion entropies which we seek to estimate from our data. In the fitting procedure, we described these using two arbitrary parameters, a and b, so that (S"(Cl-) + (1- 2t~)B"(C1-)+ tK[S"(Cl-) - A"(K+)]) = {s"(C1-,25"C) + (1- 2t~)B"(C1-,25"C) + t~[@(C1-,25"C) - B0(K+,25"C)]] + {cpo(cl-)+ (1 - 2fK)ep0(c1-) + EK[ep"(Cl-) ~ , " ( K + ) ]In J (T/298.15) 4 a + b In (T/298.15) (16)
where r(C1-) is the Stokes radius of the chloride ion and the B's are integrals involving the velocity distributions near the ions as derived from hydrodynamics. Unfortunately it is not really possible to evaluate the B integrals at the present time and they are typically used as empirical constants. A suggestion of Eastman21 that heat and entropies of transport could be related to reversible thermal effects near
Here, the heat capacity terms and fK represent mean values between 25 and 90 "C and are taken to be temperature independent. As noted in eq 13, the approximate Eastman-Agar treatment suggests that the term [B(Cl-) -
(19) R. A. Robinson and R. H. Stokes, "Electrolyte Solutions", Butterworth, London, 1959. (20) E. Helfand and J. G. Kirkwood, J . Chem. Phys., 32,857 (1960). (21) E. D. Eastman, J . Am. Chem. Soc., 50, 283, 292 (1928).
(22) J. N. Agar in "The Structure of Electrolytic Solutions", W. J. Hamer, Ed., Wiley, New York, 1959, Chapter 13, as revised in Annu. Reu. Phys. Chem., 15, 469 (1964).
1980
The Journal of Physical Chemistry, Vol. 85, No. 14, 1981
0
9
Tremaine et al.
L
TABLE 11: Initial Thermoelectric Power of the Ag/AgCl/Cl- Electrodea
1
e , / p V K-'
m(KC1) = 0.01 t/"C
z t y
z
1
I
10
O61
L
04
I
I
I
I
I
I
I
I
I
I
exptla
m(KC1) = 0.005 m(KC1) = 0.001
fitb
exptla
fitb
exptla
fitb
20 (642) (695) (826) 25 (625) (678) (806) 30 6 0 9 t 1 5 610 6 6 7 %29 660 7 8 9 2 22 787 4 0 5 7 2 i 1 5 580 628 7 4 7 2 1 2 750 552 6 0 5 i 26 596 7 1 2 i 1 3 715 50 5 4 4 2 8 525 571 i 19 567 6 9 0 i 1 9 680 60 5 2 2 i 9 70 4 9 7 2 8 500 5 4 4 2 1 3 538 6 4 4 i 12 648 80 4 7 5 i 9 476 5 2 4 i 1 6 511 6 1 6 i 17 616 90 4 5 5 i 35 454 5 0 1 t 41 485 5 6 7 i 47 586 100 (433) (460) (557) a The average of experimental values in the range t i 5 'C, adjusted to t by using the temperature dependence defined by the curve fit to eq 15-17. Error limits are one standard deviation of these points. Fitted values are from eq 15-17 using values for a, b, c, and d listed in the text. 1
I
oc
1
1
1
1
1
1
1
1
1
o HAASE 8
l
I
I
SCHONERT
0 de BETHUNE et a1
A
-_.
MACDONALD et a1
D VEKENS et at THIS WORK -*._
0
I
i
Flgure 3. Values of to for the silver-silver chbrlde thermocell obtained by various workers (ref 11-13 and 27), adjusted to an external circuit of R metal. Shaded points correspond to 5 mmol kg-' whereas open points correspond to either 1 or 10 mmol kg-'. The solid curves show the fit to our results as given in Figure 2.
(23) H. C. Helgeson and D. H. Kirkham, Am. J.Sci., 274,1089 (1974). (24) D. D. Wagman, W. H. Evans, V. B. Parker, I. Halow, S. M. Bailey, and R. H. Schumm, U S . Nut. Bur. Stand. Tech. Note, No.27b3 (1968); ibid., No.270-4 (1969). (25) K. K. Kelley, US.Bur. Mines Bull., No.684 (1960). (26) K. M. Brown and J. E. Dennis, Jr., Numer. Math., 18,289 (1972).
Parameters c and d showed considerable covariance and, as a result, increases in one could be countered by corresponding decreases in the other without significantly affecting a, b, or the residual standard deviation. We repeated the curve fit several times using different initial values for c and not allowing them to vary during the fit. The error limits in a, b, c, and d correspond to the range of values noted from fits which gave residual standard deviations within 5% of the value obtained above. Standard deviations generated by the computer program for the coefficients in each individual fit were about 0.05, 0.30, 2.5, and 10 J K-l mol-', respectively. Initial thermoelectric power data from the fit are tabulated in Table 11, along with mean values for the experimental data adjusted to the nearest temperature listed in the table. We note that attempts to fit the data by use of various additional parameters in eq 16, for instance, a + b In (T/298.15) + f ( T- 298.15), either did not converge or did not give a lower overall standard deviation. Temperature-dependent measurements on the silversilver chloride thermocell have also been reported by Haase and Schonert," at lower temperatures than those reported here. Both sets of results are plotted in Figure 3, along with the value of Vekens et al.27a t 25 "C. Thermocell (27) L. F. Vekens, J. F. Zeeland, and J. Lin,J.Electrochem. Soc., 118, 1119 (1971).
Thermoelectric Power of the Ag-AgCI Electrode
measurements relative to 25 "C have been reported by Macdonald et over a very wide range of temperatures. In addition, de Bethune et al.12have reported data for the calomel electrode, again relative to 25 "C, over the range 5-65 "C. Taking the temperature derivative of their thermocell voltages yields tovalues for the silver-silver chloride and calomel electrodes, respectively. The latter were converted to silver-silver chloride values by using thermodynamic data for Ag, AgC1, Hg, and HgZCl2from ref 24 and 25. These are also included in Figure 3. Values for to in the figure correspond to a thermocell whose external circuit includes a Thompson emf in Pt metal pnd were adjusted, where necessary, by using values for S(e) from Barnard.l8 The results from different workers a t 25 "C and the higher concentrations all agree within the reported experimental errors, except for de Bethune's data which are -0.05 mV K-' lower than the others. This discrepancy probably reflects errors in the tabulated entropies of the solids needed to convert his data from the calomel to silver chloride thermoelectric powers. The temperature dependence of de Bethune's result at 0.01 m KC1 is consistent with our data and with Macdonald's results above 60 "C. The temperature coefficient of Haase and Schonert's data is more positive than ours by -1.5 p V K-2, both at 0.01 m KC1 and a t the lower concentrations. While both de Bethune's data and Macdonald's less precise, high-temperature results tend to support our values, we note that the discrepancy between Haase and Schonert's and our data is only slightly outside the combined experimental error. Single-Ion Properties. The single-ion properties so(Cl-) and cp0(Cl-) can be estimated from the coefficients determined here by using approximations to estimate the indeterminate quantities of transport So(C1-) and ~p0(C1-)9~27-30 since from eq 16 so(C1-,25 "c)= a - ((1 - 2tK)So(C1-,25 "c) + t~[S"(C1-,25"C) - S0(K+,25"C)]} (18) c,"(Cl-) = b - ((1- 2fK)6p0(C1-)
+ tK[cpo(C1-) - fipo(K+)])(19) and e", are assumed constant and
Again we note that c," f K is the mean value over the range 25-90 "C. The currently accepted absolute entropy scale,' s0(H+,25 "C)-= -22 f 2 J K-' mol-', is based in part on estimates of So(Cl-) from vpious schemes. For our purposes, we ' largely associated simply note that So is t h o ~ g h t ~to, ~be with loosely held water molecules in the outermost layer of hydration, the so-called secondary hydration sphere, or cosphere II.31 The unadjusted Stokes radii of K+ and C1are virtually identical, as are the estimated entropies of their cosphere I1 waters of hydration3' and, as a result, their entropies of transport very probably share the same Ggn. Lin and ~ o - w o r k e r s have ~ ~ - ~reported ~ the value2s S"(KC1,25 "C) = 10.2 J K-' mol-' and note that the currently accepted absolute scale' places So(K+,25 "C) > S"(C1-,25 "C). This latter observation is supported by our analysis of the temperature dependence o,f So(Cl-), discusse? below. Hence, from Lin's value for So(KC1,25 "C), 0 IS0(C1-,25 "C) I5.1 J K-' mol-' and, from eq 18, we assign the value s0(C1-,25 "C) = 76.1 f 2.5 J K-l mol-'. Combining this with the conventional standard entropy,%J2 (28)H.K. Yow, B. P. Chakraborty, and J. Lin, Electrochim. Acta, 22, I O I R (19771. ---(29)J. Lin, J. Solution Chem., 8,125 (1979). (30)W.G.Breck and J. Lin, Trans. Faraday SOC.,61, 2223 (1965). (31)H.L. Friedman and C. V. Krishnan in ''Water: a Comprehensive ~
Treatise", Vol. 3, F. Franks, Ed., Plenum, New York, 1974,Chapter 1.
The Journal of Physical Chemistry, Vol. 85, No. 14, 1981 1881
So(HC1,25 "C) = 56.73 J K-' mol-', yields the "absolute" value s0(H+,25"C) = -19.4 f 2.5 J K-' mol-', slightly less negative than the mean literature value' -22 f 2 J K-' mol-', but in very good agreement with that determined recently by Payton et al.,32-19.6 f 0.4 J K-' mol-'. We note that modern values for standard e n t r o p i e ~differ ~~,~~ by up to 15 J K-' mol-' from those used to terive early estimates of s0(H+,25"C). The uncertainty in S(C1-,25 "C) largely cancgls when calculating the transported entropy from eq 6, S0(C1-,25 "C) = 78.6 f 0.9 J K-' mol-'. This compares to literature values in the range 78.2-81.6 J K-' mol-'. Temperature-dependent Soret coefficients reported by Agar and T u r n e P have been recalculated by A g d to yield C,(KC1,0.01 m) = 182 J K-' mol-'. Here, we assume that this value, which is constant between 9 and 35 0C,35is unchanged a t _higher tempgratures and lower concentrations so that CPo(KC1)= CP(KC1,0.01m). The problem of deconvoluting C," into its anionic and cationic contributions has not been widely discussed, probably because the validity of various attempts to deconvolute the much less sensitive parameter So is still controversial.28 Our approach here is a pragmatic one. From the comparison of Agar's approximate treatment for the electrophoretic contribution to the entropy of transport with the Helfand-Kirkwood expression (eq 13)
c = [S0(C1-,25 "C) - S0(K+,25"C)]
(20)
d = [fiPo(C1-)- C,"(K+)]
(21)
Attempting to use these as quantitative equations would be foolhardy, both because Agar's equation is approximate, and because the d term is sensitive to any systematic errors in our high-temperature, low-concentration eo measurements. We note, however, that substituting values for c and the other-parameters in eq 20 yields the result So(C1-,25 "C) - S0(K+,25"C) = 53 f 60 J K-' mol;', and is therefore a t least consistent with the value for S0(C1-,25 "C) deduced above. More important, the value of d obtained from our curve fit is such a very large positive nu-mber that we conclude, with some confidence,-C "(Cl-) - C,"(K+) I0, and therefore, from the value for C, 8(KCl), cpo(C1-)I91 J K-' mol-'. Substituting into eq 19 yields the result c,"(Cl-) 2-80 J K-' mol-', including the f 5 J K-' mol-' error limit in the b term. Ahluwalia and Cobble%have measured the temperature dependence of Cpo(HC1)to 100 "C. Combining the mean of their values between 30 and 90 "C, -139 J K-' mol-', with our upper limit for c "(Cl-) yields a lower limit for the ionic heat capacity scafe over this temperatuze range, c,"(H+) I-69 J K-' mol-'. The mean value for C,"(HCl) is slightly more negative than the room temperature res ~ l t , ~CPo(HC1,25 *~' "C) = -126 J K-' mol-'. Assuming that this difference applies also to the single-ion scale yields cP0(H+,25"C) 2 -56 J K-' mol-'. This lower limit for c,"(H+) is relatively unambiguous since it requires only the assumption that the sign of the d coefficient from the KCl thermocell data (eq 17) be interpreted by using the Eastman-Agar theory. Recently, (32)A. D. Payton, E. J. Amis, M. S. Showell, R. W. Smith, and B. D. Koplitz, J. Electrochem. Soc., 127, 2157 (1980). (33)CODATA Recommended Key Values for Thermodynamics, J. Chem. Thermodyn., 10, 903 (1978). (34)J. N.Agar and J. C. R. Turner, Proc. R. Soc. London, Ser. A, 255, 307 (1960). (35)B. D. Butler and J. C. R. Turner, J. Phys. Chem., 69, 3598 (1965). (36)J. C. Ahluwalia and J. W. Cobble, J.Am. Chem. Soc., 86,5381 (1964). (37)A. Roux, G.M. Musbally, G. Perron, J. E. Desnoyers, P. P. Singh, E. M. Woolley, and L. C.Hepler, Can. J. Chem., 56, 24 (1978).
1982
The Journal of Physical Chemistry, Vol. 85, No. 14, 1981
Tremaine et al. 60
1
I
50
IONIC MOVEMENT
/
/
I
I
i
-
Flgure 4. A schematic of Eastman's conceptual model for the entropy of transport,*' showing movement of bulk water molecules into and then out of the secondary hydration sphere of the diffusing ion. Modern opinion suggests that cosphere I may also be invoked and that volume effects may be important.
Jolicoeur and Mercierlobproposed the value cp0(H+,25"C) = 13 f 15 J K-' mol-' from Cpo data for analogous neutral and ionic quaternary compounds, including an analysis of electrostriction effects. Their analysis suggests that this is an upper limit and, combining this limit, cp0(H+,25"C) I13 J K-' mol-', with the HC1 and KC1 data cited above yields the following results for the temperature rang? 30-90 "C: cpo(H+)IO,c "(CI-) L -139 J K-' mol-', and Cpo(Cl-) I156 J K-' mol-': While the detailed relationship between ion-solvent interactions and the entropy of transport is not underthe entropy of transport is generally accepted to be due to orientation of bulk water molecules to form the secondary and possibly part of the primary hydration shell ahead of the migrating ion and their release back to the bulk liquid as the ion moves on by. Because of the sign c o n ~ e n t i o nthe , ~ entropy change associated with the orientation process isA-&' for the ion in question so that negative values of S infer "structure-breaking" ions.g A schematic drawing of the process, based on Eastman's classic discussion is shown in Figure 4. The implications of the upper and lower limits for cpo(H+)presented above can be assessed in terms-of this qualitative model by using the limiting values for CDo(Cl-)and CDo(K+) to calculate the temperature-dependent entropies of transport, So(Cl-,T) and S"(K+,T). Values for so(Ki,T) and s"(Cl-,T) from these two deconvolutions of S"(KC1,T) are plotted in Figure 5. Case I corresponds to our lower limit, c "(H+,25"C) 1 -56 J K-' mol-'. The effect of assuming tPo(K+)= Cpo(C1-)is to maintain a constant difference between the entzopies of transPo$ of each ion. The positive value of Cpo(KCl) causes So to increase with temperature so that, in terms of the Eastman-Agar model, the entropy of transferring water molecules from the bulk to the ionic hydration spheres decreases and both ions become progressively more "structure making", consistent with spectroscopic data.41 The second plot, case 11, shows the effect of increasing Cpo(Cl-) to the value 156 J K-' mol-', corresponding to Jolicoeur and Mercier's limit, cP0(H+,25"C)= 13 J K-' (38)R. J. Bearman and V. S. Vaidhyanathan,J. Chem. Phys., 39,3411 (1963). (39) P. Y. Kahana and J.-L. Lin, personal communication. (40) H. J. V. Tyrrell, Chem. Commun., 456 (1967). (41) W. A. P. Luck in "Water: A Comprehensive Treatise",Vol. 2, F. Franks, Ed., Plenum, New York, 1973, Chapter 4.
4 IO
I I
0
--I0
"STRUCTURE BREAKING''
I
1 100
I
I
I 300
200 f / T
Flgure 5. Deconvolution of so(KCI): two extremes. Case I corresponds to the lower limit cp0(H+,25 "C) 2-56 J K-' mol-'. Case I1 corresponds to the single-ion scale cp0(H+$5 "C) = 12 J K-' mol-' and suggests massive differences between S"(K+) and So(Cl-) above 100 "C.
mol-'. Here, the divergence between the entrogies of trFsport of the two ions is large so that, at 100 OC, So(Cl-) - So(K+)= 30 J K-' mol-'. A difference of this magnitude suggests that significant changes in the hydration layers of one or both ions must occur with increasing temperature. Stokes radii provide a rough measure of relative changes in the hydration properties of these ions under steady-state conditions and, in fact, the Stokes radii of K+ and C1- are nearly identical a t all temperatures, 1.25 and 1.20 A, respectively, at 25 "C and 1.48 and 1.36 A, respectively, at $00 "C. It s e e p reasonable, therefore, to conclude that S"(K+,T) and So(C1-,T)should not deviate markedly from one another as the temperature is raised, and that Jolicoeur and Mercier's value for cp0(H+,25"C) does indeed represent a plausible upper limit. The very large positive values, 126 and 117 J K-' mol-', proposed by Shin et al.42and by Criss and Cobble? respectively, are certainly not consistent with the arguments presented above.43 We conclude that a reasonable estimate of the single-ion heat capacity scale can be derived from thermogalvanic cell measurements, using the Eastman-Agar model to provide a qualitative deconvolution of the entropy of transport into its indeterminate single-ion components. Because the Eatman-Agar model is approximate, we have adopted a conservative approach leading to a reasonably unambiguous lower limit for cpo(H+)and semiquantitative support for the upper limit proposed by Jolicoeur and Mercier. These arguments correspond to an absolute ionic heat capacity scale in the range -56 Ic "(H+,25OC) I13 J K-' mol-' and suggest that cp"(H',25 is very probably negative." Accurate Soret measurements a t higher temperatures and theoretical treatments for the effect of
"6)
~
(42) C. Shin, I. Worsley, and C. M. Criss, J. Solution Chem., 5, 867 (1976). (43) The value of c "(H+,25"C) = 120 J K-l mol-' from ref 8 and 38 would suggestlothat t i e co_ntrIbutionof anions and cations of the same crystallographic radius to Cpo differs by at least 200 J K-l mol-'. Their contributions would be equal at cp0(H+,25"C) 5 -60 J K-l mol-'. (44) The Goldman-Bates electrostaticmodel for ionic hydration' also suggestse that cP0(H+,25"C) may be negative.
J. PhyS. Chem. 1981, 85, 1983-1988
ion-solvent interactions on entropies of transport would be required to refine this approach.
Acknowledgment. We are indebted to Professors A. D. Payton, R. Haase, W. G. Breck, J.-L. Lin, J. E. Desnoyers,
1983
and C. Jolicoeur and to our colleagues a t the Whiteshell Nuclear Research Establishment for many helpful comments. Bromide X-ray fluorescence analyses by Mr. P. T. Howe and X-ray photoelectron spectra by Dr. N. S. McIntyre are much appreciated.
Vibrational Structure of the Emission Spectra of Hexaamminerhodium(II1) Complexes. The Jahn-Teller Effect in the Luminescent Excited State Karuo Hakamata, Aklo Urushlyama,' Department of Chemistry. Faculty of Science, Rikkyo University, Nishiikebukuro 3, Toshima-ku, Tokyo, Japan
and Hans Kupka Instnut f i r Theoretische Chemie der Universtar DiisseMotf, 4000 DiisseMotf, West Germany (Received: September 3, 1980; In Final Form: March 9, 1981)
-
Crystalline powders of [Rh(NH&][Rh(CN)e]and [Rh(ND3)6] [Rh(CN),] were subjected to emission spectroscopy at low temperatures. Emission bands associated with the TIS 'A, transition of [Rh(NH3)6]3'and [Rh(ND&I3+ revealed predominant wz(e,) progressions, which suggest the presence of a Jahn-Teller distortion in the 3T1, excited state. A comparision of the intensity distribution with a theoretical line shape function provides the geometrical parameters and the vibrational fundamentals of the complex in the luminescent electronic excited state. Introduction Ligand field absorption and emission spectra of low-spin d6 complexes are associated with interconfigurational transitions described in O h symmetry as tzg eg transitions. Since the equilibrium interatomic distances in the molecule are generally increased when a molecule goes into the excited electronic state, the transition involves potential surfaces displaced from one another in the configuration space along some normal coordinates. In addition to these displacements, the potential surface are still frequency modified, i.e., the vibrational frequencies in the excited states are different from those of the ground state. Information about these distortions may be reliably determined from an analysis of the progressions in the phosphorescence spectra. Some of transition metal d6 complexes of O h symmetry are reported to exhibit fine structure with long vibrational progressions on their d-d emission bands at low temperatures.' In most of these spectroscopic studies, the peak interval between the adjacent members of the progressions has been assigned to the totally symmetric vibration of the ML6 skeleton in the electronic ground state, indicating a totally symmetric expansion of the complex in the emitting (excited) electronic state. However, it may happen that the emission spectra of some complexes of O h or related symmetry show vibrational progressions in which the separation of the adjacent members is found to correspond to frequencies of the e modes. This occurs when the excited state geometry of
-
(1)(a) I. N. Douglas, J. V. Nicholas, and B. G. Wybourne, J . Chem. Phys., 48,1415 (1968);(b) H. H. Patterson, W. J. DeBerry, J. E. Byme, M. T. Hsu, and J. A. LoMenzo, Znorg. Chem., 16, 1698 (1977); (c) Y. Yamamoto,Bull. Chem. SOC.Jpn., 52,84(1979);(d) K. W.Hipps and G. A. Crosby, Znorg. Chem., 13, 1543 (1974); (e) K. W. Hipps, G. A. Merrel, and G. A. Crosby, J. Phys. Chem., 80,2232(1976);(0 D. Oelkrug, M. Radjaipour, and E. Eitel, Spectrochim. Acta, Part A, 35, 167 (1979); (g)H. Yersin, H. Otto, J. I. Zink, and G. Gliemann, J. Chem. Soc., 107, 951 (1980). 0022-3654/81/2085-1983$01.25/0
the molecule (relative to the ground state) is shifted along the egnormal mode, leading to DBhsymmetry (Jahn-Teller effect). Since alg and eg vibrations have in most octahedrally coordinated complexes similar energies, care must be taken in determining these frequencies by comparing the separation between adjacent vibronic components in the emission spectrum with the ground-state Raman frequencies. In the present study occurrence of such predominant eg and al progressions in the phosphorescence spectra of [Rh(Nh3),I3+and [Rh(NDJ6I3+measured at low temperatures will be documented. The spectra are identified with transitions orginating from one of the components of the 3T1gstate, 175(3T1g). The complexes have distinct Raman lines which may be easily identified with the alg and eg modes of the metal ligand skeleton.2 The relative large separations (23 cm-' in [Rh(NHJsl3') between these two Raman active Rh-N stretching modes enable us to perform a reliable assignment in the band structure. Deuteration shifts to the vibrational frequencies of the complex ion also help us to analyze the structure of the phosphorescence spectra. The relative intensities in the progressions are well described in terms of Lorentzians weighted by the values of an intramolecular distributions,3 which involves spectroscopic parameters of both the alg and eg vibrational modes. Experimental Section A fine powder of [Rh(NH,),] [Rh(CN),] was immediately
precipitated when aqueous solutions of [Rh(NH3I6]Cl: and K3[Rh(CN)5]5are mixed under rigorous stirring. If the solutions were mixed extremely slowly in a small glass tube (2)J. M.Terrasse, H. Poulet, and J. P. Mathieu, Spectrochim. Acta, 20, 305 (1964). (3) (a) H. Kupka, Mol. Phys., 36, 685 (1978);39, 849 (1980). (4)S.M. Jargensen, J . Pract. Chem., 2 44,48 (1891). (5)Gmelins Handbuch der Anorganische Chemie, 8 A d , 1938,pp 64, 112,141.
0 1981 American Chemical Society
