THERMODYNAMIC PROPERTIES OF NONAQUEOUS SOLUTIONS
Thermodynamic Properties of Nonaqueous Solutions. I.
2611
Heats of Solution
of Selected Alkali Metal Halides in Anhydrous N-Methylformamidel
by Robert P. Held2 and Cecil M. Criss Department of Chemistry, University of Vermnt, Burlington, Vermont (Received February 3, 1966)
A precision submarine solution calorimeter has been constructed and used to measure the heats of solution of LiC1, NaC1, KC1, CsC1, NaBr, and NaI in anhydrous N-methylformamide a t 25" in the concentration range of 7 X to m. These data have been extrapolated to infinite dilution to obtain the standard heats of solution of the corresponding salts. With the exception of CsCl and KC1, the limiting slopes of the heat data vary from 7 to 280 times the value predicted by the Debye-Huckel theory. On the basis of the present results and conductance data in the literature, it is suggested that there is ionic association for some electrolytes in solutions of this high dielectric constant solvent.
Introduction Although heats of solution a t 25' have been measured for several electrolytes in numerous anhydrous solvents,3-12 only a few have been reported for electrolytes in very dilute solution^^^^^^^^^^ and even fewer in solvents with a dielectric constant greater than that of water.',* The few thermal data which do exist for very dilute solutions are, without exception, for solutions having relatively low dielectric constants. In these solutions it is not unusual for the experimental limiting slopes for heats not to be in agreement with the Debye-Huckel t h e ~ r y . ~ JBecause ~l~ of the uncertainties in the limiting slopes and corresponding uncertainties in extrapolation of heat data from more concentrated solutions, the standard heats of solution of electrolytes in these solvents reported in the literature may be in serious error. In view of the fact that N-methylformamide has a very high dielectric constant (D = 182.4 at 250)14 and conductance measurements have shown it to be a powerful dissociating solvent, l5 it appeared that this solvent would be of particular theoretical interest as a medium for exa,mining the heats of solution of selected electrolytes. Because of its high dielectric constant one would expect very little ionic association and the limiting slopes for heats of solution would be expected to be in agreement with the Debye-Huckel theory. Additionally, one would expect that deviations from the Debye-Huckel theory a t higher concentrations
would be less than the deviations in an aqueous solution of corresponding concentration. From a practical view of obtaining thermodynamic data, extrapolations to infinite dilution in this solvent should be considerably more accurate, making possible more accurate standard heats of solution. In order to minimize extrapolation errors, it is ad(1) This paper represents part of the work submitted by R. Held to the Graduate School of the University of Vermont in partial fulfillment of the requirements for the degree of Doctor of Philosophy. (2) NASA Fellow, 1963-1965. (3) S. U. Pickering, J . Chem. SOC.,53, 865 (1888). (4) F. A. Askew, E. Bullock, H. T. Smith, R. K. Tinkler, 0. Gatty, and J. H. Wolfenden, ibid., 1368 (1934). (5) C. M. Slansky, J . Am. Chem. SOC., 6 2 , 2430 (1940). (6) S. R. Gunn and L. G. Green, J . Phys. Chem., 64, 1066 (1960). (7) T. L. Higgens and E. F. Westrum, Jr., ibid., 65, 830 (1961). (8) K. P. Mishchenko and A. M. Sukhotin, Dokl. Akad. Nauk SSSR, 98, 103 g954). (9) K. P. Mishchenko and V. V. Sokolov, Zh. Strukt. Khim., 4, 184 (1963). (10) G. P. Katlyarova and E. F. Ivanova, Zh. Fiz. Khim., 38, 423 (1964). (11) B. Jakuszewski and S. Taniewska-Osinska, Bull. Acad. Polon. Sci., Ser. Sci. Chim., 9, 133 (1961). (12) B. Jakuszewski and S. Taniewska-Osinska, Lodz. Towarz. Nauk. WydziaZIII, Acta Chim., 8 , 11 (1962). (13) N. S. Jackson, A. E. C. Smith, 0. Gatty, and J. H. Wolfenden, J . Chem. SOC.,1376 (1934). (14) G. R. Leader and J. F. Gormley, J . Am. Chem. SOC.,73, 5731 (1951). (15) C. M. French and K. H. Glover, Trans. Faraday SOC.,5 1 , 1418 (1955).
Volume 69, Number 8 August 1966
ROBERTP. HELDAND CECILM. CRISS
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vantageous to measure heats of solution in as dilute solutions as possible. I n the present study heats of solution of LiC1, YaC1, KC1, CsC1, XaBr, and NaI have been measured in the range of 7 X 10-5 to m and the data extrapolated to infinite dilution to obtain standard heats of solution at 25’ for the corresponding salts. The present study represents heat measurements for solutions more dilute than any previously reported for nonaqueous solutions.
Experimental Materials. X-Methylformamide was treated with XaOH pellets and BaO for at least 4 hr. (generally overnight). (Initially CaHz was used, but BaO was found to be adequate.) The solvent was decanted into a distillation flask containing BaO and vacuum distilled through a 35-cm. Vigreux column at about 1 mm. pressure (b.p. 44’ a t 0.4 mm., 47’ a t 0.6 mni., and 55’ at 1.5 mm.). The reported boiling point is 51’ at about 1 mm.I5 After a second distillation from BaO, the product generally had a speohm-l cm.-l at 23’. cific conductance of 3-5 X Values reported in the literature range from to 4 X lo-’ ohm-l ~ m . - l . l ~ - ~As * other authors have found, 4,15 the conductivity of the solvent increased slightly with time. The solvent was not used if the specific conductance exceeded 8 X low6ohm-l cm.-l. Karl Fischer titrations on the solvent showed that the water content was less than 0.003%. Automatically recorded warming curves, analyzed by the usual extrapolation methods, showed an average melting rangie of -3.52 to -2.99’. NaCZ, KCL, CsCZ. Reagent grade KC1 was further purified by double recrystallization from conductivity water. Reagent grade NaC1 was dissolved in conductivity water, treated with chlorine, and reprecipitated according to the method described by Ives and Janz.lg CsCl was furnished by Henley and Co., and the accompanying analysis showed a 99.95% purity. The salt was used without further purification, except for the removal of water by drying in an air oven with the temperature being gradually raised to about 600’ over a period of 24 hr. All three salts were stored at 400’ until ready for use. N a B r . Since reagent grade NaBr contains traces of chloride ion, pure NaBr was synthesized from primary standard KaZCO8and fuming HBr. The solid S a B r was recrystallized from conductivity water, dried in a vacuum desiccator for 24 hr., and heated at 200’) then at 400’. N u l . Reagent grade ?;a1 was recrystallized from conductivity water, dried in a vacuum desiccator for 24 hr., and heated at 200’, then at 400’. The Journal of Physical Chemistry
LiCI. Reagent grade Li2C03 was further purified according to the method of Coley and EhringZ0 and then treated with reagent grade concentrated HC1 solution. The LiCl formed was dried in a vacuum desiccator, heated at about 350 to 400’ under a dry HC1 atmosphere. The anhydrous product was stored in closed vials over P206. Phenolphthalein solution indicated the absence of hydrolysis in all salt samples. Apparatus. The submarine solution calorimeter (Figure 1) consisted of a silver-plated brass outer jacket Q\
H
n
J YC
Figure 1. Submarine solution calorimeter: A, brass jacket; B, reaction vessel; C, evacuating tube; D, threaded coupling; E, thermistor and heater wells; F, hermetic electrical seal; G, conduit; H, sample bulb; I, stirring shaft; J, anvil; K, forked paddle; L, steel shaft; M, Teflon bearings; N, shaft housing; 0, filling tube; P and Q, tubes for purging with nitrogen; R, “0” ring; S, threaded nut. (16) Yu. M. Povarov, A. I. Gorbanev, Yu. M. Kessler, and I. V. Safonva, Dokl. Akad. Nauk SSSR, 142, 1128 (1962). (17) Yu. I. Sinyakov, A. I. Gorbanev, Yu. M. Povarov, and Yu. M. Kessler, Izv. Akad. Nauk SSSR, Otd. Khim. Nauk, 1514 (1961). Bahe, J. Chem. Eno. (18) G. A. Strack, S. K. Swanda, and L. UT. Data, 9, 416 (1964). (19) D. J. G. Ives and G. J. Jans, “Reference Electrodes-Theory and Practice,” Academic Press, Inc., New York, N. Y., 1961. (20) E. R. Coley and P. J. Ehring, Inorg. Syn., 1, 1 (1939).
THERMODYNAMIC PROPERTIES OF NONAQUEOUS SOLUTIONS
(A) 11 cm. high and 9 em. in diameter and an 80-ml. silvered glass reaction vessel (B). The neck of the inner vessel was cemented to the lid of the submarine with G.E. silicone rubber cement (RTV-60) to make a vacuum-tight seal. The space between the two vessels was evacuated through a 2.8-em. diameter tube (C), which was connected to an all-metal vacuum system through a threaded coupling (D). The reaction vessel was fitted with three wells (E) (only two are shown). One contained the calibration heater, another a thermistor, and the third a rough heater for adjusting the temperature of the calorimeter to the approximate operating range. All electrical connections were made through a ceramic hermetic seal (F) and brought to the bath surface through a conduit (G). The calibration heater was made from KO. 36 manganin wire wrapped noninductively around 4-mm. Pyrex tubing. This was painted with Glyptal and baked for several hours. The heater resistance was approximately 25 ohms. High vacuum silicone grease was used to increase thermal contact between the heater and the wall of the well. Two S o . 30 copper lead wires were used to carry the current to the heater. These were wrapped two or three times around the outside of the reaction vessel to ensure temperature equilibration between the leads and the vessel, thus eliminating the need for a heat loss correction through the leads. Two other KO.40 copper wires, used for potential leads, were attached to the Xo. 30 wires at approximately two-thirds the distance from the hermetic seal to the reaction vessel, eliminating the need to make corrections for heat generated in the leads. The instrumentation for the heater circuit was similar to that previously used. 21 Evacuated t hin-walled sample bulbs (H) were fitted to the bottom of the glass stirring shaft (I) with rubber tubing. The entire stirring mechanism could be pushed down, smashing the bulb on the anvil (J) fused into the bottom of the reaction vessel, thus introducing the sample into the solvent. The lower part of the stirrer was equipped with a fork-shaped paddle (K) to increase stirring near the bottom of the reaction vessel. The upper part of the stirring shaft (L) was fabricated from stainless steel. It passed through well-greased Teflon bearings (31) mounted a t the top and bottom of the shaft housing (K). A filling tube (0) also passed through the shaft housing and parallel to the shaft. The shaft housing was fitted with inlet and outlet tubes (P and 6)) for purging with dry nitrogen. The top of the stirring shaft was fitted with a pulley which was connected to a constant speed motor (125 r.p.ni.).
2613
The shaft housing was fitted to the top of the submarine to make a water-tight seal by means of an "0" ring (R) and threaded nut (S). Except for a few minor modifications the temperaturesensing circuitry was identical with the apparatus used previously for investigations in aqueous solutions. 22 The over-all temperature sensitivity was approximately 10-jo, as indicated by the reproducibility of AT for small heat inputs introduced over short intervals of time. The calorimeter was suspended in a thermostated bath controlled to about 3 X The bath temperature control unit was identical with that used previouslyz2 except that a Model 151 Keithley microvoltmeter was used as the bridge amplifier. Water circulated through the cooling coils was controlled to rtO.02" by means of an auxiliary thermostat. Procedure. Previously weighed thin-walled sample bulbs having a diameter of about 0.6 cm. and a stem 0.5 em. long, made from 5-mm. Pyrex tubing, were filled with sample, weighed, placed in an oven for a t least 8 hr., and then sealed under vacuum according to the method used previously. 21,23 Phenolphthalein solution indicated that hydrolysis had not occurred on any of the salt samples from this treatment. Samples ranged in size from 0.66 mg. (for LiC1) to 71 mg. (for KC1). The smaller samples were weighed on a Xettler illode1 SI5 microbalance. When the calorimeter was not being used, the interior of the reaction vessel was kept under vacuum to minimize the water adsorbed on the glass surface. This was done by placing a one-holed stopper in the opening of the reaction vessel and connecting it to the vacuum line by heavy-walled rubber tubing. In preparation for a measurement, a sample bulb was first attached to the bottom of the stirring shaft. The vacuum was then released from the reaction vessel and the stirring assembly, with the sample, joined to the top of the submarine. A specially designed delivery pipet with a long stem was inserted through the filling tube mounted in the shaft housing. By means of a two-way Teflon stopcock located a t the base of the solvent reservoir of the pipet, dry nitrogen was passed through the stem of the pipet until the interior of the reaction vessel was thoroughly purged of air. The stopcock was then turned, permitting the anhydrous solvent to drain into the calorimeter. Dry nitrogen was again passed through the pipet stem as (21) C. XI. Criss and J. W.Cobble, J. Am. Chem. Soc., 83, 3223 (1961). (22) E. C. Jekel, C. M. Criss, and J. W. Cobble, ibid., 86, 5404 (1964). (23) C. SI. Criss, Ph.D. Thesis, Purdue University, Jan. 1961.
Volume 69, Number 8 August 1966
ROBERTP. HELDAND CECILM. CRISS
2614
it was removed from the filling tube, and a stopper was placed in the opening of the filling tube to ensure that no moisture could get into the anhydrous solvent in the calorimeter. Several analyses on the solution after the calorimetric measurements indicated that the maximum water content was always less than 0.01%. Procedures used in calibrating the calorimeter, balancing the bridge, and interpolating between unit resistances on the time-temperature drift lines have been previously described.21v2a The only major change involved a choice of the time at which the difference between the before and after time-temperature drift lines was determined. Because of the relatively long solution times (5 to 90 min.), this choice is critical. An analysis of the curves using the matched-area method of D i c k i n ~ o nindicated ~~ that a 0.23 rise time should be used instead of the usual 0.6 rise time used in combustion calorimetry. This same rise time was used as well for the electrical calibrations. Heat of bulb-breaking measurements indicated that the average exothermic heat effect was 0.0044 cal. This value was either added to or subtracted from the measured heats of solution, depending upon whether the solution process was endothermic or exothermic. Because of the nonreproducibility of this value (in a few instances as much as twice the average) the heats in the more dilute solutions have considerable uncertainties for some salts. I n order to test the electrical calibrating system of the apparatus, the calorimeter was also calibrated by measuring the heat of reaction of Tris (tris(hydroxymethy1)aminomethane) with 0.1 M HC1. Five samples of primary standard Tris (Fisher), dried according to the method of Irving and Wadso% and ranging in size from approximately 0.25 to 0.076 mmole, were treated with 80 ml. of the acid solution. These gave an average value of -7113 f 29 cal./mole, which agrees favorably with the value of -7104 cal./mole reported by Irving and Wadso.25 Within the limits of experimental error, no concentration dependence could be detecked.
p = AH,"
- 2.303Rl'(~)~+v-m
where
and
The symbols have been defined previously.21 If one plots p vs. m, a linear relationship results which can be extrapolated to infinite dilution where p = AH,". The theoretical Debye-Hiickel limiting slope, ~ I I , used for calculating p , was calculated with the density data of Sinyakov, et al.,17 and the dielectric constant data of Leader and Gormley.14 This slope is 927 cal./ mole-P" kg.'/'.26In The value of I1/'a was obtained from a previously prepared plot of I us. 11/2a.28 Results of the measurements are summarized in Table I. The first, second, and third columns list the molality, l/%, and the measured integral heats of solution, respectively. The fourth column lists the theoretical values which are subtracted from the measured heats to obtain the p values which are listed in column five. A comparison of the limiting slopes of the various salts and the theoretical limiting slope is made in Figure 2. Error bars indicate the estimated limits of error for each individual point. Where error bars are missing, the estimated error is less than 30 cal./ mole. The extrapolations do not necessarily represent the best lines that could be drawn through the centers of the points, but in all cases they are drawn consistent with the estimated reliability of the individual points. Within the limits of experimental error both types of extrapolation were linear and gave identical values for the standard heats of solution, except for sodium and lithium chlorides. The standard heat for sodium chloride was obtained by using the average of the two
Calculations and Results The measured heats of solution were extrapolated to infinite dilution both by the simple Debye-Hiickel method of plotting the measured heats of solution against d G and by the extended Debye-Huckel treatment which has been recently employed for aqueous solutions of electrolytes. 21, 2 2 The merits of the latter metJhodof extrapolation have been discussed previously. 21 The extended Debye-Huckel equation can be written as The Journal of Phyaicd Chemiatry
(24) H.C.Dickinson, National Bureau of Standards Bulletin, No. 11, U.9. Government Printing Office, Washington, D. C., 1914,p. 189. (25) R.J. Irving and I. Wadso, Ada Chem. Scad., 18, 195 (1964). (26) The dielectric constant data of Bass, Nathan, Meighan, and Cole2' gave a theoretical limiting slope of 1092 cal. mole-*/%kg.'/i. However, in the opinion of the authors, the data of Leader and Gormley are to be preferred. In any event, the difference in the values for the limiting slopes has no signscant affect on the extrapolation of the present heat data. (27) S. J. Bass, W. I. Nathan, R. M. Meighan, and R. H. Cole, J. Phys. Chem., 68, 509 (1964). (28) E.C. Jekel, Ph.D. Thesis, Purdue University, 1964.
THERMODYNAMIC PROPERTIES OF NONAQUEOUS SOLUTIONS
2615
Table I: Integral Heat.s of Solution and p-Values of Electrolytes in N-Methylformamide a t 25' m
m X 104, moles/kg. of N M F
&
4.24 5.36 8.28 15.3 30.0
0,0206 0,0232 0,0287 0,0391 0.0548
CSCl 0.940 0.863 0.842 0,926 0.912
0.013 0.014 0.017 0.021 0.033
2.27 6.28 17.5 21.6 39.0 41.3 56.3 62.9 76.1
0.0151 0.0251 0.0418 0,0465 0,0556 0.0643 0.0750 01.0793 0.0873
NaCl -1.329 -1.108 -1.168 -1.050 -0.966 -1.009 -0.888 =0.902 -0.900
0.009 0.015 0.025 0.028 0.037 0.038 0.044 0.046 0.051
-1.338 -1.123 -1.193 -1.078 -1.003 -1.047 -0.932 -0.948 -0.951
0.904 1.18 1.24 2.27 2.83 9.20 12.9 16.2 21.4 26.4 28.8
0,00951 0,0109 0.0111 0.0151 0.0168 0.0303 0,0359 0.0402 0.0463 0.0514 0.0537
NaBr -4.52 -4.21 -4.12 -4.41 -4.41 -4.26 -4.07 -4.19 -4.17 -4.17 -4.02
0.006 0.006 0.006 0.009 0.010 0.018 0.022 0.024 0.028 0.031 0.032
-4.53 -4.22 -4.12 -4.42 -4.42 -4.28 -4.09 -4.21 -4.20 -4.20 -4.05
kcal./mole
6HI'/b,
P,
kcal./mole
kcal./mole
0.927 0.849 0,825 0.903 0.879
x
104,
moles/kg. of NMF
.\/m
14.1 21.8 34. 4b 40, 4b 51.5 84.2 118
0,0375 0.0467 0.0587 0.0635 0.0715 0.0918 0.109
1.94 2.73 2.76 4.69 6.42 8.66 10.9 15.2 16.3 24.8 36.0
0.0139 0,0165 0.0166 0.0217 0.0253 0.0294 0.0330 0,0390 0.0404 0.0498 0.0600
LiCl -12.5 -11.6 -11.5 -10.62 - 10.18 -10.21 -9.83 -10.23 -9.79 -9.95 -10.06
0.009 0.009 0.010 0.013 0.015 0.018 0,020 0.023 0.024 0,030 0,036
-12.5 -11.6 -11.5 -10.63 -10.20 -10.23 -9.85 -10.25 -9.81 -9.98 -10.10
0.735 1.03 1.57 5.04 7.74 12.7 13.7 24.0 27.8
0.00857 0.0101 0.0125 0.0224 0.0278 0.0356 0.0370 0.0490 0.0527
NaI -8.26 -8.17 -8.17 -8.23 -8.28 -7.99 -8.17 -8.10 -7.93
0.005 0.006 0.007 0.013 0.017 0.021 0.022 0.029 0.031
-8.27 -8.18 -8.18 -8.24 -8.30 -8.01 -8.19 -8.13 -7.99
AH.,'
kcal./mole
KCl 0.344 0.342 0.304 0.326 0.337 0.347 0.321
6HI'/2Cr,
kc a1./mole
0.023 0.028 0.035 0.038 0.042 0.053 0.062
Pl
kcal./mole
0.321 0.314 0.269 0.288 0.295 0.294 0.259
Approximate estia No attempt has been made to assign numerical values to the errors of the individual heat measurements. These are an average of two or more measurements. mates of the errors are indicated by the error bars shown in Figure 2.
'
extrapolations. The estimated standard heat for lithium chloride was obtained from an extrapolation of the p vs. m plot. Although the data are not precise enough to determine decisively accurate values of the experimental slopes, certain trends are clear. Cesium and potassium chlorides have slopes that, within experimental error, are consistent .with the theoretical limiting slope for heats of solution given byz9
Sodium chloride, bromide, and iodide have slopes between 7 and 10 times the theoretical limiting slope. Most significantly, lithium chloride shows a sharp break in very dilute solutions and approaches infinite dilution with an estimated slope in the order of 280
times the slope predicted by the Debye-Huckel theory, making accurate extrapolation to infinite dilution impossible. The most dilute thermal data previously reported in a high dielectric constant solvent are for formamide (D = 109) in the range of 0.03 to 0.12 m, approximately 100 times more concentrated than the present measurements.8 A plot of AH, us. shows a slope that is opposite in sign from that observed in the present work. For the low dielectric constant solvent, liquid ammonia (D = l6.9), Gunns has measured heats of solution of elect,rolytes down to slightly less than m and has found the limiting slope to be about 12 times more posit'ive than the theoretical slope. Calorimetric measurements in methanol (D = 32.6) down t'o concentrations of about
d&
(29) Since densities of the solutions were used in the calculation of 6 ~ the , variable is d G instead of the usual&.
Volume 69, Number 8 August 1966
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ROBERTP. HELDAND
CECIL
n1.
CRISS
small, possibly indicating a small amount of ionic association. They also found the conductance vs. curves to be slightly concave to the concentration axis, an effect similar to that found by Coates and Taylor3*for lithium salts in liquid HCN. However, because of the high dielectric constant of this solvent, French and Glover discard the possibility that the concavity is caused by ionic association. Unfortunately, no conductance data are available for LiCl in S-methylformamide. On the basis of these and the present results, it appears to the authors that there probably is ionic association in this solvent for some electrolytes in spite of its high dielectric constant. This is an unexpected result and one that should be investigated further. Table I1 lists the standard heats of solution, obtained by extrapolating the measured integral heats to infinite dilution. The indicated errors are the standard deviations of the points from the extrapolated lines. Because of the extremely positive limiting slope for LiC1, the standard heat of solution for this salt is only an estimate. Also listed in Table I1 are heats reported by Strack, Swanda, and Bahe,l8 calculated from solubility data. The directly measured calorimetric values and those calculated from solubility data agree remarkably \yell for sodium and potassium chlorides, in spite of the questionable assumption that the activity coefficient does not vary with temperature. The fact that values for sodium bromide do not agree may be caused by the much higher solubility of sodium bromide, making invalid the assumption that the activity coefficient is independent of temperature.
4;
* !-
NoBr
-8,0w
*
-8.5 -10.0
-
-II.O
I-
-12.0
-
-'3'0
LiCl
J
1
Y
' .di ' .oh
.d3
.d4 .d5 .06 .07
m
.0'8
.09
.I 0
.;I
Figure 2. Integral heats of solution (kcal./mole) a t 25" in N-methylformamide as a function of l/m.
3 X m show slopes considerably exceeding the theoretical.13 On the other hand, Wallace, Mason, and Robinson30measured the heat of dilution of sodium chloride in ethylene glycol (D = 37.7) down to m and obtained a slope in agreement with the theoretical limiting slope. Even in the relatively high dielectric constant solvent water (D = 78.5), slopes considerably exceeding the theoretically predicted slopes are observed for electrolytes of higher valence type. 31 I n general, these positive slopes have been explained in terms of incomplete dissociation of ion pairs.Bt31 I n a high dielectric constant solvent such as Nmethylformamide, one would anticipate complete dissociation of electrolytes. However, ionic association in high dielectric constant solvents is not unknown. The conductance measurements by Coates and Taylor32 on several electrolytes in liquid HCN show that certain lithium salts, including lithium chloride, are associated. French and Glover15 measured the conductance of several inorganic electrolytes in N-methylformamide and generally found deviations from the theoretical Debye-Hiickel-Onsager slopes to be positive, but The Journal of Ehgsical Chemistry
Table I1 : Standard Heats of Solution of Electrolytes in N-Methylformamide a t 25" Solute
csc1 KC1 NaCl LiCl NaBr NaI
AHB', kcal./molea
0.890 0.308 -1.244 ( - 13.1)' -4.393 -8.258
a This work. See ref. 18. tion of p in the p us. m plot.
A H S O , kcal./mole
3= 0.042 3= 0.018
0.0
rf 0.046
-1.197
i: 0.105 f 0.085
-1.539
Estimated from the extrapola-
(30) W. E. Wallace, L. S. Mason, and A. L. Robinson, J . Am. Chem. SOC.,66,362 (1944). (31) H. S. Harned and B. B. Owen, "The Physical Chemistry of
Electrolytic Solutions," 3rd. Ed., Reinhold Publishing Corp., New York, N. Y.,1958,pp. 335, 336, 577,578. (32) J. E. Coates and E. G. Taylor, J . Chem. SOC.,1245 (1936).
CALCULATION OF HALLEFFECT IN IONIC SOLUTIONS
Heats of solution in N-methylformamide a t 25’ are much more negative than those in water. Data from the literature and unpublished data in this laboratory on other nonaqueous solvents indicate that, in general, heats of solution in nonaqueous solvents are more negative than those in water. This
2617
phenomenon is being investigated further and will be reported in a future communication.
Acknowledgment. The authors are indebted to the United States Atomic Energy Commission, which supported this work through Contract ilT-(30-1)-3019.
Calculation of the Hall Effect in Ionic Solutions’”
by Harold L. Friedmanlb I B M Watson Research Center, Yorldown Heights, N . Y . (Received February 4,1966)
The theory of electrical conductance in ionic solutions recently reported by the author has been extended to apply to the transport in combined electric and magnetic fields. Calculations are made with the “brownon” model, essentially the model used in the DebyeHuckel-Onsager conductance theory. General expressions and numerical results are obtained for the ideal and limiting-law terms of the Hall conductance. The calculations indicate that the effect is large enough to be measurable, a t least for solutions of the more mobile ions. For symmetrical electrolytes the limiting-law term opposes the ideal term in the Hall conductance, while for unsymmetrical electrolytes it may either aid or oppose the ideal term.
1. Introduction When an electric field in the x direction and a magnetic field in the y direction of a Cartesian coordinate system act on a conducting body, the electric current that flows tends to have a component in the z direction.lC Depending on the external electrical connections to the body, one may observe this current component, the Hall current, or one may determine the electric field in the x direction required to reduce this current to zero, the Hall field.213 This phenomenon is most easily observed in materials in which the carriers of electric charge have relatively high mobility. If the carriers are all of one species and if their concentration is low, then the measurement of the Hall effect can be used quite simply to determine the carrier concentrati~n.~ For example, this is true in silicon crystals in which the carrier concentration may be as low as 10-lo M and the mobilities of the carriers (electrons or
holes, depending on the impurities in the silicon) as high as 3000 cm. ”v. The Hall effect due to ionic carriers is difficult to ob(1) (a) Paper presented a t the 148th National Meeting of the American Chemical Society, Chicago, Ill., Sept. 1964; (b) Department of Chemistry, State University of New York, Stony Brook, N. Y.; (c) throughout this paper we shall assume that the electric field defines the z axis and the magnetic field the y axis of a Cartesian coordinate system. (2) The latter is the usual arrangement. For example, see A. G. Redfield, Phys. Rev., 94, 526 (1954). However, in the statistical calculations it seems easier to assume that the Hall current flows unimpeded by any external electric field in the z direction. (3) See S. R. de Groot and P. Masur, “Non-Equilibrium Thermodynamics,” North-Holland Publishing Co., Amsterdam, 1962, for an account of some of the phenomenological aspects. (4) R. E. Peierls, “Quantum Theory of Solids,” Oxford University Press, Oxford, 1955. (5) In some circumstances one can observe components of the Hall current due to particular species, depending on the use of electrodes at which only these species act reversibly [J. Swanson, IBM J . Res. Develap., 1, 39 (1957)l. This can be avoided by using electrodes of the same composition as the solution.
Volume 69, Xumber 8 August 1966
