*lug. 5, 1961
THERMODYNAMIC PROPERTIES OF
conclusions: first, the increments to T D F from this additional complexity of the model would be small (of the order of 0.004); second, the increments would, however, be more strongly dependent on halogen atom mass than the three genuine vibrations considered above; third, in aggregate, the additional complexities would not account for the degree of sensitivity to halogen atom mass indicated experimentally for either TI?? or TDF. For a consistent reaction coordinate motion, then, the obvious models fail to reproduce the experimental results. What of the possibility that each of the reactions actually involves a somewhat different reaction coordinate motion? If one insists upon linear or nearly linear transition states, one's freedom in calculation is limited mostly to the juggling of force constants and bond distances, differences in reaction coordinate motion being described essentially as differences in applicable values of a parameter such as the p of the Bigeleisen-
[ COSTRIBVTIOS
FROM THE
SODIUM BND
BARIUMCHLORIDES
3223
Wolfsberg treatment. Comparison of Table I V and the first column of Table I11 leads us to coiiclude that one might by this means bring the calculations for the methyl chloride and methyl bromide reactions into reasonable consonance, but TIF for the cyanization of methyl iodide is just too large to fit into such a picture. Departures from linearity in the configurations of the activated complexes result in lowering the calculated values of T I F ; but, the shifts are moderate even for CN- attack a t 90 O , and no better correspondence between calculated and apparent experimental values of T I F can be achieved by the assumption of halogen dependence of the single XBC. The rather large scatter in the data furnishes no refuge from these conclusions. Acknowledgments.-We are indebted to Mrs. Eula Ihnen who performed the mass spectrometric analyses. This research was supported by the U. S. -4tomic Energy Commission.
DEPARTMENT OF CHEXISTRY,
PERDUE UNIVERSITY,
LAFAYETTE, INDIANA]
The Thermodynamic Properties of High Temperature Aqueous Solutions. I. Standard Partial Molal Heat Capacities of Sodium Chloride and Barium Chloride from 0 to l o o o l BY CECILM. CRI&
AND
J. W. COBBLE
RECEIVED FEBRUARP 22, 1961
h sensitive submarine type solution calorimeter using electronic amplification and automatic recording has been constructed to measure heats of solution up t o 100". Searly 300 integral heats of solution of sodium chloride and barium chloride have been determined-at various concentrations from near 0 to 95". From the extrapolated values of the heats at infinite dilution, values of C,O as a function of temperature have been calculated for these salts. The observed heat capacities show maxima between 50 and 70" and then decrease as the temperature is further increased.
Introduction Within the past several years there has been an increasing interest in the thermodynamic properties of aqueous solutions a t higher temperatures, both from a practical and theoretical point of view. One of the best methods of obtaining these properties a t higher temperatures is to extend the known thermodynamic functions a t 23" by use of partial molal heat capacities over the desired temperature range. Usually, i t is the standard state functions (i.e.,a t infinite dilution) that are desired; therefore, it is the partial molal heat capacity a t infinite dilution and a function of temperature which is of real interest. Unfortunately, only a few reliable values have been reported a t temperatures much above Furthermore, what values are available were obtained from extrapolations derived from specific heat measurements of concentrated solutions. The reliability of extrapolations from such concentrations to infinite dilution is subject to question. Indeed, even the (1) Supported in part by a grant from t h e National Science Foundation. (2) From t h e Ph.D. Thesis of Cecil M. Criss. Purdue University. 1961. (3) M.Eigen and E. Wicke, Z.Elektrochenz., 66, 354 (1951). (4) E. Wicke, RI. Eigen and T h . Ackermann, Z. physik. Chem. NF, 1, 340 (1954). (6) Th. Ackermann, Disc. Faraday SOL.,24, 180 (1957). ( 6 ) Th. Ackermann, Z. Elektrochem., 62,411 (1958).
theoretical limiting slope for @cP a t 25" is uncertain by 25% for a 1 : l electrolyte.' Gucker* can has suggested that more reliable values of @cPo be obtained by combining the temperature coefficients of the relative apparent molal heat contents, @L, with apparent molal heat capacities of more concentrated solutions. Harned and Owen9 have suggested that the use of the temperature coefficient of theLelative heat content can lead to better values for Cp2. Gulbransen and Robinsonlo in still another method have combined the heats of dilution, -@L, a t two temperatures with the integral heats of solutign a t the same two temperatures to calculate CI,2 for NaCl(aq.) at 22.5". The approach used in this investigation is a slight variation on the latter method and will hereafter be referred to as the "integral heat method.'' It involves only heat-of-solution measurements. The amount of heat released when a solute is dissolved in water according to the equation MX(c)
+ aq. --+ MX(aq.)
(1)
(7) E. -4. Guggenheim and J. E. Prue, Trans. Faraday Soc., 60, 710 (1954). ( 8 ) F T. Gucker, Jr., Ann. N. Y. Adad. Sci., 61, 680 (1949). (9) H.S Harned and €3. B. Owen, " T h e Physical Chemistry of Electrolytic Solutions," 3rd E d . , Reinhold Publ. Corp., Sew York, N. Y., 1958, p. 352. (10) E. A. Gulbransen and A. L. Robinson, J . A m . Chcm. S O L . 66, , 2637 (1934).
3234
CECIL11.CRISSAND J. W. COBBLE
can he expressed by AH. = n1171 nJl2 - I~IRIO nZII2 (3) where €71and Rz are the partial molal beat contents of the water and solute, respectively, Hl0is the heat content of pure water, Hz is the heat content of the pure solute and nl and nz are the number of moles of water and solute, respectively. At infinite dilution
+
-
A H s o = ?&zQ
- nlH2
(3)
Over sufficiently small temperature intervals the temperature coefficient of this expression is AC*O
=
- nsCpn
n21)ip20
(4)
where AC, is the change in heat capacity of reaction 1 acd C,, is the heat capacity of the pure solute. Thus the problem is reduced to finding an accurate value for AHsoa t two temperatures. Experimental Apparatus.-The submarine calorimeter (hereafter referred to as laboratory ralorimeter C S 1 ) was a 425 cc. glass dewar-type flask fitted with a standard taper joint a n d an evacuated stopper and contained a platinum resistance thermometer for temperature measurements. The glass stopper had three 23 cm. exit tubes, two of which were made from precision tubing from about two cm. above the top of the stopper. One of these tubes contained the stirrer, the upper portion of which was rnade from a matching piece of precision bore tubing. The stirrer was hollow and contained a heating element in order t o bring the calorimeter to the desired operating temperature. Two insulated metal slip rings were attached t.o the top of the stirrer and connected to the heating element so t h a t the calorimeter could be simultaneously stirred and heated. The stirrer was driven by a synchronous motor a t approximately 600 r.p.m. T h e other precision bore tube contained the combined calibration heater and sample holder. The upper portion of this tube was also made from a matching precision bore tube. The sample bulbs were connected by rubber tubing to t h e lower end of the sample holder-heater. The bulbs could be broken by a vertical movement of the rod which caused the bulbs to be smashed on a small anvil which was fused to the bottom of the calorimeter. The heating element of the calibration heater was made by winding about SO inches of No. 36 nianganin wire noninductively around a six mm. Pyrex tube. This then was painted with “Glyptal” and baked for several hours. Four copper lead wires were attached: two No. 30 wires t o carry the current and two A-0. 40 wires to measure the potential across the heater. The space inside the tubing was filled with silicone oil to conduct heat from the heating elements to the surroundings for both this heater ar.d the rough heater previously mentioned. The remaining tube in the stopper contained the platinum resistance thermometer which was adjusted so as not to touch the walis of the exit tube. The calorimeter was placed about 16 cm. below the surface of a bath thermostated to a t 0.002”. The modulus of the calorinicter under least ~ these conditions was about 1 X 1Tj-J c d . m i t ~ . - (leg.-’. The resistance thermometer \vas counected to a standard Mueller bridge. This bridge x i s thermally and electrically shielded by specially constructed shielding and was internally calibrated. Corrections xere applied to the resistances when necessary. In preliminary experiments, the output of the bridge was connected to a Leeds and Xorthnip, moving-coil, reflecting-type galvanometer which had a n optical ent that gavea sensitivity of 1 X ’. During e of these moisurenients i t was decided to use a t1.c. linear breaker-type amplifier and recorder in placc of the galvanometer. I t rras operated close to full gain and the output voltage attenuated by a voltage divider. A portion of this voltage was used to drive a four mv. recorder. T h e over-all gain was such that a 0.35 pv. signal to the amplifier gave a full scale deflection of the recorder pen, resulting in a temperature sensitivity of 2 x lo-& “C. The power source for the calibration heater was a commercially available coulometric constant current source,
-
1701. s3
accurate to better than r t O . l % . A mechanical timer built into the instrument provided time measurements t o =t0.1 second. The two No. 30 wires from the calibration heater were connected directly t o the output of the current source and the two No. 40 wires from the heater were connected to a volt box so that periodic checks on the voltage drop across the heater could be made. All voltages were measured with a Leeds and Northrup type K-3 universal potentiometer. The current source was periodically calibrated hy means of a 10.000 ohm standard resistor and potentionie ter . Corrections were made to the heat output of the heater caused in the slight difference in the resistance of the manganin wire a t various calorimeter operating temperatures. Corrections were also applied for heat generated in the leads and the heat leak from the leads of the heater. The largest of these corrections was in the order of 0.2%. Materials.-All water used in the measurements was prepared from ion-exchange repurified distilled water. The specific resistance of the water varied from 2.7 t o 18.0 megohm-cm. The BaC1, used in all measurements was J. T. Baker analyzed reagent, dihydrate. T h e specifications indicated that the greatest impurity did not exceed 0.03%, making it unnecessary for further purification, except for the removal of water. Samples of XaCl were also J. T. Baker analyzed reagent and were used without further purification. Specifications indicated that the greatest impurity was 0.004% (including potassium). All salt samples were dried over 400°, weighed into sample bulbs and then returned t o the 400’ oven for a t least 8 hr. They were then removed, cooled in a desiccator and sealed under vacuum immediately. T h e stock supply was kept in the furnace and was removed only when weighing samples. A drop of phenolphthalein on the salts indicated no apparent hydrolysis for iYaC1. However, a slight pink coloration was observed with the BaCl1, indicating a slight amount of hydrolysis, but i t has been shown by using synthetic saniples containing Ba(OH)*to be less than 0.1%. Experimental Procedure.-Very thin-walled sample bulbs having a diameter of about 8 mm. and a stem about 2.5 cm. long were made from 7 mm. Pyrex tubing. The stem had a narrow neck near the base of the bulb. These bulbs were filled as described above and sealed under vacuum by melting the glass around the neck of the bulb with a very thin flame, with due care to avoid excessive heating of the sample. For dcterminations above 25“, water was placed in the calorimeter a t room temperature and then heated to the desired operating temperature by the rough heater and permitted t o come t o a uniform temperature a few hundredths of a degree below the equilibrium temperature. For temperatures below 2 5 ” , water was placed in the calorimeter near 0” and heated to operating temperature. For the lowest temperature, 0.02”, the water in the calorimeter was cooled further by inserting a long “U” shaped tube in the opening for the sample holder-heater through which Dry Ice cooled acetone was passed. When the calorimeter water was very close to O o , the tube was removed and the sample holder-heater inserted in its proper place. T h e system was then permitted to remain for several hours until a uniform temperature was established. T h e bridge was kept as close t o balance as the last decade would permit, using the recorder (or galvanometer) t o interpolate between unit resistances of the last decade. I t h e n a linear time-temperature drift line was observed, it was assumed that a uniform temperature gradient had been established and a determination was started. An electrical calibration generally preceded and followed each determination, except at the lowest temperature. At this temperature the chemical determination was made first and was then followed by two electrical calibrations. When heat was introduced into the calorimeter (either electrical or chemical), the bridge was balanced again to keep the recorder pen from going off scale. A “best” straight line was drawn through the linear portion of each of the time-temperature curves and extrapolated to the time a t which either the sample bulb was broken or the calibration made. The differences between these lines were always determined at the six-tenths rise time” and compared with a standard deflection obtained (11) H. C. Dickinson, U. S. Bur. Standards Bull., 11, 189 (1914).
THERMODYNAMIC PROPERTIES
Aug. 5, 1961
by moving the last decade of the bridge one unit, ;.e., a value of 0.0001 ohm. This standard deflection was an average of several values obtained before, during and after each run. The amount of heat releasedl2 when the sample bulb was broken was divided by the number of moles of the sample dissolved to determine the integral heat of solution per mole, AH., for that particular concentration. In general, two or more determinations were made for a particular concentration and the results were averaged.
Calculations and Results A procedure for extrapolating heat of solution data to infinite dilution has been proposed.’ The relative apparent molal heat content, @I,, can be expressed by an extension of the Debye-Hiickel expression
where 6~ is the theoretical limiting slope, v = v+ 4v-, v+ and v- are the number of positive and negative ions produced by dissociation of one molecule of electrolyte, Z+ and 2- are the charges on these respective ions, I is the ionic strength, cQ/~) is a special function13 defined by 3
u(I%) = I,,s - I1
+ Z’/: - (1 +
1%)-1
-
2 In (1
+ Ph)]
(e)
and B is a constant for the specific electrolyte. If the first term on the right side of equation 5 is subtracted from both sides and the left side plotted against molality, a straight line with the slope - 2.303RT2 (dB/dT) v+ v- should be obtained. For the purpose of extrapolating heats of solution to infinite dilution, this equation can be written as p = AH.0
B - 2.303RTa dd-F Y+
Y-
m
(7)
where AHSOis the integral heat of solution a t infinite dilution 3
AH^ - Y IZ+ z-1 aEI mu 2
(8)
and
“‘13’”’l All the data for both BaClz and NaCl were extrapoLy
= [(l +
ZV2)-1
--
(9)
lated to infinite dilution by plotting as a function of m. It is believed that this method of extrapolation to infinite dilution is superior to the of d G plots* This is largely true because the extraPolation using a linear m Scale Can be made from more concentrated solutions and the distance Over which the extrapolation nluAt be made is smaller thall with a dm scale. The extrapolations of p to infinite dilutioI1 ivere also carried outsuch that both dp/dm and the ternperature CoefficielltS Of AHSOWere a smooth function of temperature. In some cases this did not represent the best line that could be drawn through the (12) Except a t the highest temperature, there was no noticeable heat of bulb breaking. (13) Tables of this function are listed in Harned and Owen, ref. 9, p. 176.
O F SODIUM AND
BARIUMCHLORIDES
3225
centers of the experimental points, but in all cases the extrapolations were consistent with the average errors involved in the heats. It should be noted that the extrapolations are also in agreement with the known heats of dilution a t some temperatures. lo, The average values of AHa a t various concentrations and temperatures are listed in Tables I and 11. The first column gives the number of individual determinations that are involved in determining an average value for the listed heats. Columns two and three list the average molality and f i . Column five gives the theoretical values that are subtracted from the observed heats in column four to obtain p values which then are listed in column six. The extrapolated value of the integral heat of solution a t infinite dilution, AHSO, for each temperature is listed with the data for that temperature. It is of interest to note that the present integral heats of solution of NaCl a t infinite dilution are in agreement, within experimental error, with most of the previously reported values. The heats of dilution of NaCl a t 20 and 25” reported by Gulbransen and Robinsonlo combine with the heats of solution a t 20 and 25’ reported by Cohen and Kooy15 to give 1,080 and 915 cal./mole for the integral heat of solution a t infinite dilution.16 A similar treatment of the data of Lipsett, Johnson and Maass’l gives 1,072 and 918 cal./mole for the same quantities a t 20 and 2f1O.l~ Likewise, a similar treatment of the data of Wiist and LangeIg yields 926 cal./mole a t 25”. The integral heat of solution a t infinite dilution and a t 25’ for BaClz was found to be more negative than the commonly accepted valuezoof 3,160 cal./ mole. However, when a BaClz sample was permitted to be in contact with the laboratory air for a few minutes, AHsochanged to 3,150 10 cal./ mole, which suggests that the values reported in this research are perhaps to be preferred. Tables I11 and IV summarize the values of evaluated from equation 4. The heat capacities for the anhydrous-salts, C,,, are those repoited by Kelley. z 1 , 2 z Alchough the values of obtained by the integral heat method as used in this research repre-
*
cPOz
cP,”
(14) See Harried and Owen, ref. 9, P. 707. ~1~~~~~ E. Cohen and J. KooY, 2. 9hYstk. Chem. ( L E W d , 139A, 273 (16) These values are the same, within the experimental error, as those calculated by Gulbransen and Robinson1o from t h e same data. so~~,7~9~l~o~;;P;;; F. M. G.Johnson and 0. Maass, J. A m . C h e w
(18) The dilution d a t a of Gulhransen and and those derived from the heat of solution d a t a of Lipsett, Johnson and Maass” do not agree. Therefore, the dilution d a t a of Gulhransen and Ruhinson were applied t o the heat of solution of t h e most concentrated soiution for which t h e dilution d a t a were valid (;,e., a t 4; 0 841). (19) J. Wiist and E. Lange, Z . p h y s i k C h e m . . 116, 161 (19%). (20) Id*.D. Kossini, D. D. Wagman, W. H . Evan$, S. Levinc and I. Jaffe, “Selected Values of Chemical Thermodynamic Properties,” Circular 500, National Bureau of Standards, 1952. (21) K. K. Kelley, “contributions t o the , l a t a on Theoretical Metallurgy. XI. Entropies of Inorganic Substances. Revision (1948) of Data and Methods of Calculation,” U. S. Bureau of Mines, Bulietin 477, 1950. (22) K, K. Kelley, “Contributions t o the Data on Theoretical Metallurgy. XIII. High-Temperature Heat-Content, Heat Capacity, and Entropy Data for the Elements and Inorganic Compounds,” U. S. Bureau of Mines, Bulletin 584, 1960.
-
CECIL>!II.CRISSAND J. W. COBBLE
3226 TABLE 1
TABLE I (coiztinued)
THE INTEGRAL HEATSOF SOLUTIOX AXD p I-ALUES OF S O D I U M CHLORIDE
3.43 9.24 13.27 19.16
No. of detns.
0.02 0.0586 1897 18 1879 ,0961 1911 i 21 28 188P i 2 1 ,1152 1933 33 1900 .I384 1936 f 14 39 1897 f 14 AHan = 1905 =k 8 cal./mole
5.00" 3.43 9.25 13.30 19.16
9 24 19.14
1
9 24
9.50 19.16 20.09
9.69 2 0 . 06
1.45 2.88 5 31 t; .XI
8 98
9 93
10 66 20. *56
1
->
I
0,899 1.47 2.44
2 1
:3 82
1
i
6.87 9.74 11.62 14.32
1
20.58
2 1
3 31
3.68 9 91 1-1 "0 20 36
0.0586 1700 i 15
19 1686 i 15 ,0962 1665 f 4 30 1635 i 4 ,1153 1089 i 5 36 1653 i 5 ,1384 1674 f 6 42 1632 i 6 AHsn = 1658 It 11 c d i n i o l c
15.00" 0.0961 1260 0985 1282 ,1384 1285 ,141s 1261 AI?',O = 1'45 i 2
34.96O 0.0300 656 16 010 ,375 5 1 3 0388 503 i I:: 20 ,0491 6:3jzt 27 26 610 I27 0.58 =k 9 :32 626 i !i 0618 07x3 65.3 ,I, 016 654 42 612 ,0829 ,0987 606 I- 3 49 617 i : 676 3:; 023 . 1078 ,1197 (iX0 5s 622 ,1435 (j17 68 609 AH,O = 615 f 6 cal./rnole 5,-
36 57
341 i 7 386 i 2 67 3-11 f 2 80 340 _I 2 340 i 2 cal./iiiole
.\/G
AHs (cal.jmoleJ
-ax-
I'/&
(cai.)
3.68 9.95 14,25 20.62
54 83" 124 0 060'7 ,0998 146 ,1194 154 ,1436 167 AHBo=
3.67 9,90 14.04 20.49
64.86' 0.0606 -155 f 5 47 0995 -138 f 5 74 ,1185 -121 f 4 88 104 .1431 -108 AHSO = -200 i 2 cnl
9.93 14.39 20.33
1245 I246 4!1 1239 ,j1 12;3(1 cnl./mole
*
AHB@=
HzO)"
9 91 11.41 20.30
33 36
25.00" 952 i 33 17 935 i 33 0.0380 951 i 18 24 907 i 18 ,0537 ,0729 941 i 15 .?2 909 f lc5 908 i 47 ,0799 9-15 i '47 31 ,094; 959 i 2 41 $115i 2 0996 937 f 6 4% 894 f G 8-34 44 XRO ,1032 ,1414 '365 i 3 59 DOG 5 AIIB" = 914 i ,5 cal.,.'~r~ole
'
(moles/kg.
4 19
19.9;" 0.0984 109s i 9 39 1 (Id9 3: 0 , 1416 1 I lfi i 11 3,5 1061 A: 11 AH2 = 1071 i 8 cal./mole
45.00' 377 i 7 . (IO96 :
