JOURNAL OF RESEARCH of the National Bureau of Standards Vot. 85, No.1, January- February 1 980
Enthalpies of Dilution of Aqueous Electrolytes: Sulfuric Acid, Hydrochloric Acid, and Lithium Chloride
Y.C.Wu
Center for Consumer Technology, National Bureau of Standards, Washington, DC 20234
and
T. F. Young*
G. H. Jones Laboratory, University of Chicago, Chicago, Illinois 60637
August 8, 1979
Calorimetric measurements at 25°C of the enthalpies of dilution of aqueo us H2 S04 (0.00090 to 6.4 mol · kg-I ), LiCI (0.026 to 6.7 mol · kg-I ), and HCI (0.018 to 1.6 mol· kg- I) have been performed using two different isothermal calorimeters. The results of this work and that of three earli er calorimetric investigations and one Raman spectral investigation have been used to calculate values of the relative apparent molal enthalpies, and relative partial molal enthalpies for these electrolytes.
Key words: Calorimetry; electrolytes; enthalpy of dilution; heat; hydrochloric acid; lithium chloride; relati ve apparent molal enthalpy; relative partial molal enthalpy; sulfuric acid; thermochemistry.
1. Introduction performed a semi-theoreti cal calculation of the relative ap parent molal enthalp), of sulfuric acid. They also found a
The relative apparent molal enthalpy (L) I or heat con systematic difference of 460 calories (l cal=4.184 1) betw een tent of sulfuric acid is a co mplicated fun ction of the molal th eir values and those reported in the literature [5]. This ity. The determination of this quantity requires an extrapo discrepancy was also confirmed later by Harned and Owen lation of enthalpies of dilution as measured do wn to ex [1]. Several years later, Giauque and his co-workers at the tremely low molalities. Universi ty of California began an analysis of the thermody / There have been numerous reports and discussions of th e namics of sulfuric acid [6] . Thus, the work of Young and relative apparent molal enthalpy of sulfuric acid [1 - 4).2 At Blatz [2], the research of Giauque et al., and the earlier the extreme dilutions attainable experimentall y, sulfuric measurements of Gro enier and Young [7] indicated a need acid is known to have un dissociated bisulfate ions [2]. This for additional experimental work on the dilution enthalpy of incomplete dissociation at the lowest dilutions complicates sulfuric acid which, in turn, led the junior a uthor (YCW) to the extrapolation procedure, causes deviations from the undertake this investigation, which also included measure Debye-Huckellimiting law (DHLL), and makes the final cal ments on aqueous HCl and LiCl, as a part of his Ph.D. dis culated values of the relative apparent molal enthalpy sertation. While some of the results obtained herein have dependent on the method of data treatment. been cited by Giauque et al. [6] and used both in the Na Young and Blatz [2] performed an analysis of this prob tional Bureau of Standards Technical Note 270 Series [3], lem in 1949. They took the degree of dissociation, and and in the review of Pitzer et al. [8], independent publica thence the enthalpy of dissociation, into consideration and tion of the results was delayed by circumstances encoun tered by the senior author (TFY). Publication at this time ·Late professor of chemistry at the University of Chicago. serves both to better document the experimental results and I Th e reader is referred to th e trea ti se of Harn ed and Owen [I] for the definition of th e terms the method of data treatment and to honor the memory of used inlhis paper and to the glossary (sect. 6)for an ex planat ion orlhe sy mbols whic h we have used.
1 Fi gur es in brackets indicate references at th e end of this paper. the late T. F. Young and his dedication to science.
11 2. Experimental Procedure dilution of HCI at about 0.02 mol , kg- ', where the heat liberated was about 60 mcal, the corresponding uncertainty Two calorimeters of different sensi tivities were employed is about 25 percent. However, the heat liberated for the en depending on the molality. A calorimeter with lower sensi thalpy of dilution of sulfuric acid in the same molality range tivity, as described by Young and his co-workers [9, 10], wa s was about fifty times larger and the corresponding uncer used for most of the measurements where the molality was tain ty was less than 1 percen t. 1 greater than 0.01 mol kg- '. For those measurements below 0.01 mol kg- ', a more sensitive differential calorimeter was 3. Results and Calculation necessary. The latter instrument contained a thermel of 500 junctions on each side of a plastic plate which was held by The method of treating the data is essentially the same as petroleum "wax" in the center of a large Dewar flask hav desc ribed previously [10]. The molalities of th e initial and ing a volume of two liters. Its design was somewhat si milar final so lutions are, respectively, m, and m2. The heat abo to that of the calorimeter used by Lange and his co-wo rkers sorbed is Q, and Q divided by the number of moles con [11]. Details of the construction and operation have b een tained in the so lution is the enthalpy of dilution from m, to described by Fagley [12] and Kasner [13]. m2, II ¢J d llm'!2. The derivative of¢JL with respect to m'!2 is All of the chemicals used in this study were purchased 5, which can be obtained from a "chord-area" plot [15, 16]. from Baker Chemical Company) as "Chemically Pure The experimental data are given in tables 1,2 and 3 and in Analyzed Reagents." Relatively concentrated stock solu figures 1 and 2, where, for sulfuric acid, we also show the tions were pre pared and were analyzed by standard meth data of Groenier [7], of Lange et al. [5], and of Giauque et ods. The two acids were analyzed by titration with sodium al. [6] . In order to calculate ¢J L at a given molality using the hydroxide which had been standardized with potassium relationship acid phthalate using phenolphthalein as an end-point in dicator. The hydrochloric acid and the lithium chloride were analyzed gravimetrically by precipitation as silver (1 ) chloride. Sulfuric acid was also analyzed by measurement of o its density and comparison with data given in the Interna tional Critical Tables [14]. Duplicate analyses and analyses it is necessary to provide some form of extrapolation to zero with different methods agreed to within 0.1 percent (for all molality to aid in the integration of the chord-area plot. For stock solutions). All stock solutions were further diluted by HCl and LiCI, we have used th e Debye-Huckel limiting law mass to the various molalities necessary for each experi (DHLL) value of S° of 477 cal, moj-'!2 kg' /2 [16]. ment. Some of the solutions produced during the dilution For H2 S04 the situation is more complex and warrants experiments were subjected to additional tests of analytical additional discussion. From Debye-Huckel theory, S° for a accuracy. 2-1 electrolyte is 2480 cal, mol-312 . kg" 2 [2] . In order to join The laboratory's distilled water was further purified be this value with the experimental data in figure la, we con fore use by redistillation with al kaline permanganate in a sider one mole of H2 S04 to be a mixture of a moles of block-tin still [13]. The specific conductance of all water H · H · S04 and (I-a) moles of H· HS04, where the dot be used was lower than 10-6 ohm- ' . cm- '. tween the symbols indicates the dissociation which has oc curred. The relative apparent molal enthalpy of sulfuric The temperature sensitivity of the differen tial calorim· eter was about 2 f../K, which corresponds to an uncertainty in acid will be the heat measurement of 1.5 mcal. At a molality of 0.001 ¢J L (H 2 S0 4 ) = a¢J L(H· S04) 'l mol , kg- ', the heat liberated on dilution of sulfuric acid was H· + about 50 meal with a corresponding uncertainty of 3 per· (l-a)¢JL(H ' HS0 4 ) + (l-a)~, ,, + .ll",H (2) cent. For lower molalities, the heat liberated would have decreased, thus magnifying the relative error. Therefore, a has been evaluated by Young and Blatz [2] from Raman the heat of dilution at 0.001 mol, kg- ' was about the limit spectral data; we have taken the enthalpy of di ssociation of that this could be measured using the then existing instru bi sulfate ion at infinite dilution (~i'S) as 5200 cal , mol-' mentation. [1]; we have estimated ¢J L for (H' H· S04) from the ¢J L data
The temperature sensitivity of the less sensitive calorim for Li 2S04 [1]; we have used an average ¢J L for HCl and LiCl eter was about 20 f../K, which co rresponded to a sensitivity in obtained in this investigation (see tables 6 and 7 and refer the heat measurement of 15 mcal. Thus, for the enthalpy of ence [17]) in estimating a value of ¢J L for (H' HS04 ) ; and we have taken the enthalpy of mixing of the ions (1l."H) to be J Ce rtai n commerc ia l mate ri als arc id entifie d in th is paper in o rder to a deq uate ly specify th e ex zero [10]. The results of our semi-theoretical calculations periment al procedures. S uc h identificatio n does not imply recomme ndati o n o r e ndo rse ment by the Na tio nal Bureau of Sta nda rds. for ¢J L and 5 for H 2 S04 are shown in table 4; the theoretical
12 2 TABL E I. Experirnental dilution enthalpiesfor aqueous H2S04 at 25°C. cu rve is the so lid curve from zero to 0.30 mol" • kg- I12 show n in figure lao Since this sem i-theo retical curve, base d MiDi! upo n th e above auxiliary information and ass umptions, is 112 1/2 I1rn 1/2 rnl rn2 MiDi! seen to be in good agreement with th e experimental data moll12 . kg- l12 mo1 1/2 . kg- l12 cal· morl cal· mOr312 . kg 1/2 from 0.04 to 0.30 moll i2 . kg-I12, we feel reasonably co nfi· 0.031705 0.030 134 -52.85 33649 dent in relying upon it in the low molality region 10 perform .0332 14 .03 1637a -50.71 32 170 the integration of the chord·area plot in obtaining
.040484 .038529 -66.6 1 34074 for H2 S0 4 • .041051 .039057 - 65.49 32841 .056369 .053568 -83.86 29932 .056548 .053796 - 78.62 28559 TABLE 3. Experirnental dilution enthalpies fo r aqueous LiCI at 25°C. .095864 .09 1232 -93.33 20150 .100000 .095259 -93.38 19698 .21840 .20680 - 83.67 7207.5 ~D i l 11 2 112 .25 180a .23839 -77.97 5814.8 rnl m2 IlHDil lJ.rn l 12 .25180 .23875 -73.08 5602.5 moll12 . kg- I 12 moll12 . kg- 1I2 cal· marl cal. mol - 3 /2. kgll2 .37394 .35398 -61.78 3094.8 .37900 .35948 -58.88 30 17.3 0.50658 0.16218' - 112.95 327.96 .37900 .35989 -57.97 3035.0 .53508 .50658 - 8.3 10 291.57 .38659 .36672 -57.35 2886. 1 .80307 .75627 -12.764 272.75 .42253 .40030 - 53.42 2403.3 1.0000 .94600 - 15.745 291.57 .42253 .40145 - 50.40 2390.4 1.2898 1. 2165 - 16.237 358.04 .473 11 .44907 -48.02 1997.7 1. 3381 1.2568 - 28.573 35 1.62 .47311 .44985 -45.78 1967.9 1.4394 1.3475 - 34.947 380.3 1 .50564 .48041 - 44.78 1774.5 1. 97 16 1. 86 14 - 64.330 583.81 .62997 .59868 -35.60 11 37.9 2.5982 2.4359 -148.75 9 16.59b .7 1542 .68034 -3 1. 73 904.7 a Typograp hi cal error in th e thesis [1 8]. 1. 0934 1.0328 - 35.26 581.6 b This po int is not shown in figur e 2. 1. 0934 1.0349 -34.04 581.8 2.5344 2.3640 -352.88 2071.6 a Numbers follow ed by an (a) indicate correcti ons for typographi cal er· rors in th e thesis [18]. TAB LE 4. Calculated values of"'L and Sfor H 2S04 at 25°C.
( a m l !2 , 1,ln/2 13 30000 20000 + 10000 DHLL 0.1 0.2 0.3 0.4 0.5 (1 a) 2000 1500 J 1000 Ie I 500 ;,~ o ~ ____ ~ ____ ~ ______~ ____ ~ ____ ~ ____ ~~ ____ ~ ____ ~ ____ ~ o 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 (1 b) <;;' I FIGURES la and lb. Plots 0/5 (cal' mot'12· kg "') as a/unction 0/ ml !2 (mol l !2. kg-I 12)/or aqueous H,50. at 25°C. + indicates the experimental data of Ihis investigation, .... indicates th e results of Croenier [7], -+- indicates the results of Lange, Ma nh eim , and Robinson [5J and ..... indicates the results of Giauque el ai. [6J. The solid curve from zero to 0.3 mol- Ill. kg-Ill was calculated semi-theore tically using equation 2 and the rest of the curve was drawn in accordance ....· jlh the chord-area principle [IS, \6). For each of the long-chords th ere are two points: one indicates the ce nter of the chord and the other is corrected for curvature [16}, i.c. the true derivative (d¢l./dm 112 is not equal to A 14 ------ 600 -I 550 i 500 Hel -+- 450 + +/ 400 +~+ -+- ++ / 350 -+- 300 ...., .... ~ "" -+- / 0 0.5 1.0 1.5 2.0 FIG URE 2. Plots 0/5 (cal mot-,n. kg "') as a/unction 0/ m'n (mol' n. kg- OI')/or aqueous Hel and LiC! at 25°C. Th e data for He ] arc indica ted by +, while that fo r Liel arc indicated by ...... Tables 5, 6 and 7 give valu es of (4) It is interesting to note that our values of and £,jor aqueo us H,S04 at 25°C TABLE 6. Values oj¢J[> L" and L,for aqueous HCI at 25°C. - - - ml/2 ¢JL L. L, m l/2 ¢JL L, L, mo l' 12. kg- 1I2 cal· mar' cal 'mor' cal'mol-' 0101'12. kg- ' 12 cal'mor' cal 'mol-' cal · mol-' 0.005 40 69.5 -0.00001 0.1 45.53 67.01 -0.0039 .01 120 215.5 -.00017 .2 87.30 127.9 -.0292 .02 370 663.0 -.0021 .3 127.1 185.6 -.0949 .03 680 1173.5 -.0080 .4 165.7 242.2 -.2201 .04 101 5 1676.0 -.0190 .5 203.8 299.1 -.4290 .05 1340 2120.0 -.0351 .6 242.3 353.6 -.7545 .06 1640 2498 - .0557 .7 281.7 422.0 -1.238 .07 1910 2822 - .0805 .8 322.6 489.6 - 1.925 .08 2160 3104 -.1088 .9 365.4 562.6 -2.877 .09 2380 3336 -.1395 1.0 410.6 643.0 -4.187 .10 2585 3540 -.1721 l.l 458.6 732.1 -5.961 .12 2935 3874 -.2436 1.2 510.3 831.5 -8.334 .14 3220 4120 - .3176 .16 3450 4310 -.3966 .18 3650 4469 -.4781 .20 3820 4605 -.5657 .22 3965 4708 -.6475 .24 4090 4800 -.7366 .26 4200 4879 -.8265 .28 4300 4850 -.9180 .30 4370 4990 -1 .0004 .35 4550 5100 -1.214 TABLE 7. Values oj¢>vL., aTld L,joraqueous LiO at 25°C. .40 4690 5184 - 1.424 .45 4801 5250 -1.535 m I l2a ¢JL L, £, .50 4892 5303 -1.852 0101'12. kg-'12 cal'mor' cal· mol-' cal 'mor' .55 4969 5345 -2.060 .60 5031 5382 -2.276 0.1 44.80 65.75 -0.00377 .65 5086 5415 -2.499 .2 84.37 121.6 -.02684 .70 5133 5446 -2.766 .3 119.9 162.6 - .08216 .75 5175 5475 -3.040 .4 152.4 214.9 -.1801 .80 52 14 5506 -3.367 .5 182.7 256.4 -.33 17 .85 5249 5547 -3.756 .6 211.6 296.5 - .5506 .90 5282 5566 -4.149 .7 239.6 336.4 -.8546 .95 53 12 5598 -4.650 .8 267.2 377.4 -1.2710 1. 00 5342 5634 -5.262 .9 295.0 421.5 - 1.845 1.10 5400 57 19 -6.954 1.0 323.7 469.7 -2.630 1.20 5460 5822 -9.401 l.l 353.6 522.5 -3.681 1.30 5522 5942 - 12.79 1.2 385.3 581.5 -5.090 1.40 5589 6086 -17.55 1.3 419.3 648.4 -6.974 1. 50 5665 6273 -24.63 1.4 456.1 723.9 -9.457 1.60 5752 6500 -34.50 1.5 496.0 808.8 - 12.667 1.70 5852 6762 -47.36 1.6 539.7 904.3 - 16.8 17 1.80 5967 7056 -63.56 1.7 587.3 1009.8 -21.995 1.90 6095 7377 -83.41 1.8 639.1 1123.5 -28.274 2.00 6237 7737 -108.1 1.9 695.0 1246.6 -35.872 2.20 6567 8536 - 171.7 2.0 755.2 1378.6 -44.924 2.40 6958 9366 -250.9 " We note that while the experimental data extend to 2.60101'12. kg- I12 , 2.60 7368 10196 -344.4 we have chosen to terminate this table at 2.0 mol"2 . kg- 1I2 rather than rely 3.00 8267 11695 -555.6 on on ly one measurement at 2.6 mol' /2. kg-' 12. 16 5. References [8] Pitzer, K. 5 ., Roy, R. N. and Sil vester, L. F., J. Am . Ch em. Soc. 99, 4930 (1977). [9] Young, T. F. and Smith, B., J. Am. Ch em. Soc. 58, 716 (1954). [ !O] Young, T. F., Wu, Y. C. and Karwetz, A. A. , Disc. Faraday Soc. No. [I] Harned, H. S. and Owen, B. B. , Th e Physical Chemistry oj Elec tro 24,37 (1 957). lytic Solutions, 3 rd ed., Reinhold Publishing Co., New York, 1958. [I I] Lan ge, E.and Robin son , A. L., Ch ern. Rev. 9, 89(193 1). [2] Yo ung, T. F. and Bl atz, L. A., Ch ern. Rev., 44 , 93 (1949). [1 2] Fagley, T . F., Ph.D. Thes is, Uni versit y of Chicago (1949); performed [3] Wagman, D. D. , Evans, W. H. , Parker, V. B., Halow, I., Bail ey , S. M. under th e di rection of Professor T. F. Young. and Schumm, R., Selec ted Values of Chemical Thermodynamic [1 3] Ka sner, F., Ph .D. Thesis, Uni ve rsity of Chi cago (196 1); perfo rmed Properties, Nat. Bur. Stand. (U.S.), Tech. Note 270-3,273 pages under th e directi on of Professo r T. F. Young. (Jan. 1968). [1 4] (nternational Critical Tables oj Num erical Data, Ph ysics, Chemis try, [4] Smith·Magowan, D. S. and Goldberg, R. N., A Bibliography of and Technology, Vo !' III, p. 56, E. W. Washburn, editor-in chief, So urces of Experimental Data Leading to Thermal Properties of McGraw-Hill Boo k Co., In c., New York (1930). Binary Aqueous Electrolyte So lutions, Nat. Bur. Stand. (U.S.), Spec. [1 5] Young, T. F. and Vogel, O. G., J . Am. Chern. Soc., 54, 3030 (1 932). Pub!. 537, 89 pages (March 1979). [1 6] Young, T. F. and Groeni er, W. L. , 1. Am. Chem. Soc., 58, 187 (1936). [5] Lange, E., Monheim, J. and Robinson, A. L., J. Am. Ch em. Soc., 55, [1 7] Parker, V. B., Thermal Pro perties of Aqu eo us Un i-un ivalent El ec tro- 4733 (1933). lytes, Nat. Stand. Ref. Data Ser., Nat. Bur. Stand . (U .S.) 2,7 1 pages [6] Giauque, W. F., Hornung, E. W., Knuzler, J . E. and Ru bin, T. R., (Apr. 1965). J . Am. Ch em. Soc. 82, 62 (1960). [1 8] Wu, Y. C., Ph .D. Thes is, University of Chicago, Chi cago , Illi nois [7] Groeni er, W. L. , Ph.D. Thes is, Universit y of Chicago (1 936); per (1957). formed under the directi o n of Professor T . F. Yo ung. [1 9] Wu, Y. C. a nd Friedman, H. L., J . Phys. Chern . 70, 166 (1966). I ( 17