THERMODYNAMIC PROPERTIES OF HYDROCHLORIC ACID
Oct., 19GO
1445
ELECTROMOTIVE FORCE MEA4SUREMENTSIN AQUEOUS SOLUTIONS AT ELEVATED TEMPERATURES. 11. THERMODYNAMIC PROPERTIES OF HYDROCHLORIC ACID' EIY R. 3. GREELEY,~ WILLI.4M T. SMITH, JR.,M. H. LIETZKEAND R. W. STOUGHTON Cl~emistryDivision, Oak Ridge National Laboratory, Oak Ridge, Tennessee and the Departrnmt of Chemistry, University of Tennessee, Knoxville, Tennessee Received March 28, 1960
The mean ionic aztivity coefficient, relative partial molal heat content, relative partial molal heat capacity, and osmotic coefficient of hydrochloric acid have been ocalculated from e.m.f. data for concentrations from 0.001 to 1.0 m a t temperatures The extended Debye-Huckel equation was shown to represent the data about from 25 to 200' anc, in some cases to 275 as well at temperatiires to 275' as at room temperature.
.
Introduction The thermodynamic properties of dilute aqueous hydrochloric acid solutions have been obtained from electromotive force measurements from 0 to 60' by Harned 2nd Ehlers3" and from 0 to 95' by Bates and B o w w . ~ With ~ the increasing use of aqueous solutions a t higher temperatures, it was of interest to extend the measurements on hydrochloric acid to as high tt temperature as possible. A previous communic:~tion*described the measurements of the electromotive force of the cell Pt-Hz(p) IHCl(m)I AgC1-Ag
and the evaluation of the standard potential of the silver-silver chloride electrode to 275'. The present paper presents the properties of hydrochloric acid derived from those measurements. Experimental The previous paper4 gives the experimental details used to obtain all of the data presented here. A high speed digital computer was uscd to perform the involved calculations and least squares, procedures.6
Calculations and Dismssion Mean Ionic Activity Coefficient of HC1.-As noted in the first paper in this ~ e r i e sthe , ~ mean ionic activity coefficient of hydrochloric acid was expressed using an extended form of the DebyeHuckel equation
where S = limit,ing slope, po = density of wat,er, I = ionic strength of solution, A = denominator coefficient = 50.29(DT)-'/2 8, d = ion size parameter, Ext := conversion from rational t>opractical scale plus extended terms of Gronwall, LaMer and Sandved,G B = linear term coefficient, and the , , = higher ierms if desired ( i e . ) DP,etc.). At HC1
.
(1) This pailer is based upon work performed for the United States Atomic Energy Cornmission a t the Oak Ridge National Laboratory operatrd by Union Carbide Corporation. (2) This paper is baried in part on a thesis by R. S. Greelcy presented t o the Department of Chemistry of the University of Tennessee in partial fulfillment of the requirements for the Ph.D. degree. June, 1959. (3) (a) €I. S.Ilarned and R. W. Ehlera, J . Am. Chem. Soc., 55, 2179 (1933). (b) It. G. Rates and V. E. Bower, J . Research Natl. Bur. Standards, 63, 283 (19,54). (4) R. S. Gieeley, et al., THISJOFRNAL,64, G52 (1900). (5) M. H. Lietzke, "An ORACLE Code for Least Squares," Oak Ridge Nationnl Laboratory Publication ORNI, CF-59-2-20. February 4 , 1858.
(6) T. H. Gronwall, 358 (1928).
V. K. LaMer and K. Sandved. P h y s i k . Z.,29,
concentrations from 0.005 to 0.1 m only the linear term BI (in addition to the first two terms on the right hand side) was included in equation 1 and the values of it and B were determined a t each temperature from the e.m.f. data for those solutions by varying it until the standard error of fit was minimized for the least squares fit of
Values of the mean ionic activity coefficient of hydrochloric acid (saturated with silver chloride) a t concentrations from 0.001 to 0.1 m and a t temperatures from 25 to 275' were calculated from equation 1 using these values of it and B and are listed in Table I. The values of d and B were given in the previous paper.4 I n these calculations the solubility of the AgCl was added to the molality of HC1 to give the concentration of chloride ion, it being assumed that both electrolytes were completely dissociated. The -4gC1 solubility was known a t various HC1 concentrations as a function of temperature to 200' and ranged from 0.001 to 0.002 m a t this The extended Debye-Huckel equation with the BI term was found to be applicable a t all temperatures for the concentration range 0.005 to 0.1 m HC1. Straight lines were obtained for E'" us. I that were within the limits of experimental error (f0.4 mv.) and which permitted extrapolation to infinite dilution. However, the value of the ionsize parameter, d, inqeased markedly with temperature becoming 11 A. at 200' and 20 A. a t 275'. In contrast, when fitting the data for the entire concentration range 0.005 to 1.0 m HC1 a t 25 to 200' and using either a BI term only or both BI DP terms in the extended Debye-Huckel equation and in equation 2, the minimum standard error cf fit was obtained when CE was constant a t 4 =t 1 A. The standard errors of fit were slightly smaller if the quadratic term were included. At 225, 250 and 275' use of the D parameter was necessary and a value d = 4 A. gave the best fit of the data. Interestingly enough, Bates and Bower3 found that it increased from 4.3 to 6.0 in fitting their data a t 25 and 60' over the concentration range 0.001 to 0.1 m; whereas Harned and Ehlers3" found d increased only from 4.22 to 4.40 in going from 25 to 60' over the concentration range 0.1 to 1.0 m. Lietzkc 2nd
+
(7) R. J. Raridon. Ph.D. Thesis, Vanderbilt U n h e n i t y , S a s h \ ill? Tenn.. 1958, p. 93.
1446
\-01.
PfEAN
m
250
0.001 002 ,005 ,0075 01 02
0.9655 ,9522 ,9284 ,9149
021i 05 076 I 2
.810!! ,7972 -, ,b32 75-10 8061
0
1 0
TABLE I IONIC ACTIVITYCOEFFICIENT O F HYDROCHLORIC 4CID, 900
125O
150'
1m I 5- 0
2000
0.963 ,949 ,924 ,910 899 868 857 ,819 ,795 ,776
0.960 ,946 ,920 ,905 ,893 ,861
0.955 ,940
0.949 .934 ,906
,849
837 ,794 .765 ,744
,746
,722 ,692 ,713
0.939 ,926 ,898 .882 ,869 ,833 ,819 ,772 ,739 .714 ,647 ,591 ,560
0.925 ,915 ,859 .862 .860 ,824 810 i60 ,724 .694 ,618 ,554 ,514
GOO
9044 8754 8650 8310
.912 .896
,807 .i80 ,758
.728 ,762
,889
,876 ,840 826 ,779 ,746 ,720 ,670
,884 ,849
.694
655 ,653
,621
,608
Stoughton8 also found that the A (and hence d ) parameter for the hgzSO4 activity coefficient and the HS04- acid quotient in sulfate media were essentially temperature independent to over 200' for the ionic strength range 0.1 to 3.0. On the other hand, differences in the value of d are compensated to a certain extent by changes in the value of B so that, as was found here, the value of y i changes little whichever fit is chosen to represent the data. For instance, at 200' the value of y h a t m = 0.1 for d = 7 and B = -0.422 was 0.694 and for 6 = 4 and B = 0.0787 was 0.675. This diflerenoe is only 2.8Oj, which is essentially within the experimental error a t that temperature. Values of d , B and D were determined at each temperature using the e.m.f. data for solutions 0.005 to 1.0 l?i a t 200' and 0.01 to 0.5 m a t 225, 250 and 275', From these values of y f for solutions 0.2, 0.5 and 1.0 were calculated using equation 1 and are listed in 'Table I. In Table I1 are listed the values of 6, B, D. their standard errors and the standard errors of fit as determined above.
+
TABLE 11 D FROM LEASTSQUARES FITOF EO" = EO - 4.606RT -___ (BI 012)
V A L U ~OF S 8, B
ASD
+
3
Temp O C . ', 25 60
90 125 150 175
200 225 2.50 275
6, A. 4 3 1 1 s.3 1 1 1.3 1 1.0 f 1 &.O f 1 .1.0 It 1 '1.0 1 1 ,L.O f 1 4.0 i 1 4 0 * 1
B . m-1 + O . 130
+
.124
+
,101 ,112 .0960
* + + $+ -
+
,0945 ,0787 .os40 ,410
,129
Ufit,
OB
D,m-2
UD
0.0059 .0091 .0073 .0086
$0.0026 - .0024
0.0060 ,0090 ,0072 ,0085 ,0079 ,0081 ,0143 ,0403 .23A ,304
.0080 .0083 ,0150 ,0230 ,139 ,190
64
+
,0056
- ,0134 - .0109 - ,0245
-
,0222 ,443 +1.09 +O.lFQ
+
mv. 0.25 .38 .33 .43 .45 .50 .81 .46
3.09 3.83
The logarithm of the activity coefficients for several of the ccmcentrations listed in Table I were fitted over the temperature range 25 to 200' by the method of least squares t o a quadratic function of the cmtrigrade temperature. The constants of these equations and the standard errors of fit are listed in Table 111. The values of y f and log y h decrease regularly TT-ith temperature a t each molality from 25 to about 225'. I n fact, the change with temperature of y f ( 8 ) A I T LwtzLe and R. W. Stoughton, T r m 1186, 1188, I l u i ) . 1118-1119.59) 6 4 , 133 (1900)
~ O V R V A L ,63, 1183,
225O
27.5'
0.904 ,898 ,875 .859 .846 808 793 738 698 ,663 572, ( .5i2)
0 85 85 84 83 82 76
-( 1
71 66 .62 54 ( 53)
TABLE I11 CONSTAKTS OF QUADRATIC EQUATIONS EXPRESSIP~G LOG-,i HC1
concn., m 0 005
01 02
.05 .075 .1 2 5 1 0
-3 -4 -5
-7 -8 -9 -1
-1 -7
As A FIKCTION OF TEMPERUWRE 5
165 X 202 X 499 X 558 X 501 X 136 X 072 X 084 X 682 X
Constant."----b 10-2 -1 854 X 10-6 10-2 - 5 125 X 10-7 10-2 - 9 286 X 10-6 10-2 - 1 765 X 10-4 10-2 - 2 362 X 10-4 l o - ? - 2 914 X 10-6 10-1 - 3 508 X 10-4 10-1 - 4 F7b X 10-4 10-2 - 6 007 X 10-4
* Constants in the equation log
(1
- 3 870 X - 3 087 X - 2 755 X - 2 143 X - 2 065 X - 2 076 X -5 093 X - 9 513 X - 1 874 X y i=a bf
+
-
Sfit
lo-' 0 0001 10 7 0002 10-7 0005 10-7 0010 10-7 0015 10-7 0026 10-i 0031 10.0038 10-6 0013 -Irt*
a t 0.05 to 1.0 771 is almost linear from 60 to 200'. Above 225' the activity coefficients decrease more rapidly and then betneen 250 and 275' they hegin to increase for concentrations greater than 0.01 m. Since the main temperature-dependent factor in the expression for log y A , a t least at the lower concentrations, derives from the DT product term in the limiting slope, this behavior is understandable. Since, as was shown in the previous paper,4 the e.m.f. data were in reasonable agreement with the data of Harned and Ehlers3" and of Bates and Bower3hat 25, 60 and 90", the activity coefficients are also in agreement with their vnlues. I n order to obtain values of the activity coefficients at higher temperatures for comparison with this study, the extended equation of Harned and Ehlersg was solved a t appropriate temperatures arid concentrations. .Igreement with yalues in Table I was uithin 1y0a t all concentrations to 200'. The mean ionic activity coefficients of hydrochloric acid listed in Table I are stoichiometric activity coefficients based on the assumption that the HC1 was saturated with AgCl and that both nere completely ionized. Since complexes involving species such as -4gCL- are known to exist in HC1 solutionslo and since some undissociated HC1 may be present in solution at the higher temperatures and concentrations, l 1 the activity coefficientc; of the actual species involved are not knon-n. (9) E q u ~ t i o n13 of ref 3s ma5 used n i t h d = 4 3 .%eucept B was set equal to 0.1390-0 00467 t , I) was set equal to 0 0070-0 000032t, a n d t h e extended terms Z of Gronaall, et al., n e r e omitted. (10) J. H. Jonte and D. S. Martin, J r , J . Am. Chem. Soc., 74, 2052 (1952), A I . H Lietzke and R. W Stoughton, abad , 79, 2067 (1957). (11) Roughly0 274 of t h e total HCI In thpsysterii mas present in t h e \ m o r s p a r e nhoir 0 01 i n i i 0 I 7n HCI at 200 t o L i 1" + e ref. 4
THERMODYNAMIC PROPERTIES OF HYDROCHLORIC Ak~u
Oct., 1960
Relative Partial Molal Heat Content and Heat relative partial molal heat content Lz and heat capacity JZare given by
Capacity,-The
=
J2 = (-$)m,p aZ
--9.212RT
(bTT-)m,p log
yic
The change in the logarithm of the mean ionic activity coefficient of hydrochloric acid with temperature from 25 to 200° was determined by taking the first derivative of the quadratic equations the coefficients of which are given in Table 111. The change of .og y . t with pressure was neglected. Then values of L z were calculated by using equation 3 and 1hese are listed in Table IV. Values of J z calculated from the first and second derivatives of the quadratic equations, the coefficients of which are given in Table I11 are listed in Table V. T.4BI.F:
IT’
rr9LITRS O F THE ILELATIT-E PARTIAL MOLA4L HF:4T C O N T E N T OF
HYDROCIILORIC ACID
-____
_-L2
(c31.)-
Temp., “C.
0.005 m
0.03 m
0.1 m
0.2 m
0.5 m
25 GO 90 125 150 175 “00
30 8 GG 0 1Oi 167 221 2883 335
15%
246 321 397 498 580 669 767
306 418 534 693 825 9 72 1140
416 587 767 1020 1230 1470 I 730
T’9LUES O F THE
Temp., O C .
25
en
205 260 33-1. 395 462 L47
1.0 m
565 839 1130 1550 1900 2310 2770
T ~ B LVE RELATIVE PARTIAL hIOLAL HEATCAPACITY OF HYDROCHLORIC ACID
---O.OO!i m
0.83 I.:? 1.5 2.0 2 3
-
-
-Jz (ca1Jdegcee)0.01 ?n 0.05 m 0.1 m 0.2 m
0.90 1.2 1.5 1.9 2.2 2.6
1.4 1.7 2.0 2.3 2.6 2 8
2.9
.‘3.2
2.0 2.4 2.7 3.1 3.4 3.8 4.1
2.9 3.6 4.2 5.0 5.6 6.2 G.9
0.5 m
1.0 m
4.3 5.5 6.5 7.9 8.9 10.0 11.2
6.8 8.8 10.8 13.2 15.1 17.2 19.4
1447
72 = 46,12O(c - c0)T cal./degree it?) Although the e.m.f. data of the present investigation could not be fitted to a quadratic within experimental error, the temperature variation of the e.m.f. being more complex, the approximate equation 5 and values of c - co reported by Harned and Owen’l were used to estimate JZ at 200’. Values of 1.7, 2.4, 4.8, 6.1, 7.4, 9.4 and 12.7 cal./deg. were obtained for 0.005, 0.01, 0.05, 0.1, 0.2, 0.5 and 1.0 m, respectively, which values may be compared with those in Table V. The agreement is satisfactory considering the approximations made. NO attempt was made to estimate the first and second derivatives of log y f at temperatures above 200’ since the data were less precise. It is interesting that the and J , values at elevated temperatures when plotted as functions of the square root of I show deviations from the limiting slope on the high side at low concentrations and vice versa in a manner similar to that observed in dioxane-water mixtures12 a t comparable values of the dielectric constant. This behavior indicates that the dielectric constant or the DT product is perhaps more important than the exact nature or temperature (per se) of the solvent in causing such deviations. Osmotic Coefficients.-The osmotic coefficient of a strong electrolyte is related to the activity coefficient by
zz
d
= 1
+
m d In
If the mean ionic activity coefficient of the electrolyte is expressed by the extended Debye-Huckel equation using both a linear and a quadratic term, equation 6 can be integrated13yielding [(i A ~ I
@ = I - - ‘‘
+A
~ - 2 IIn ( 1
+ ~ . \ / -i )
Reasonable agreement for the partial molal heat contents and heat capacities with the values of Harned and Ehlers3” and of Bates and Bower3bwas obtained a t 25, 60 and 90’. Since these quantities were obtaked by fitting log y . t over the range 25 to 200°, support is lent to the accuracy of the values at temperatures above 90’. The part;al molal heat content and heat capacity FJ2 at each molality increase steadily with temperature. Harncd and Owenl2 report that, since the E’ values and the e.m.f. values of Harned and Ehlers at each molality fit a quadratic function of the centigrade temperature, the relative partial molal heat capacity must vary with temperature directly with the difference between the coefficients of the quadratic terms, c - CO.
The extended Debye-Huckel equation used in this derivation did not contain the term Est shown in equation 1, since this term was small (being comparable to the experimental error) and since the extended equation with the adjustable parameters -4,B (and D) in general fits activity coefficient data equally well without it. In order to check equation 7, the A , B and D values of an extended Debye-Huckel equation were obtained by a non-linear least squares method from the activity coefficients of several of the alkali halides at 25’ using the data listed by Robinson and Stokes14a t 0.1 to 3.5 m. The osmotic coefficients of each alkali halide were then calculated by equation 7 using the derived A , B and D values. Conversely, the A , B and D values of equation 7 were obtained by a non-linear least squares method from the osmotic coefficients of the alkali halides at 25’ listed by Robinson and Stokes,13and the activity coefficients then calculated from the extended Debye-Huckel equation. It was found that in each case, the calculated coefficients agreed with those listed to within about 0.003 of a unit. Further, the
(12) H S. Hsrned and B B. Owen, “The Physical Chemistry of Electrolytic Solntions,” Third Edition, Reinhold Puhl Corp , Piew York. N. Y., 1958, p 476.
(13) G. Soatohard, private communication. (14) R. -4. Robinson and R. H. Stokes, “Electrolyte Solutions,’ Academic Press, Ino., h’ew York, h’. Y., 1955. p . 468.
YO 135 150 175 200
2.’7 3 I
1448
F. J. KELLY,REGINALD MILLSAND JEAN M. STOKES
Vol. 64
acid obtained are listed in Table VI. It is found that agreement between the osmotic coefficients HYDROCHLORIC determined at 25O and the values listed by RobinACID son and Stokes13 is within 1% over the range 0.1 ZOOo 90' 125' 250° 275' m 25' 60' to 1.0 m. 0.01 0.969 0.967 0.965 0.961 0.951 0.94 0.94 .88 .90 .05 .950 .946 .941 .933 .916 The osmotic coefficients of HCl from 0.01 to 1.0 .I .945 .939 .933 .923 .901 .85 .89 m regularly but slowly decrease with increasing .941 .932 .920 .892 .2 .948 .84 .89 temperature from 25 to 200'. As with the activity .5 ,981 .9?0 ,956 .939 .896 (I .O) ( .98) coefficients, the osmotic coefficients then decrease .983 ,912 (2.0) (1.3) 1.0 1.05 1.03 1.02 more sharply from 200 to 250' and finally increase calculated and listed values still showed close again a t 275'. At higher concentrations the osagreement when the calculations were extended to motic coefficient values are much less precise since values of m below or above (to about m = 4.5) greater weight in equation 7 is put on the term containing D which is known with much less accuracy those used in evaluating the parameters. Because equation 7 was found to hold so well for than A or B. calculating osmotic coefficients of alkali halides Acknowledgment.-The authors wish to express from activity coefficient data a t room temperature, their sincere appreciation to Nr. Gerald North it was felt worthwhile to use it for such calculations for taking much of the e.m.f. data, to Mrs. Laura for HC1 a t various temperatures. The values of B Meers for helping with many of the calculations, and D used are those shown in Table 11. The and to Mr. Raymond Jensen for hand checking values of the osmotic coefficients of hydrochloric some of the compiiter calculations. TABLE VI
VALUES OF THE OSMOTIC COEFFICIENTS O F
SOME TRASSPORT PROPERTIES OF AQUEOUS PENTAERYTHRITOL SOLUTIONS A T 95' BY F. J. KELLY,REGINALD MILLSAND JEAN 31. STOKES School of Phusical Sciences, Australian Rational Uniaersity, Canberra, Australia, and the Physical Chemistry Department Universzty of New England, Armidale, N.S.W. Australia Received March 82, 1960
The following properties of aqueous pentaerythritol solutions are measured and discussed: viscosity and density, diffusion coefficient and self-diffusion coefficient, and the limiting conductance of sodium and potassium chlorides in the solution.
Introduction The transport properties of the pentaerythritol molecule, C(CHZOH)(, are of interest because of its high symmetry. Being moderately soluble in water, it is suitable for comparison of properties of non-electrolytes with those of ions in solution. The studies now reported were undertaken to provide data needed in the interpretation of diffusion measurements in the ternary system sodium chloride-pentaerythritol-iyater, n-hich are a t present in progress. Materials.-Pentaerythritol for all measurements except those of self-diffusion was prepnrcd by repeated recrystallization of good commercial material; the measured properties \yere unaffected by the later recr3rstallizatioiis, and a further check of purity is provided by the excellent agreement between the limiting mutual diffusion coefficient of this material and the limiting self-diffusion coefficient obtained with material purified in a different way. For the self-diffusion measurements (R.M.) the inert material was prepared by repeated vacuum sublimations of commercial pentaerythritol of 95-99% purity' (n1.p. 256") to give a purified product of m.p. 260-261 '. Radioactive pentaerythritol labelled with 14C was synthesized from 14C-paraformaldehyde,2 using the classical (1) From Light & Co., Colnbrook, England. (2) From t h e Radiochemical Centre, Amersham, England.
synthesis by condensation of paraformaldehyde with acetaldehyde in the presence of calcium h y d r ~ x i d e . ~In order to keep the specific activity of the synthesized compound as high as practicable, the active starting material was diluted with about one gram of inactive paraformaldehyde. The other reactants were then added in the same proportions as in the above method. The product was purified by repeated cryst,allizations followed by vacuum sublimations, to give labelled pentaerythritol of m.p. 256". Further purifications involving niore recrystallizations would have resulted in considerable loss of active material. To check that the compound was sufficiently pure, some runs were made with a specimen melting a t 252'. Within experimental error, there was no detectable difference in diffusion rate; it thus seems that any impurities present have a negligible effect. Potassium and sodium chlorides used in the diaphragm-cell calibrations and the conductance measurements were of analytical reagent quality, dried a t 400". Conductance water a t equilibrium Tyith the atmosphere was used for all solutions; its specific conductance was -1 x ohm-' cm. -l. All data in this paper refer to 25". (3) H. Gilman and A. H. Blatt, "Organic Syntheses," COIL Vot. 2nd Edition. John Wiley and Sons, Inc., Kew York, N. Y.
