the present paper, with the calculated values for AA4 by each method. Only in the case of the association energy for -kg-SO, is the energy small enough that the two approaches give approximately
the same value. The study in molten sulfates was a t a much higher temperature, TOO", but this is not enough. Temperatures much above these, as used by Flood in his applications to slags, make the simpler theory applicable.
THE ENTHALPY AND EPI'TROPY OF DILUTIOX OF LITHIUM PERCHLORATE BY F. R. JOSES'-4ND R. H. KOOD Departnienf of Chernistrg, Uniz'ersitg of Delaware, n-ewark, Delnuiare Received 12'ovember 3,1962 The heat of dilution of lithium perchlorate in the concentration range of 4.0 to 0.01 molal has been measured s i t h a new twin calorimeter. The results have been calculated using a new method for correcting for heat leaks in the twin calorimeter. The relative apparent molal heat contents have been determined by a least squares extrapolation of the heats of dilution. The excess relative partial molal enthalpy and entropy of lithium perchlorate have been calculated from the relative apparent molal heat content and the activity coefficient. The excess relative partial molal entropy of lithium perchlorate fits the correlation of TVood a t all concentrations using the value P = 0.455 for the perchlorate ion.
Introduction The deviations of activity coefficients of electrolyte solutions from the Debye-Huckel limiting law have received considerable attenlion in the last forty years.2 However, deviations in the entropy (excess relative partial molal entropy) from the predictions of the Debye-Huckel lav have received much less attention. Frank and Robinson3a and Friedman3b have discussed the factors influencing the general trend of the entropy and, in particular, Frank and Robinson have shown that the structure of the water around an ion has a great influence on the entropy of concentrated solutions. Pitzer and Brewer4 have shown that there is a rough correlation between the heats and free energies (and thus between entropies and free energies) of the 1-1 electrolytes. The existence of this correlation means that the structural effects which influence the entropies also influence the heats and free energies. Wood6 has shown that the entropies of dilution of many 1-1 electrolytes can be correlated with a single parameter for each ioii. I n the case of the negative ions the parameter is related to the size of the ioii. The regularities present in the entropies indicate that a theoretical understanding should be less complicated for the entropies than for the free energies. The fact that there is only one parameter for each ion means that any specific interactions between the ions do not affect the entropy to any great extent. The regularity in the entropies also indicates that it is possible in some cases to predict the entropies of dilution. This should be particularly useful in correcting the entropies of formation of complex ions for the influence of the other ions present. This is often necessary because the entropies of formation often must be measured at very high ionic strengths.6 At present the correlation cannot be used to predict the entropies of dilution of com(1) Abstracted iii part from the thesis of F. Robert Jones. (2) H. S. Harned and B. B. Owen, "Electrolytic Solutions," 3rd Ed., Reinhold Publ. Corp., New York, X. Y., 1958. (3) ( a ) H. S. Frank and Robinson, J . C h e n . Phys., 8, 933 (1940): (b) H. L. Friedman, tbad., 84, 1351 (1960). (4) K. Pitaer and L. Brewer in G. N. Levis and M. Randall, "Thermodynamics," as revised by K. Pitzer and L. Brewer, McGiaw-Hill Book Co., New York, N. Y., 1961, p. 396. ( 5 ) R. H. Wood, J . Phys. Chenz., 63, 1347 (1989). (6) F. 3. C. Roasotti in J. Lewis a n d R. G. Wilkins, "Modern Coordination Chemistry, Principles and Rlethods," Interscience Publishers, New York, N. Y., 1960, y. 1.
plex ions because t'his kind of ion does not, seem to fit. the correlat'ion very well. For instance, of t.he 1-1 electrolytes which contain oxy-anions and for which data are available, only HXOs and LiSOs fit tmhecorrelat'ioii while SaNOa,KXO,, RbNOs, CsN03, NaC103, KC103i and NaC103do not fit t'he correlatioi1.7.8 Since L i S 0 3 behaves normally, it was of interest t o see if the combination of lit,hium ion with the perchlorat,e ion would also behave normally. Experimental Heats of dilution were measured in a calorimeter of the twin Joule type.g The calorimeter vessel was made from stainless steel coated with Teflon and had a capacit,y of about 1850 ml. The lid was brass coated with polyethylene. Temperature differences between the two vessels were measured with a 50 junct,ion chrome!-const.antan thermopile connected to an electronic chopper amplifier. The noise level was about 0.04 U.V. (1.3 x peak to peak. Glass pipets of 10, 25, and 50 ml. volume were used. The vessels were held in a submarine immersed in a const,ant temperature bath (constant to better than 10-3"). Electrical calibration was used in all runs. The results are expressed in terms of defined calories ( 1 cal. = 4.1840 absolute joules) , The results were corrected for the heat losses of the vessels. van der Waals and Hermanslo have described a method of making this correction when the heat leak from one vessel t o the other and the heat of stirring are negligible. A derivation of the heat leak correction for the geneml case has been made and will be published elsewhere. The over-all performance of the calorimeter was checked by measuring t,he known" heat of dilution of 0.6432 M hydrochloric acid (50 ml. diluted to 1850 ml.). The results of four measurements were 8.79, 8.69, 8.68, and 8.67 cal. while the calculated value is 8.68 cal. The lithium perchlorate %-assupplied through the courtesy of HEF, Inc.12 Analysis for sodium and potassium using a Beckman flame photometer gave 0.01% sodium and 0.0% potassium. Gravimetric analysis for heavy metal oxides as R z 0 ~gave less than 0 . 0 0 6 ~ 0R20, as FesOs. 9 4 A I solution showed no turbidity (7) Enthalpies of dilution have been taken from the following; for S a ClOa and NaC104: M. Colomina and J . Nicolas, Anales real SOC. espan. fis. quim. (Madrid), B46, 137 (1949); f o r all other salts: F. D. Rosaini, e l al., Kational Bureau of Standards Circular 500, U. S. Govt. Printing Office, Washington, D. C., 1952. (8) Activity coefficients have been taken from R. A. Robinson and R. H Stokes, "Electrolyte Solutions," ileademic Press, New York, N. Y., 195% (9) A more complete description will be published elsewhere. (10) J. H. van der Waals and J. J. Hermans, Rec. t m c . chim., 69, 949 (1950). (11) F. D. Rossini, et al., National Bureau of Standards Circular 600, "Selected Values of Chemical Thermodynamic Propertiea," U. S. Govt. Printing Office, Washington, D. C., 1952. (12) HEF, Inc., Philadelphia 44, Pa.
ENTHALPY AND ENTROPY OF DILUTION OF LITHIUMPERCIILQE ~ T E
August, 1963
1577
TABLE I CALORIMETER DATA Concn., mole/kg. water Initial Final
No. of Moles
expts.
3.981 0.09159 0.1682 2 3.981 .04570 ,08411 3 3,981 ,01616 ,02775 3 3.981 ,01643 ,03028 1 2.856 ,06864 ,1262 3 2.856 ,034126 ,06297 2 ,02082 2 2.856 ,01129 1.825 ,04570 .08412 5 ,04201 4 1.825 ,02283 2 ,01388 1 ,825 ,00753 2 ,06297 1.338 ,034-19 2 ,04201 ,02280 0.8747 ,6960 ,01825 ,03363 2 ,02523 3 ,5180 ,013869 ,3430 ,00912 ,01682 3 a The average value and the maximum deviation from the
- A H dilution,a av., cal./mole
420.7 f 0 . 2 445.9 f 1.1 469.0 f 0 . 4 469.3 304.9 f 1 . 0 326.7 f 0 . 0 354.8 f 1 . 7 221.1 f 1 . 1 238.0 f 0 . 5 263.3 f 1 . 8 188.4 f 0 . 2 159.6 f .1 151.7 f . 3 140.3 rt . 4 125.0 f 3 . 0 average are given.
on the addition of silver nitrate. The first stock solution was standardized by evaporating to constant weight a t 150" (found 3.976 and 3.974 iM)and by converting to the sulfate and evaporating to constant weight (found 3.979 and 3.978 M ) . The molality used was 3.975. The second stock solution was standardized by evaporation to constant weight at 150" (found 3.982 and 3.981 M ) . The solutions were prepared by volumetric dilution of the stock solutions. The densities of all solutions were determined a t 25' using a Westphal balance. The densities agreed with the results of Geffeken'3 and Mazzucchelli and RossiI4to within 0.1 yc. The amount of water vapor in the air space of the calorimeter changes when the salts are mixed. The maximum air space was 10 ml. for the pipets m d 110 ml. for the calorimeter vessel. Calculations showed that the correction for the heat of vaporization was less than 0.2 c d . per mole for all experiments.
Results The results of the calorimetric measurements are given in Table I. In calculating the average of the runs, the results obtained from the first stock solution were weighted by a factor of one-half because several improvements in experimental equipment and technique were made after these runs were complete. The solutions prepared from the first stock solution were 0.15% lower in concentration. The concentrations of the solutions prepared from the second stock solution were used in the calculation of the results, except that the actual number of moles was used to calculate the heat of dilution. The error introduced in this way is less than 0.1%. The measurementfi in Table I vere combined to give a series of heats of dilution in the 0.1 to 0.007 m range. The extended Debye-Huckel equation
4L
=
(--
1
+
I ad%
3
9~ final, cal./mole
99.0 75.3 47.9 49.6 88.3 67.1 42.2 75.3 56.9 35.3 67.1 56.9 51.7 45.8 38.6
QL initial, cal./mole
519.7 521.2 516.9 518.9 393.2 393.8 397.0 296.4 294.9 298.6 255.5 216 5 203.4 186.1 163 6
wt.
QL initial
factor
4.0 3.6 1.5 0.4 7.2 2.4 1.1 11.0 4.4 0.5
av.
519.8
393.7
296.1
dataandeq. 1for 4L(ml)-&,(m2). Omen and Brinbleyls and Guggenheim and PrueI6 have used similar extrapolations (without the Cma/2term) and shown that the equatioiis fit the data for sodium chloride up to 0.1 rn, The experimental points were weighted according to the estimated accuracy of the data using 0.2% f 0.03 cal. as the estimated standard deviation of single measurement. The results of the calculations which were performed with the aid of a Beiidix Gl5D digital computer are given in Table 11. Repeating the least squares fit with a = 1.6 changed the calculated values of apparent relative molal heat content by 0.15 cal./ mole or less. Repeating the extrapolation with a = 1 and setting all of the weights equal to 1 changed the calculated values of relative apparent molal heat content by 1.0 to 2.5 cal. per mole. The extrapolation is probably good to = t 2 cal./niole. TABLE I1 TO IUFINITE DILUTION
EXTRAPOLATIOX OF +L Concn., molesjkg Initial Final
- A H dilution, ---cal./mole~ Exptl. Calcd a
0 09159 0 04570 25 2 09159 01516 48 3 ,04570 .01516 23 1 06864 03426 21 8 06864 01129 49 9 03426 01129 28 1 04570 02283 16 9 04570 00753 42 2 02283 00753 25 3 09159 01643 48 6 a Calculated by eq. 20 using the values a = C = 531 calculated for a least squares fit.
Weighting factor
23 7 1 90 51 1 1 10 27 4 1 00 21 2 1 80 0 94 46 1 24 9 0 75 18 4 3 10 39 9 0 48 21 5 45 32 49 4 1.0, R = -318, and
+
Bm
+ Cmaiz (1)
where
and A is the Debye-Hiickel slope (688 cal. moles-1/2), was used to extrapolate the data to infinite dilution. The constants B and C were evaluated by the method of least squares setting a = 1, using the experimental (13) W. Geffeken, Z. P h y s i k . Chem., BB, 81 (1929). (14) A. Mazzucchelli and A. Rossi, Chem. Abstr., 21, 3007 (1927).
The calculation of the values of 4~ at concentrations about 0.1 m is given in Table I. The values of the relative apparent molal heat content ( 4 ~ at ) the final concentrations were calculated from eq. 1 and the values B = -318 and C = 531 determined by the method of least squares. The values of the relative apparent molal heat content at the initial concentration were calculated from the heat of dilution and the final value of the relative apparent molal heat content. (15) B. B. Owen and S. R. Bnnkley, Ann. N . Y . A c a d . Sei.,61, 753 (1949). (16) E A. Guggenheim and J. E. Prue, T r a n s . Faraday Soc., 60, 710 (1954).
F. R. JONES AND R. H. WOOD
1578
The weighted averages of all determinations at, each concentration are given in Table I. The values of the relative apparent molal heat content (&,) and relative partial molal heat content (Lz) a t even concentrations given in Table I11 were calculated by a method similar to the one given by Seatchard and Epstein.17 The data were represented by the formula
Values of B for a = 2.0 and a = 1.4 ivere calculated for each value of the relative apparent molal heat content (4L) given in Table I. The relative apparent molal heat content was evaluated a t even concentrations by reading B from a plot of R vs. m. The average difference between values of the relative apparent molal heat content calculated from the plots for a = 1.4 and a = 2.0 was 0.6 cal. per mole. The relative partial molal heat content 6 2 ) was evaluated from the same plot and the formula. -
Lp
= -
1
A 4 d G
+ ud&
+2Rm+-
(3 -
ma 2
The average difference between values for the relative partial molal heat contents calculated from the plots for a = 1.4 and a = 2.0 was 3 cal. per mole. The values in Table 111 below 1 molal are from the u = 2.0 plot and the values for 1 niolal and above are from the a = 1.4 plot. T ~ B L111 E
-
VALUESOF
+L,
1’2,
Concn, moles/kg. of uater
0 01 .05 10 20 30 ,40
50 60 . 80 1 00 1 50 2 00 300 4 00
AUI)
?‘ASE 9L
40
78 102 134 157 172 184 195 212 228 269 311 408 522
FOR
T,ITHIU\I PERPHLORATE \T 25’ L2 Ti3 57 109 142 389 187 460 211 488 227 494 241 494 253 489 274 464 307 449 395 387 489 314 793 180 1011 93
a t 0.01 As a check on this procedure the values of and 0.05 molal were calculated using the least squares fit equation. The results were within *0.3 cal. per ; mole of the values determined from the plot of I? us. 4 (17) G. Soatehaid and L. F. Epstcin, Chrm. Rev., 30, 211 (1942).
Vol. 67
for a = 2.0. The values of TAgE given in Table IV were calculated using the activity coefficient measurements of JonesIs as revised by Robinson and Stokes8 and the formula -
TASE =
L, - RT In (yi)”
Where A%“ is the relative, non-ideal partial molal entropy, T is the absolute temperature, and yi is the mean molal activity coefficient.
Discussion The heats of dilution of lithium perchlorate can be checked against the measurement of Austin and who measured the heat of dilution of 4.178 X mole of 1 m LiC104 with 0.006267 mole of 0.01515 m LiClO,. The result of Austin and Rfair (167 4 cal. per mole) is just barely consistent with the calculation from our data (153 f 10 cal. per mole). A plot of TAzE given in Table I11 23s. the square root of molality shows that lithium perchlorate is a “normal salt”; ie., it fits the standard curves for TASE given by Wood.5 The standard curves are characterized by the sum of the ion parameters (P+ P-) for the two ions. For lithium perchlorate the sum of the ion parameters necessary to fit the data varies from 1.28 at low concentrations to 1.31 at high concentrations. Taking the average value of the sum of the ion parameters (P+ P-) = 1.297 and subtracting the value for the lithium ion P- = 0.842j gives a parameter for the perchlorate ion (P- = 0.455). This value checks fairly well with the P- = +0.42 estimated by Wood5 from a consideration of the size of the perchlorate ion. Davies and co-workersZ0have collected ample evidence for the occurrence of incomplete dissociation in many aqueous salt solutions. It is just those salts that seem to be incompletely dissociated which do not fit the entropy correlation. The limited data which are available seems to indicate that for the oxy-anions, the smaller cations tend to be completely dissociated and at the same time fit the entropy correlation (HXo, and Li9 0 3 us. XaK03 and RbSOa; LiClO4 us. IYaC104; lIg(K03)2 us. Wa(?;O&). Thus there may be a fairly large family of oxyanion salts of the smaller cations which do have “normal” entropies of dilution. Acknowledgments.-The authors wish to thank the Research Corporation for a grant and Sfr. Huihert Jongenburger for some helpful discussions of the h a t leak corrections and hlr. Scott Boice for assistance with calculation of L,.
+
+
J. Phys. Chem 51, 516 (1917). (19) .J. &I. Austin and A D Llair, %bid.. 66, 519 (1962). ( 2 0 ) C. W. Dsries in R’. J Harnrr “The Structure of Flectrol) tie Solutions,” J o h n Wiley and Sons, Ne\%T o r k . N. I-., 1969, 1). 19. (18) .J, 11. Jones,
