THEENTROPIES OF AQUEOUS IONS
Aug., 1938
4.45, 5.25, 4.00 and 3.90 cal. with an average of 4.4 * 0.4 cal. The heat absorbed in the dilution of 10 ml. of 0.5 molal lead nitrate solution with 875 ml. of water was also measured, with the results: 8.40, 8.30, 9.45, and 9.00 cal., average 8.8 * 0.4 cal. Combining this value with the data of Plake,3 the heat absorbed in the dilution to zero concentration of the lead nitrate solution was found to be 9.3 cal. With the aid of the Debye-Hiickel theory, the increase in heat content with dilution was estimated to be 0.8 cal. greater for the final solution than for the initial phosphate solution. Combining these quantities, one finds A I P = -2460 * 360 cal. for the above equation (31 Hake
[CONTRIBUTION FROM
THE
Making use of the heats of ionization of phosphoric acid recently published by the writer,' one obtains also the following results Pba(PO4)g
+ 2Hf
Pba(PO& = 3Pb++
3Pb++
+ 2HPO4--;
+ 2Po4---;
AH'
AHa = 7860
*
860
*
400 cal. 1OOOcal.
All values given are for 25'.
Summary Values have been obtained for the heats of solution a t infinite dilution and 25' of the following substances: CsC104, A H " = 13,260 * 100 cal.; RbClOd, AH" = 13,570 * 60 cal.; RbC103, A H n = 11,410 * GO cal.; Pba(PO&, AHo = 78tiO * 1000 cal. BERKELEY, CALIF.
X pli)rrk Chrnz A162, 257 (19'32)
1829
RECEIVED M A R C H 30, 1938
CHEMICAL LABORATORY OF THE UNIVERSITY OF CALIFORNIA ]
The Entropies of Aqueous Ions BY WENDELL M. LATIMER,KENNETH S. PITZER AND WENDELL V. SMITH In the course of the research program for the evaluation of the entropies of aqueous ions, in progress for some time in this Laboratory, a considerable body of data has accumulated which makes possible the calculation of the entropies of eleven additional ions. Because in most cases the entropy values depend on those for other ions, an extensive revision would be necessary in order to make these new values the best possible. Consequently it seemed best to make a complete revision of all ionic entropies and to include the new ions a t the same time. In order to avoid unnecessary length, specific references have been given only where the data are not included in some summary publication. Most of the new calculations are based upon data taken from recent publications in this research series' and from the references cited in the earlier summary paper.2 In general entropies have been taken from the excellent summaries of Kelleyj3 heats of reaction from Bichowsky and Rossini,?and (1) (a) Pitzer, Smith and Latimer, THIS JOURNAL. 60, 1826 (1938); (h) Pitrer and Coulter, ibid., 60, 1310 (1938). (c) Pitzer, ibid., 60, 1828 (1Y38); 59, 2365 (1937); (d) Smith, Pitzer and Latimer, i b i d . , 59, 2640, 2642 (1937); (e) Pitzer and Smith, i b i d . , 59, 2633 (1937); (f) Smith, Brown and Pitzer, ibid., 69, 1213 (1037); ( g ) Brown, Smith and Latimer, i b i d . , 58, 1728,2144, 2228 (1936); 59, 021 (1037). (2) Latimer, Schutz and Hicks, J. Chem. Phys., 2,82 (1934). (3) Kelley, Bur. M i l r e s Bt!ll., 350, 1932 and 394, 1936. (4) Bichowsky and Rossini, "Thermochemistry of Chemical S u b stances," Reinhold Publishing Corporation, New York, N. Y.,1936.
activity coefficients and other free energy data from the Landolt-Bornstein Tabellems The calculations are summarized in Table I and the best values of the ionic entropies collected in Table 11, Different methods of obtaining a given entropy are included only if they are independent in the least accurate step. An attempt has been made to include all sources of error in estimating the uncertainty in the final values. For this reason the uncertainty given for a final value is often much larger than the difference between the various values for that quantity would indicate. The standard state for ionic entropies has been defined in several earlier papers, wherein the theoretical significance and practical importance of ionic entropies also have been discussed. As the body of data becomes larger, however, its consistency becomes more notable, and offers more and more evidence of the validity of the third law of thermodynamics when applied to crystalline inorganic salts. The possibility of difficulties in the case of hydrated crystals has arisen recently and has been discussed elsewhere.lb It is felt that errors from this source cannot have any serious effect on the values obtained in this paper. (5) Landolt-Barnstein "Physikalisch-chemische Tabellen." including Supplements 1, 2 and 3 , Verlag yon Jiilius Springer, Berlin. 1923--193fi
rLABI.t
I
SVMMARY OF EKTROH CAICULATIUNS I nit< cal pcr d t g r t c p i r xi3olra
+ +
HzO(1) H + OH HCl(g) = H + C1 AgCl(s) '/LH2 I-IC
+
R.c
i l l 1 JII
-3 5 ;5 I
-19
+ C1
24'" -31 I4
5 -1g
-14 89
ion
THEENTROPIES OF AQUEOUSIONS
Aug., 1938
1831
TABLE I (Concluded) Reaction
-43.9 -21.518 -36.2
CU 2 H + = CU++ f Hz Cu 2Ag+ = CU++ f 2Ag Zn 2 H + = Zn++ f H2 Cd 2 H + = Cd++ f Hz Fe 2 H + = F e + + HZ Fe++ f H + = F e + + + f 0.5Hz Sn 2 H + = Sn++ HZ 2Hg 2 H + = Hgz++ f HZ PbClz = P b + + f 2C1Mg(0H)z f 2 H + Mg++ 2Hz0 = CS+ f Al+++ f 2SO4= CsAl(S04).~12H~0(~) CaCzO,.HZO = Ca++ CzO4- 4- HzO(1) Ag+ 2NHdaq) = Ag(NHdz+ Pbs(PO4)z f 2 H + = 3Pb++ 2HPO4HPOI' f H + HzPO4H + = H3P04(aq) HzPO4HPOa' H + f Pod"
- 2.7 -49.2 - 4.5 2.5 - 1.2 -19.8 14.0 11.9 - 1.7 -13.3 2 -22.5 - 11.91' -77.3'" 30.3 16.0 -43
+ + + + + + +
+ +
+
+
+
+
+ 12H20(1)
+
+
TABLE I1 ENTROPIES OF AQUEOUS IONSAT 298.l0K. Units: cal. . per dezree per mole. .
H+ Li+ Na+ K+ Rb+ CS + Ag NHi' +
0.00 4.7 * 14.0 * 24.2 * 28.7 * 31.8 * 17.54 * 26.4 *
c11.0 0.4 .2 . .7 .6 .15 .5
BrIC10ClOzClOaclodBrO3-
Ion
AS&i
HF(g) = H + f FBaFa = Ba++ f 2FCaFn = e a + + f 2F-
13.50 * 19.7 * 25.3 * 10.0 24.1 * 39.4 * 43.6 * 38.5 *
0.10 .2 .5 2 0.5 .5 .5 1.0
(6) Harned. Keston and Donelson, THISJOURNAL, 58, 989 (1936): I S , 1280 (1957). (7) Heat of solution: Zimmerman, private communication. (8) Hamer, TEISJOURNAL, 67, 9 (1935). (9) (a) Harned and Hamer, ibid., 6'7, 27 (1935); (b) (So&2s04 = 48.0 cal. per degree per mole); Schutz, Ph.D. Dissertation, Univ. of California, 1933. (10) (SnRbCIOs = 36.3 cal. per degree per mole), Ahlberg, Ph.D. Dissertation, Univ. of California, 1930. (11) (SoRbcioa = 38.5) estimated from values for CsC104,1* KClOa, RbClOI and KCIOII, using the formula of Latimer, THIS JOURNAL, 43,818 (1921). (12) (AFof soln. of AgIOa), Kolthoff and Lingane, J . P h y s . Chem., 43, 133 (1938). (13) Owen, THISJOURNAL, 57, 1526 (1935).
T1+ Ag(NH3)z' Mg++ Ca++ Sr++
Ba++ Fe++
cu++ Zn++ Cd++ Hgz
+ +
Sn++ Pb++ Al+++ Fe+++ OH -. 1' -
-
soF-
SOC"+
+
SOzn++ S°Cd++-
S°FB++ S°Fe+++
SOsn++ S0H82++ SOPb++
SOMU++
SO*,++ + soc*o,S'*g(NHs)2+
S0EfP0aSOHzPOpS0HJPO4
SoPo&'
30.5 * . 4 57.8 * 1.0 -31.6 * 3 -11.4 * 0 . 3 - 7 . 3 zt 1 . 5 2.3 * 0.3 -25.9 * 1 . 0 -26.5 * 1 . 0 -25.7 * 1 . 0 -16.4 * 1 . 5 17.7 * 3 4 . 9 * 1.0 3.9 * 0.9 * 10 -76 -61 a 5 - 2.49 * 0.06 2.3 * 2
103-
HSHSOa-
-
-
2.4 * 2
{ - 0.4*2 ( - 4.2 * 2 -25.9 * 3 -26.6 * 1 -25.7 * 1
i
-16.4 * 1 . 5 -25.9 * 1 - 6115 - 4.9 * 1 17.7 * 3 3.9 * 0.9 31.6 * 3 -76 * 10 9.6 * 1 57.8 * 1 - 2.3 * 1.5 28.0 * 1 . 5 44.0 * 1 . 5 -45 * 2
28.0 * 1 . 0 14.9 * 1.0 32.6 * 1 . 5 3 * 3 30.6 * 2 4.4 * 1.0 29.9 * 1.0 35.0 * 0 . 2 28.0 * 1 . 5 - 2.3 * 1.5 -45 * 2 22.2 * 0 . 8 -13.0 * 1 9.6 * 1 25 * 5 46.7 * 0 . 4 10.5 =t 1 . 0
Summary The calculation of the entropies of aqueous ions have been completely revised and extended t o include eleven additional ions. BERKELEY, CALIF.
RECEIVED MARCH30, 1938
