SOLUTION THERMOCHEMISTRY OF POLYVALENT ELECTROLYTES
3059
The Solution Thermochemistry of Polyvalent Electrolytes. IV. Sodium Carbonate, Sodium Bicarbonate, and Trona1*
by J. Paul Rupert, Department of Chemistry, Univers&tyof Pittsburgh, Pittsburgh, Pennsylvania
16215
Harry P. Hopkins, Jr., and Claw A. Wulf€lb Department of C h a r y , Cam& (Received March 26,1966)
Institute of Technology, Pittsburgh, Pennsylvania
16213
~
~~~
The standard enthalpies of solution of sodium carbonate, sodium bicarbonate, and trona have been determined calorimetrically as -6.36, 4.46, and 5.67 kcal./mole, respectively, after correction for the heat effects arising from hydrolysis. Three solution thermochemical paths, leading to the enthalpy of formation of trona, agree well at -641.0 kcal./mole. Our data, when combined with those from other sources, also permit calculation of the standard entropies of trona as 72.6 cal./(mole OK.) and of the aqueous bicarbonate ion as 23 cal./ (mole OK.).
This study was undertaken as a continuation of our investigation of polyvalent electrolytes. In addition to the commercid importance of the sodium carbonatebicarbonate system, it is of interest because of the subsidiary processes concomitant with dissolution. Analyses of the observed enthalpies of solution of a carbonate or bicarbonate are complicated by the heat effects due to such secondary phenomena-in this case, hydrolysis. In a closed calorimetric system, with minimal vapor space, these secondary equilibria may be derived from the changes in state represented by eq. 1-3
+ HCOa-(aq) = H+(aq) + COa-a(sq)
H2COa(aq) = H+(aq)
(1)
HCOa'(aq)
(2)
H20(l)
H+(aq)
+ OH-(aq)
(3)
Values for the equilibrium constants governing these ionizations have been taken from literature data as follows: Kl = 4.45 (+0.05) X lo-' (ref. 2-5), K z = 5.68 (*0.07) X lo-" (ref. 6, 7), and Ks = 1.01 X (ref. 8). Pitzero has determined the standard enthalpy increments (calorimetrically) to be A H I o = 1.84, A H 2 O = 3.60, and A H a 0 = 13.36 kcal./mole. Other values for A H 1 , derived from the temperature dependence of equilibrium constants, are reviewed by
Wissbrun, et d.'O For our purposes, as will be shown later, uncertainties in this quantity of even 1 kcal./ mole are negligible. For AH2" a value of 3.82 kcal./' mole has been reported6 from the temperature de(1) (a) Presented at the 149th National Meeting of the American Chemical Society, Detroit, Mich., April 1965; (b) to whom correspondence should be addressed. (2) (a) S. Aybar, Commun. Fac. Sci. Univ. Ankara, B10, 44 (1962); Chem. Abstr., 59, 13397 (1963); (b) S. Aybar, Commun. Fac. Sci. Ankara, B5,22 (1954). (3) R. Nasanen, P. Merilainen, and K. Leppanenen, Acta Chem. Scand., 15, 913 (1961). (4) H. S. Harned and R. Davis, Jr., J. Am. Chem. SOC.,65, 2030 (1943). (5) Y.Kauko and H. Elo, 2.physik. Chem., A184,211 (1939). (6) Y. Kauko and A. K. Airola, Suomen Kemistilehti, B10, 7 (1937). (7) V. Y. Eremenko. W r o k h i m . Materialy, 28, 233 (1959); Chem. Abstr., 55, 7014 (1961). (8) H. 5. Hamed and €3. B. Owen, "Physical Chemistry of Electrolytic Solutions," Reinhold Publishing Corp., New York, N. Y., 1958. (9) K.S. Pitzer, J . Am. Chem. SOC.,59, 2365 (1937). The enthalpy of ionization of water, A H S O , has been determined by J. D. Hale, R. M. Izatt, and J. J. Christensen, J. Phys. Chem., 67, 2605 (1963), and by C.E. Vanderzee and J. A. Swanson, ibid., 67,2608(1963),as 13.336 f 0.018 kcal./nole. Since our primary interest is in the quanAHE",we have used the older value of Pitzer in conjunctity AHa" tion with his value for AHz". The difference between these values for AHt" is insignificant in our work. (10) K. F. Wissbrun, D. M. French, and A. Patterson, Jr., ibid., 58, 693 (1954).
-
Volunae 69, Number 9 September 1966
3060
J. PAUL RUPERT,HARRY P. HOPKINS, JR., AND CLAUSA. WULFF
pendence of Kz, and a value of 4.2 kcal./mole (presumably at 18") is due to Thomsen."
Experimental Fisher sodium bicarbonate (NaHC03), certified to have a purity of 99.98% or better, was used without further purification. The sodium carbonate (Na2C03) employed was Fisher Certified reagent grade, listed as 99.9% Na2C03(minimum). Eefore use the sodium carbonate was dried in an oven for at least 2 days at 120". Through the courtesy of Mr. R. E. Clagett, an analyzed sample (minimum 99%) of trona (Na2C03* NaHC03.2H20) was supplied by the Allied Chemical Corp. Owing to its incongruent solubility, this last sample was used without further purification. Its heat of solution was the same as that of a synthetic sample, prepared previously by Professor Clark C. Stephenson and one of the present authors (C. A. W.). All samples were dissolved into 950 ml. of distilled water at 25.0 f 0.1'. Enthalpies of solution were calculated from the measured heats using gram formula masses of 84.01, 105.995, and 226.05 for sodium carbonate, sodium bicarbonate, and trona, respectively. The solution calorimeter, which has been described previously,12 has as its temperature-sensing device a laboratory-wound resistance thermometer. The Mueller bridge circuitry and adjuvant electrical standards have also been described.
Discussion NaCO3. In solutions of sodium carbonate, the predominant secondary equilibrium can be characterized by the change in state C0,-2(aq)
+ H2O(l) = HCOs-(aq) + OH-(aq)
(4)
the eauilibrium constant for which is given bv K4 = &/& = 1.8 X For any molal concentrations, m, of carbonate originally dissolved, the extent of reaction 4 is described by the degree of hydrolysis CY = (HCO,-)/m. Assuming the activity of the water to be unity (minimum mole fraction of 0.995 in our solutions) and the common form of the Debye-Huckel relation for ionic activity coefficients (presumed valid for the dilute solutions considered in this study), CY can be related to K4 and the ionic strength, I , by I
log K 4 = log a2/(1
- CY)+ log m + l.O18I1/*/(l
+ Ill*)
These values accord well with older experimental degrees of hydrolysis reviewed in Mel10r.l~ From Pitzer's data we obtain AH4" = 9.8 kcal./mole. Representative values of CY and aAH4" are included in Table I. Sixteen determinations of the enthalpy of solution of sodium carbonate to give final concentrations in the range 0.007 to 0.085 m are also listed in Table I. ~
~~
Table I: Enthalpies of Solution and Hydrolysis for Na&Os" m
a
aAHro
0.00702
0.126
1.234
5.039
0.960
5.121 5.152 5.184 5.274
0.588
5.369 5.356 5.448 5.530 5.561
0.323
5.61U 5.727 5.722 5.736 5.782
0.00848 0.00921 0.01025 0.01138 0.01356 0.01664 0.02171 0.02547 0.03219 0.03998 0.04885 0,05735 0.06670 0.06833
0.098
0.060
0.033
0.07531 a
-AHobsd
5.730
Units : kcd./mole.
The integral enthalpy of solution, AH(m)obsd,may be written as
+ h(m) +
(7) where $ J L ( ~is) the apparent molal heat content of the solution at concentration m and ME0is the standard enthalpy of solution of Na2COs m(m)obsd = AHs0
NazCO,(c) = 2Na+(aq)
CYm4O
+ C03-2(aq)
(8)
A least-squares analysis of m o b s d - t#&n) V.S. CY [assuming the +L(m) of sodium carbonate to be similar to those for the alkali sulfates*]gives the straight line m o b a d - 4L(m) = -6.31 9 . 0 4 ~kcal./mole, ~ with an average deviation of 0.02 kcal./mole. From this analysis the extrapolated standard enthalpy of solu-
+
(5)
(11) J. Thomsen, "Thermochemische Untersuchungen," Johann Ambrosius Barth Verlag, Leipzig, 1883. (12) W. F. O'Hara, C. H. Wu, and L. G. Hepler, J. C h a . Educ., 38, I = m(3 a) (6) 519 (1961). Supplement to "Mellor's Comprehensive Treatise on Inorganic Equations 5 and 6 have been solved s ~ u ~ t a n e o ubys ~ y and ,(13) Theoretical Chemistry," Vol. 11, Suppl. 11, Part 1, John Wiley an iterative process, for a in the range 0.007 to 0.090 m. and Sons, Inc., New York, N. Y., igm.
and
-
The Journol of Physical Chemistry
SOLUTION THERMOCHEMISTRY OF POLYVALENT ELECTROLYTES
tion is determined as A H S O = -6.31 f 0.05 kcal./ mole, and AH4' = 9.0 kcal./mole in accord with Pitzer's d a h D A better value of A H S O may be obtained from an analysis m o b a d - am4' vs. m'12 [the usual concentration dependence of +L(m)1. Known 4~ values for unhydrolyzed 2-1 electrolytes, such as the alkali sulfates,8show that the linearity of 4~ with m'/' holds best below m = 0.03. A leastsquares straight line for m o b e d - aAH40 = AHso Am'/' in the region 0.007 to 0.032 m is m o b s d aAH4' = -6.37 1.24m112 f 0.03 kcal./mole (where the uncertainty is the root-mean-square deviation). From this A H S O = -6.37 kcal./mole, and the concentration dependence is similar to +L(m) for other 2-1 electrolytes. We have selected A H S O = -6.36 f 0.08 kcal./mole. Trona. Here again the major secondary equilibrium is represented by eq. 4. We define the extent of the hydrolysis by a = (OH-)/m, which, making the same arsumptions as before, is related to K4by
+
+
log K4 = log a(1
+ a)/(l - a) + log m +
+ Ill2)
1.01811/2/(1
(9)
Table 11: Enthalpies of Solution and Hydrolysis for Trona" m
I
=
m(4
- a)
(10)
Table I1 contains representative values of a and aAH4O along with 11 determinations of the heat of solution to give final concentrations between 0.0045 and 0.0550 m. The observed enthalpy of solution, AHobad,can be represented by AHobsd = AHiiO
+
+L
(m)
+ aAHdO
where AHn0 is the standard enthalpy of solution for trona (eq. 11). Na2CO3.NaHCOa.2H20(c)= 3Na+(aq) C03-2(aq)
+
+ HCOa-(aq) + 2H20(1)
(11)
Considering the nature of the solute, an a priori estimate of 4L(m) is difficult to make, and a reduction of the data was made by plotting m o b a d - crAH4O vs. m'/'. A least-squares analysis gives the straight line m o b a d - ~ A H ~ O= 5.65 f 1.90 m'/' 0.04 kcal./mole, which leads to an extrapolated value of AHllo = 5.65 f 0.05 kcal./mole. The slope of this straight line compares remarkably well with the sum of ,pL values for a 1-1 and a 2-1 electrolyte. The relative partial molal heat content of water in the solution was assumed negligible within the estimated uncertainty. NaHCOa. In solutions of sodium bicarbonate, the most important secondary reaction is
*
2HCOa-(aq) = HzCOa(aq)
+ COa-'(aq)
(12)
a
0.00429
0.026
0.00442 0.00893 0.00904
0,011
0.01381 0.01452 0,02159 0.05264
0.0017
0.05264 0.05264
aAHdo
AHobsd
0.256
5.991
0.108
5,997 5.911 5.947
0.017
6.041 5.972 6.033 6.077 6.033 6,020
' Units: kcal./mole.
The extent of eq. 12, defined as a = (C03-2)/m (where m is the molal concentration of the sodium bicarbonate originally dissolved), can be calculated from the equilibrium constant K12 = K2/K1 = 1.2 X by Ki2
and
3061
=
a2/(1- ~ ( Y ) ~ ~ c o ~ - ~ Y H ~ o ~(13) /Y~Hco~
Equation 13 may be reduced to a = 0.01 (independent of m) without loss of precision because aAH120-the quantity of interest-is only 20 cal./mole, which is less than the experimental uncertainty. The observed enthalpies of solution have been fitted to a straight line, by the method of least squares, in the region 0.011 to 0.38m'/2 0.090 m, and are given by m o b s d = 4.49 f 0.02 kcal./mole. Several determinations below m = 0.01, where the heat effects approached the lower limit of the calorimeter's sensitivity, were not included in the least-squares analysis. For the change in state represented by
+
NaHCOa(c) = Na+(aq)
+ HCOa-(aq)
(14)
the standard enthalpy increment is then 4480 - 20 cal. = 4.46 f 0.05 kcal./mole. The standard Gibbs free energy for eq. 14 is calculated from the solubility, given in Mellorla as 1.22 m, a tabulated mean activity coefficient14 -yf = 0.503, and the relation dG14' = -RT In 4m2yf2,as AG14" = 0.58 kcal./mole. From the above data A & 4 O = (4.46 - 0.58)/0.298 = 13 cal./(mole OK.). Utilizing the standard entropy values for NaHC0sl5and Na+(aq),I5 we calculate S O H C O ~ (14) S. T. H a n and L. J. Bernardin, Tappi,41, 540 (1958). (15) F. D. Rossini, D. D. Wagman, W. H. Evans, S. Levine, and I. Jaffe, "Selected Values of Chemical Thermodynamic Properties," National Bureau of Standards Circular 500, U. S. Government Printing Office, Washington, D. C., 1952.
Volume 69,Number 9 September 1966
J. PAUL RUPERT,HARRY P. HOPKINS,JR.,AND C u u s A. WULFF
3062
*
= 23 1cal./(mole OK.). This value agrees with that tabulated by Latimer, Pitzer, and Smith16based solely on eq. 1. From the standard enthalpies of solution of Na2C03 (-6.36 kcal./mole), trona (5.65 kcal./mole), and NaHC03 (4.45 kcal./mole) we can compute AHX,' = -6.36 4.46 - 5.67 = -7.6 f 0.2 kcal./mole, for
+
Na&03(c)
+ NaHC03(c) + 2H20(l) = Na&03.NaHC03.2H20(c) (15)
In view of the assumptions made concerning these solutions, independent routes to evaluating AHl5" would be desiderata in checking our extrapolation procedures. To this end we have measured the following heat effects. Each value is the average of several determinations (in cal./mole) : (a) Na&Os(c) into water to give a 0.055 m solution, AH = -5739 f 20; (b) NaHCOa(c)into (a) to give 0.05 mCOa-2 and HCOI-, AH = 4220 20; (c) NaHC03 into water to give a 0.055 m solution, AH = 4585 f 10; (d) Na2COainto (c) to give 0.055 m C03-2 and HCOs-, AH = -6128 10; (e) trona into water to give a 0.055 m solution, AH = 6056 f 20. The enthalpy increment AHl5' can be obtained from the sum AHa A H b - AH, = -7.67 0.06 kcal./mole and from the sum AHo A H d - AHe = -7.60 d= 0.04 kcal./mole. The excellent accord among the three values for A H I ~ O gives a posteriori support for the extrapolation methods used to account for hydrolysis effects.
*
*
+
+
*
Torgeson" by a closely related procedure obtained AHlS0= -7.76 f 0.02 kcal./mole, in reasonable agreement with our average value of -7.64 f 0.10 kcal./ mole. For eq. 15, AGlao = -2.47 kcal./mole18 and A&' = (-7.64 2.47)/0.298 = -17.2 cal./(mole OK.). The above values and tabulated datals for Nazcos, NaHC03, and H20(l) lead to A H t O = -641.0, AGf" = -569 kcal./mole, and So = 72.1 1.0 cal./ (mole OK.) for trona. An estimate for the entropy from LatimerW rules is 73.9 cal./(mole OK.).
+
*
Acknowledgment. The authors are pleased to acknowledge the suggestions and encouragement of Professor Clark C. Stephenson (M.I.T.) and the use of laboratory facilities of Professor Loren G. Hepler. The generosity of the Solvay Procesa Division of Allied Chemical Corp. through its Pittsburgh branch manager, Mr. R. E. Clagett, in providing an analyzed sample of trona is gratefully acknowledged. This work was supported, in part, by the National Science Foundation, to whom the authors are also grateful. ~~
(16) W. M. Latimer, K. S. Pit~er,and W. V. Smith, J. Am. SOC.,60, 1829 (1938). (17) D.R. Torgeson, Ind. Eng. Chem., 40, 1152 (1948).
Chem.
(18) Personal communication, C. C. Stephensen, Massachusetts Institute of Technology. (19) W. M. Latimer, "Oxidation Potentials," F'rentice-Hall, En&wood Cliffs,N.J., 1952,p. 359.
