2396
J. Phys. Chem. 1980, 84,2396-2398
Actlvlty Coefficient of Aqueous NaHCO, Kenneth S. Pitzer" and J. Christopher Peiper Department of Chemistry and bawrence Berkeley La6oratory, University of California, Berkeley, California 94 720 (Received December 27, 7979)
The determination of the activity coefficient and related properties of sodium bicarbonate presents special problems because of the appreciable vapor pressure of C02 above such solutions. With the development of reliable equations for the thermodynamic properties of mixed electrolytes, it is possible to determine the parameters for NaHC03 from cell measurements or NaC1-NaHCO3 mixtures. Literature data are analyzed to illustrate the method and provide interim values, but it is noted that further measurements over a wider range of concentrationswould yield more definitive results. An estimate is also given for the activity coefficient of KHCO3.
The activity coefficient of aqueous NaHC03 is not It is then convenient to rearrange eq 1 to known with accuracy comparable to that for other simple salts. The results of Han and Keslerl and of Han and In YHCOs- - In (K,K,) = In Bernardin2 were based on old experiments of limited precision and were presented only on small graphs which are presumably representative of their accuracy. The isopiestic method, which is widely applicable to most salts, fails (or is complicated) by the significant vapor pressure Now all quantities on the right side are known to sufficient of C02 as well as H 2 0 for NaHC03 solutions. In view of accuracy for each experiment. Hence the limit at zero ionic the importance of bicarbonate in various solutions with strength yields KIK,; this was the original treatment. We Na+ the principal cation, we have sought other methods shall use the same data to evaluate also In (ycl-/yHco,) as of determination of the activity coefficient for NaHC03. a function of m1 and m2. The effectiveness of the equations of Pitzer and Kim3 for The solutions investigated by Harned and Bonner5 do mixed electrolytes makes it feasible to use experiments on not extend much above an ionic strength of 1 M while rather complex mixtures provided all important paramethose of Harned and Davis4are more dilute. In this range ters for other solutes are accurately known. With this Pitzer and Mayorga6 found that third virial coefficients strategy in mind we examined the excellent experiments could be neglected. Then eq 17 of Pitzer and Kim3yields of Harned and Davis4and of Harned and Bonner5with the electrochemical cell Pt,H2,CO2/NaHCO3(ml),NaCl(mz),In (?Cl-/YHCOa') = zmNa(BNaC1 - BNaHCOs) + C02(m3)/AgC1,Ag.These investigators extrapolated their 2'%l,HCOs(mHCO3- mCl) (4) results to zero molality to obtain the first dissociation constant of carbonic acid. We shall use the data for finite where the virial coefficients related to dissolved COz are molalities to determine the ion interaction parameters omitted since their effect is believed to be negligible. The (virial coefficients)for Na+,HCOf in this mixed electrolyte. coefficients BMx are given by This is feasible because the corresponding parameters for Na+,Cl- are accurately known, and any other parameters (5) B M X = /3(O)MX + /3"'MX&) are expected to have very little effect. g(I) = (1/2I)[l - (1 + 211/2) e ~ p ( - 2 P / ~ ) ] (6) The chemical reaction for this electrochemical cell is where I is the ionic strength and /3(O) and /3(l)are the two '/2Hz(g) + AgCl(s) + HC03- = C1- + Ag(s) + parameters primarily related to the short-range forces HzO(1) + COzk) (A) between M+ and X- ions. Also we note that in this case and the corresponding equation for the cell potential is mNa= I = ml + m2 and (mHco8- mcl) = ml - m2. Then
(=)
ln(ycl-/yHcos-) = 2I[Ap(O) + Apcl) g(n1 + 2(ml - m2)0 (7) A@" = (?(i)pqaci -(
The standard potential of this cell is related to other quantities by eq 2, where Eo(Ag,AgC1)is the standard E A o = Eo(Ag,AgC1)- ( R T / F ) In (KIK,) (2) potential for the Ag,AgCl electrode, K1 is the first dissociation constant of carbonic acid as usually defined, and K , is the Henry's law constant for solubility of COP The product K I K , is the equilibrium constant for reaction B. C02(g)+ H20(1) = H+(aq) + HC03-(aq)
(B)
Also mcl = m2 and in adequate approximation for these solutions mHC03= ml. 0022-3654/80/2084-2396$0 1.OO/O
i
? ( i ) ~ a ~ ~ ~ 3=
0,1
(8)
The subscripts are omitted hereafter from 0. In view of the characteristics of the silver-silver chloride electrode' it seemed best to use the Eo(Ag,AgCl) values from the same laboratory.6 Modern physical constantse were used (F and R ) with the conversion factor 1.00033 included since the original measurements were in the International volts in use at that time. The resulting factor is (RIF) = 8.61451 X (Int V)/K. All of the experimental values of Harned and Davis4and of Harned and Banner: 678 in all, were included in a least-squares calculation. Each set of data at a given temperature was assigned a weight inversely related to the 0 1980 American Chemical Society
The Journal of Physical Chemistry, Vol. 84, No. 19, 7980 2397
Activity Coefficient of Aqueous NaHC03
standard deviation of fit of that set treated separately. No experimental point ;showed excessive deviation, hence none was discarded. Preliminary calculations indicated that the temperature dependence of APS, A@(1),and 6' was negligible over the temperature range 0-50 O C and in view of the accuracy of the data. This is consistent with the very small temperature coefficients of such parameters determined by Silvester and Pitzer'O for similar solutes. A familiar three-term expression was used for the temperature dependence of In (KIK,) with the result In (KIKs)= -5023.23/T
+ 119.330 - 21.1469 In T
TABLE I: Activity Coefficient of NaHCO, at Solute Fraction y in Mixture with NaCl and the Osmotic Coefficient of NaHCO, (at 25 "C)
m 0.01 0.02 0.05 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
(9)
The other parameters were found to be AP(O) = 0.04&
(10a)
= O.22ij3
(lob)
The statistically indicated uncertainty in each of these last three quantities is 0.01. However, Abco)and B are rather closely coupled for the presently available data where m 1 is never large. Thus, for the more concentrated solutions I and (mz- ml)have similar values, and, from eq 7, one notes that (A$o) - 6') is determined much more accurately than either parameter individually. This particular uncertainty could be removed if the same type of cell measurements were extended to solutions with higher ml; indeed, with data for still higher m values, third virial coefficients could also be determined. If we now introduce the parameted for NaC1, P ( O ) = 0.0765, P(l) = 0.2664, the resulting values for NaHC03 are
P ' 1 ) ~ a ~ ~=0 30,0411
(12)
Since the accuracy of the NaCl values is high, the uncertainties of these values correspond to those stated above for the A@values. These values are within the pattern of values found for other simple 1-1 electrolytes.6 These results allow the calculation of the activity coefficient of NaHC08 in mixtures with NaC1. Equation 15 of Pitzer and Kim3 simplifies to In
= -A,[P/(l
+ 1.211/2) + (2/1.2)
+
In (1 + 1.211")] + I[(l+ Y)BNaHCO3 + (1 - Y)@NaC1 + ~ [ Y B ' N ~ H c o , + (1 - Y ) B ' N ~ c I I (13) yNdCO3
Bj = Pj(0)
B: = (Pj(')/2F7[-l
+
Oj(l) g(I)
(14)
+ (1 + 2P/2+ 20 e~p(-21'/~)] (15)
Here y is the solute fraction of bicarbonate. The DebyeHuckel parameter A, was taken from Bradley and Pitzer;ll the value is 0.391 at 125 "C. In Table I the resulting activity coefficient of NaHC03 is given for y = 0 (the trace activity of NaHC03 in NaC1) and for y = 1 (pure bicarbonate). For the trace activity P ( O ) N ~ C O ,and 6' appear as a simple sum; hence the special uncertainty discussed above disappears and the results should be quite accurate. For the pure bicarbonate, however, 8 disappears and the term 2r@(o)NaHCOs remains, yielding somewhat greater uncertainty. The activity coefficient of 0.539 at 1 M for pure bicarbonate in Table I may be compared with Han and Kesler's value' of 0.56. The agreement is as good as could
r(Y=l) 0.898 0.863 0.804 0.749 0.688 0.650 0.62, 0.60, 0.58, 0.57, 0.55, 0.54, 0.53,
r(Y=O) 0.900 0.868 0.813 0.764 0.712 0.681 0.659 0.643 0.631 0.621 0.613 0.606 0.601
dY=l) 0.966 0.954 0.934 0.915 0.895 0.883 0.875 0.869 0.865 0.862 0.859 0.857 0.856
be expected in view of the data upon which Han and Kesler's calculations were based. The osmotic coefficient of pure NaHC03 is also given in Table I as calculated from eq 16. - 1 = -A,mliz/(l 1.2m1/2) rn[P(O)+ P(l) e~p(--2rn'/~)](16)
+
+
+
The value of In (KIKs)from eq 9 is -18.004 at 25 "C, which agrees reasonably well with the original interpretation of the data of Harned and Davis4yielding -17.995. Also AHo/R for chemical reaction B is -1282 K from eq 9, while Harned and Davis reported values yielding AHo/R = -1238 K. Recently Berg and VanderzeeI2 made calorimetric measurements on carbonate systems and reviewed the available literature; their value for AH"/R is 1274 f 20 K, and they recommend for In (KIKs)the value -18.001. The agreement of the AHo/R values is significant since we made no use of their calorimetric data. For In (KIKs), however, Berg and Vanderzee were dealing with essentially the same data which we considered and which Harned et al. interpreted originally. There are no experimental data for KHC03 of accuracy equal to those discussed above for NaHC03. However, MacInnes and BelcheP did measure at 25 " C a similar cell with a glass electrode instead of the hydrogen electrode. While their absolute accuracy is less and the absolute agreement with the values from Harned's laboratory is not very good, the precision of measurement of MacInnes and Belcher seems good. Their results indicate that the quantity In (ycl/yHco,) is the same for solutions of K+ as for Na+ to their precision of measurement. Thus our values for Abco)and Abc1)can be used as an estimate for solutions of K+, yielding for KHC03 PC0)= -0.0006 and Ptl) = -0.013, at 25 "C. In summary, we have presented a method for the determination of the activity coefficient and related properties of aqueous bicarbonates from cell measurements on mixtures with the corresponding chlorides. Cell data from the literature yield reasonably good values for the parameters defining NaHC03 properties and excellent agreement with recent calorimetric measurements of the heat of ionization of carbonic acid. Cell measurements designed with this method in view could yield much more accurate parameters for the thermodynamic properties of aqueous bicarbonates. Acknowledgment. This research was supported by the U.S. Department of Energy through Contract W-7405Eng-48. References and Notes (1) S. T. Han and R. B. Kesler, Tappi, 46,308 (1963). (2) S.T. Han and L. J. Bernardin, Tappi, 41,540 (1958).
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J. Phys. Chem. 1980, 84, 2398-2402
(3) K. S. Pitzer and J. J. Klm, J . Am. Chem. SOC.,96, 5701 (1974). (4) H. S. Harned and R. Davis, Jr., J. Am. Chem. Soc., 65, 2030 (1943). (5) H. S. Ham4 and F. T. Bonner, J. Am. Chem. Sac., 67, 1026 (1945); F. T. Bonner, Ph.D. Dissertatlon, Yale Universltv, New Haven. CT. June 1944. (6) K. S. Pitzer and G. Mayorga, J. Phys. Chem., 77, 2300 (1973). (7) R. G. Bates et al., J. Chem. Phys., 25,361 (1956); see also R. G. Bates and V. E. Bower, J. Res. Natl. Bur. Stand. Sect. A , 53, 283 (1954).
(8) H. S. Harned and R. W. Ehlers, J. Am. Chem. Sac., 54, 1350 (1932); 55, 3179 (1933). (9) E. R. Cohen and B. N. Taylor, J. Phys. Chem. Ref. Data, 2, 663 (19731. (10) L. F. Sllvester and K. S. Pltzer, J . Solution Chem., 7 , 327 (1978). (11) D. J. Bradley and K. S. Pitzer, J. F‘hys. Chem., 83, 1599 (1979). (12) R. L. Berg and C. E. Vanderzee, J. Chem. Thermodyn., 10, 1113 (19781. (13) D. A. k c I n m a n d D . Belcher, J. Am. Chem. Soc.,55,2630(1933).
Activity Coefficients of Sodium Bromlde in Llquid Sulfur Dioxide at 273.15 K Norman N. Lichtin Department of Chemistry, Boston Universiyv, Boston, Massachusetts 022 15
and John F. Reardon* Department of Chemistry, Boston State College, Boston, Massachusetts 02 115 (Recelved: January 14, 1980)
Activity coefficients of sodium bromide have been determined in sulfur dioxide at 273.15 K by the solubility method using sodium-22 bromide in the presence of (i-Am),NI and (i-Am),NB(i-Am),as cosolutes. For the NaBr-(i-Am),NI system dissociation constants of the four possible ion pairs were determined separately by conductance measurements. Calculation of the ionic concentrations in the saturated solutions permitted evaluation of the solubility product constant, Kep,of sodium bromide, 2.54 It 0.09 X lo-* M2at 273.15 K. The experimental activity coefficientscalculated from Kapagreed with thcae calculated with the equation of Gronwall, LaMer, and Sandved (GLMS) with an a value of 0.277 nm, as compared to the sum of crystallographic ionic radii, rc, of sodium bromide of 0.291 nm. For the NaBr-(i-Am)4NB(i-Am)4system the dissociation constant of NaB(i-Am),, which could not be synthesized, was calculated with Bjerrum’s equation to be 17.25 X 10”’. The dissociation constants of the other possible ion pairs were known. Ionic concentrations were again calculated. Experimental activity coefficients of NaBr calculated from the known KBpagreed with those derived from the equation of GLMS with an a value of 0.300 nm. The demonstration of the applicability of the equation of GLMS to solutions of simple ionophores in sulfur dioxide means that solutes are more highly dissociated than previously thought.
Introduction We have previously reported on the reactivity of ions1 in SOz as well as on the state of aggregation of both ionogens2 and ionophores3 in SO2 through conductance measurements. In this paper we report the results of an investigation of the thermodynamics of simple ionophores in liquid SOz. In the interpretation of our previous results we had always assumed the applicability of the DebyeHuckel limiting law for SO2 solutions. The object of the research reported here was to determine the appropriate form of the activity coefficient function for solutions of simple ionophores in SOz. We chose the solubility method because, through the use of radioactive solutes, we hoped to measure extremely dilute solutions in which the existing theoretically derived expressions might be more valid. Solutions of ionophores and ionogens in SO2 have been the subject of a moderate degree of electrochemical and thermodynamic investigation. The earlier electrochemical work has been reviewed by B ~ r o w Recently .~ Miller and Mayeda5 and Tinker and Bard6 have carried out voltammetric and coulometric studies of electrooxidationsin SO2. No activities or activity coefficients resulted from these studies. Eversole and c o - w ~ r k e r determined s~~~ stoichiometric mean rational activity coefficients, fN, of KSCN and KI in SOz from 283.15 to 298.15 K by a vapor-pressure lowering method. They assumed complete dissociation of both salts a t all temperatures and also the applicability of the Debye-Huckel limiting law in their analysis. Tokurag and co-workers have measured the partial molar volumes of a 0022-3654/80/2084-2398.$0 1.OO/O
series of quaternary and simple ionophores in SOzat 298.15
K. Anticipating a high degree of association of solutes in
SO2,we chose solutes for which dissociation constants, Kd, were known or might be measured. For solute we initially chose NaCl for which we determined a solubility of 1.10 f 0.03 X M at 273.15 K. We could not obtain reproducible results in the presence of cosolutes in a reasonable amount of time. We then employed NaBr for which preliminary measurements indicated the low solubility we desired. For cosolutes we used (i-Am)4NIand (i-Am)4NB(i-Am)4.Both consist of large ions with low charge density and are highly dissociated and highly soluble. From the measured solubilities and the dissociation constants for all possible ion pairs, we have calculated ionic concentrations and have evaluated the Nernst solubility product constant, KeP. From KBpand the ionic concentrations we have determined mean molar ionic activity coefficients. These experimental values have been compared with values calculated with the aid of theoretical expressions derived from the Debye-Huckel and the Gronwall, LaMer, and Sandved models.
Experimental Section Solubilities were measured in vessels like that shown in Figure 1which were attached to the sulfur dioxide vacuum line at C. Each vessel was equipped with three calibrated volumetric flasks B (25-35 mL). The solute, NaBr, in its filtration capsule, and the cosolute were loaded through 0 1980 Amerlcan Chemical Society
