2976
JAMESN. BUTLER AND RIMAHUSTON
to note, however, that the thermal quantities ( A H and A s ) for the ethylene silver complex forming reaction are in the same range as those found by Denning, Hartley, and Venanzi2I on the formation of (allyl NR3)+ PtC13- complexes where R is either an H atom or an ethyl group. I n comparison with the results of Cvetanovic and coworker^^*,^^^ using ethylene glycol, the thermal parameters and the stability constants in water are all larger. One rather surprising feature of the present study is that in contrast t o the situation in ethylene gly-
col and in conformity with static experiments, the substitution of alkyl groups adjacent (compare propylene and 1-butene to ethylene) t o the double bond does not cause any large decrease in stability constants. Thus, the earlier gas chromatographic results would seem t o be due t o the medium, ethylene glycol, rather than any specific property of the complexing reaction. (21) R. G. Denning, F. R. Hartley, and :L. M. Venansi, J . Chem.
Soc., 324 (1967).
Activity Coefficients and Ion Pairs in the Systems Sodium Chloride-Sodium Bicarbonatewater and Sodium Chloride-Sodium Carbonate-Waterl by James N. Butler and Rima Huston Tyco Laboratories, Inc., Bear Hill, Waltham, Massachusetts
Of?l&$
(Received January 6 , 1970)
The mean activity coefficient of NaCl in electrolytes containing NaHCOa and Na2C03has been measured by the potentiometric method, employing both sodium amalgam electrodes and sodium-selective glass electrodes in cells without liquid junction. Harned’s rule is obeyed over the ionic strength range from 0.5 to 3.0 with a coefficient a12= 0.047 f 0.003, independent of ionic strength or whether the anion is cos2-or HC03-. These results, as well as the equilibrium constants for protonation equilibria, are discussed in terms of a model where Naf forms ion pairs with the carbonate anions. Association constants (at I = 1.0) log K1’ = 0.96 0.13 (for the formation of NaC08-) and log K1” = -0.30 f 0.13 (for the formation of NaHC03) are derived. Constants obtained at other ionic strengths and corrections to I = 0 are given. The relation of ion pairing to the salt effect on the carbonate protonation equilibria is discussed. Systematic deviations of several millivolts observed in the glass electrode data at pH 8 to 9 and ionic strengths below 1 indicate that caution must be exercised in interpreting such measurements.
*
Introduction Despite the critical importance of bicarbonate and carbonate ions in natural water systems, little is known about the activity coefficients and ion-pairing equilibria of these species in the presence of alkali metal cations. One indirect study has been made2 of the activity coefficients of NaHC03 and Na2C03 alone in aqueous solutions, but no direct measurements have been made of multicomponent activity coefficients, either of NaCl in the presence of carbonate species, or of carbonates in the presence of substantial concentrations of NaC1. On the other hand, a large body of data has been collected on the protonation equilibria of carbonate^,^^^ mostly in media where extrapolation to infinite dilution is possible. A t t e r n p t ~have ~ ~ ~ been made to obtain quantitative information about ion-pairing equilibria The Journal of Physical Chemistry, Vol. 74, No. 16,1970
from such data, but these rest on a number of ad hoc assumptions regarding single-ion activities and the
(1) Presented at the Symposium on Metal Ions in the Aqueous Environment, 158th National Meeting of the American Chemical Society (Division of Water, Air, and Waste Chemistry), New York, N. Y . , Sept 1969. (2) A. C. Walker, U. B. Bray, and J. W. Johnson, J . Amer. Chem.
floc,, 49, 1235 (1927). (3) (a) L. G. Sillen and A. E. Martell, “Stability Constants o f Metal-Ion Complexes,” The Chemical Society, London, Special Publication No. 17, 1964; (b) C. Culberson, D. R . Kester, and R. M. Pytkowics, Science, 157, 59 (1967); A. Distkche and 8 . Distkche, J . Electrochem. SOC.,114, 330 (1967); C. Culberson and R. M. Pytkowics, Limnol. Oceanogr., 13, 403 (1968). (4) F. 8. Nakayama, private communication (submitted to J . Phys. Chem.). (5) R. M. Garrels, M. E. Thompson, and R. Siever, Amer. J. Sci., 259, 24 (1961).
2977
ACTIVITYCOEFFICIENTS OF NaCl constancy of liquid-junction potentials, and for that reason are difficult to relate t o thermodynamic data.6 This paper describes several experiments designed to obtain the thermodynamic mean activity coefficient of NaCl in the presence of NaHC03 or NazC03, and attempts to relate these results to a model involving ion pairing between Na+ and HCO3- or c03’-.
with Eo evaluated from the known composition and activity coefficients of the NaCl stock solution.14 Correction of y12 to round ionic strength was made by assuming Harned’s rule15 log
Experimental Section Activity coefficients of NaCl were obtained as described previously from potential measurements of the Ce117- 9
YlZ
= log
710
- a121(1 - Xl)
(2)
where ylo is the mean activity coefficient of XaC1 alone a t ionic strength I , and a12is estimated from the uncorrected data. A second iteration did not change the value of a12 obtained from the corrected data.
Na(Hg)INaC1, NaX, H201AgC11Ag (where X represents HCOPor 1/2C032-); or from measurements of the celllo Na glasslNaC1, NaX, H2OlAgCllAg
Table I : Activity Coefficient Measurements in NaC1-NaHC03 Electrolytes at 25”; [Cell: Agl AgClI NaC1, NaHCOs, H201Na(Hg)]” Total
Two different types of sodium-selective glass elecionic -log 712 strength, AE, -log YlZ trodes were used. Electrode B was a Beckman No. (cor) I x 1 PH mV (exptl) 39278 sodium ion electrode (glass compositionl1#l2 0.1668 0.5031 1.0000 11.02 0 0.1672 probably LAS-10-23), and electrode C was a Corning 0.1784 0.5073 0.7486 8.83 8.50 0.1791 No. 476210 sodium ion electrode (glass composition 0.1763 8.25 0.1770 KAS-11-18). 0,1767 0.5133 0.5055 8.18 18.15 0.1782 Solutions were prepared by weight from Fisher 0.1780 18.30 0.1795 0.2064 ? 0.5215 0.1793 8.21 48.00 0.2092 Certified reagent grade chemicals and triple-distilled 0.2089 ? 48.30 0.2117 water. NaCl contained less than 0.01% bromide, less 0,1941 0.5240 0.0761 8.22 68.50 0.1974 than 0.002% iodide, and less than 0.0002% materials 0,1899 68.00 0.1932 reducible by sodium amalgam. NaHC03 and NazC03 0.1824 1.0000 9.0 0 0.1838 1.0981 contained less than 0.003% chloride, less than 0.01% 0.2087 1.0400 0.4122 8.6 27.20 0.2102 0.2094 27.28 0.2109 bromide or iodide, and less than 0.005% reducible 0.2225 0.2219 1.0115 0.1135 8 . 4 62.50 metals. Solutions were analyzed for chloride by 62.70 0.2234 0.2228 potentiometric titration with standard AgN03, for 1.0049 0,0444 8.2 87.10 0.2255 0.2252 carbonate by potentiometric pH titration with standard 87.30 0.2272 0.2269 HC1, and for bicarbonate by titration with standard a Component 1 is NaC1, component 2 is NaHC08; I = ml + NaOH. GranI3plots of these titration curves indicated mz,X I = m l / I (protonation equilibria not included in calculating negligible material other than chloride reacting with the ionic strength); p H of 0.5 m NaHCOs stock solution was 9.0; silver ion, and less than 0.2% excess base in the carbonp H of 1.0 m NaHC03 stock solution was 8.12. ‘yl2 corrected to round ionic strength (0.50 or 1.00) in last column. ate.6 For the amalgam electrode measurements, 0.001 m NaOH was added to the iSaC1 stock solution to minimize hydrogen evolution. The pH of each mixed (6) J. N. Butler and R. Huston, “The Use of Amalgam Electrodes to solution was measured separately, and was in every Measure Activity Coefficients of Multicomponent Electrolyte Solutions,” Interim Report No. 2, Office of Saline Water, Research and case high enough to avoid interference with the sodium Development Progress Report No. 486, 1969, Interim Report No. response of the glass electrode. 3, in preparation, 1970. Results Representative potential measurements obtained with the amalgam electrode cell are given in Tables I and 11. The values (AE) given are the difference in potential between a cell containing the mixed electrolyte and a cell containing the NaCl stock solution. The amalgam composition was the same, since both cells were fed from the same amalgam reservoir and were measured simultaneously. The Ag-AgC1 electrodes were matched to better than hO.01 mV. Activity coefficients of NaC1 in the mixed electrolyte (YIJ were calculated from the equation
(7) J. N. Butler, P. T. Hsu, and J. C. Synnott, J . Phys. Chem., 71, 910 (1967). (8) J. N. Butler, “The Use of Amalgam Electrodes to Measure Activity Coefficients of Multicomponent Electrolyte Solutions,” Interim Report No. 1, Office of Saline Water, Research and Development Progress Report No. 388, 1968. (9) J. N. Butler and R. Huston, J . Phys. Chem., 71,4479 (1967). (10) R. Huston and J. N. Butler, Anal. Chem., 41, 1695 (1969). (11) G. A. Rechnitz, Chem. Eng. News, 45, 146 (1967). (12) G. L. Gardner and G. H. Nancollas, Anal. Chem., 41, 202 (1969). (13) G. Gran, AnaZyst (London), 77, 661 (1952). (14) R. A. Robinson and R. H. Stokes, “Electrolyte Solutions,” Butterworths, London, 1965. (15) H. S. Harned and B. B. Owen, “The Physical Chemistry of Electrolyte Solutions,” Reinhold, New York, N. Y., 1958. The Journal of Physical Chemistry, Vol. 74, No. 16,1970
2978
JAMES N. BUTLER AND RIMAHUSTON
Table I1 : Activity Coefficient Measurements in
Table I11 : Harned Rule Coefficients
NaCI-NazCOa Electrolytes a t 25": [Cell: AgIAgCl/NaCl, NazCOs, HzOlNa( Hg)] Total ionic
AE9
-log
YlZ
strengtha
x1
pHb
mV
(exptl)
0.5685 0.5575
1.0000 0.9096
8.3 10.24
0.5062
0.4868
10.89
0.4699
0.1880
11.07
0.4585
0,0944
10.99
0 3.57 3.70 26.98 26.65 56.50 56.10 77.30 76.97
0.1707 0.1707 0.1718 0.1817 0.1789 0.1794 0.1761 0.1893 0.1865 0,1832 0.2085 0.2076 0.2265 0.2240 0.2301 0.2273 0.1448 0.1845 0.1786 0.2112 0.2104 0.2475 0.2466 0,2715 0,2692 0.1832 0.2441 0.2420 0.2764 0,2744 0.2797 0.2784
1.0315 1 0092
1,0000 0.5069
9.04 10.1
0.9923
0.1357
10.8
0.9883
0.0483
10.9
3.0487 3.0247
1.0000 0.7459
10.90 10.98
2.9973
0.4831
11.15
2.9762
0.2621
11.00
2.9523
0.0532
11.35
1.0315' 1.9883c
1.0000 0.5051
9.04 10.3
2 . 6857'
0.1444
11.0
2 . 8762'
0.0458
11.2
I
0 25.50 25.40 66.10 65.80 94.28 93.95 0 14.70 14.00 31.80 31.71 54.40 54.30 100.92 100.65
0 15.15 14.90 45.64 45.88 74.50 74.34
PH
IQ
0.50 1.00
8.2-9.2 8.2-8.6
0.050 f 0.009 0.045 & 0.003
I
NaC1-NaaC03 0.50 1.00 3.00
10.2-11.1 10.5-10.9 10.9-11.4
0.048 =t0.016 0.049i0.003 0.044 rt 0:003
a Note: I is formal ionic strength, held constant for the series; mz; for NaCI-NazCO3, I = for NaCI-NaHC03, I = ml ml 3mz. The effect of protonation equilibria on ionic strength is not included. Errors on ala are 9570 confidence limits obtained by the method of least squares, allowing the intercept to vary.
+
+
... ... ... .,.
...
... ...
+
a I = ml 3mal X 1 = ml/Z (protonation equilibria not included in calculating ionic strength). pH of 0.33 m Na2C03 = 11.06; pH of 1.0 m NazCOs = 11.42. e These four solutions were a t constant total molality rather than constant ionic strength.
Within experimental error, Harned's rule was obeyed for the amalgam electrode measurements in all solutions tested. Values of a12 obtained by a leastsquares fit to the corrected ylz data in Tables I and I1 are given in Table 111. For all solutions tested at ionic strengths from 0.5 to 3.0, whether the second component was NaHC03 or NazC03, the Harned rule coefficient fell in the range 0.045 to 0.050. This is an unexpectedly simple result. The glass electrode measurements in general confirmed the amalgam electrode results, but were less precise and apparently also less accurate. I n particular, systematic deviations of the glass electrode measurements (Figure 1) occurred a t low fractions of KaC1 in a direction which would imply that the activity of sodium ion in the vicinity of the glass surface was considerably enhanced over that in the bulk. (These were not observed with the amalgam electrode cell.) The Journal of Physical Chemistry, Vol. '7.4, No. 16, 1970
NaC1-NaHC03
-log 71% (cor)
0 1669 0.1671 0.1682 0.1812 0.1784 0.1821 0.1788 0.1932 0.1904 0.1824 0.2081 0.2072 0.2269 0.2244 0.2308 0.2280 0.1465 0,1851 0.1792 0.2112 0.2104 0.2475 0.2466 0.2719 0.2696
aiz
0 17 0
0.1
02
I
I
I
I
03
04
05
06
I 07
I OB
I 09
1.0
XI
Figure 1. Activity coefficients of NaCl in NaC1-NaHCOa electrolytes a t ionic strength 1.0 m. Note deviations of glass electrode data and agreement of amalgam electrode data with Harned's rule.
The most pronounced deviations of this type were found in dilute NaC1-KaHCO3 electrolytes; they were noticeable but less pronounced in SaC1-Sa2COa electrolytes a t low concentrations and were negligible at high concentrations (Figure 2 ) . Differences between glass electrodes B and C were noticeable, particularly in the dilute NaC1-SaHC03 electrolytes. There may also be an aging effect. Full data from these experiments are available.6 These differences appear to result from a specific but as yet unexplained effect on the glass electrode. Although the solutions used in the amalgam electrode experiments were somewhat more basic than those used in the glass electrode experiments (because of the addition of approximately 0.001 m S a O H to the NaCl stock solution), the effect of this on ionic strength is negligible, corresponding to less than 0.002 mV error. The amalgam electrode experiments were also carried
2979
ACTIVITY COEFFICIENTS OF NaCl Y L”
the solutions contain a fixed concentration of chloride already, the reference electrode was Ag-AgC1. The indicator electrode was a conventional glass pH electrode (Beckman 39301). The potential of the cell
0 NaiHg) electrode
+ Glass electrode (8) 026-
A
Glass elcctrodc (C)
0 24
Ag/AgCIICl-, Na+, C O F , HCOs-, etc.lglass 022N
r; D f oeo018-
f
\
IrnV
016-
0140
I 01
may be written in the form
I 02
I 03
I 04
,,A
05
06
07
08
09
10
out in closed vessels using solutions saturated with hydrogen, but any concentration changes due to removal of carbon dioxide by the hydrogen were estimated to have a negligible effect (
