ISOPIESTIC MEASUREMENTS ON THE SYSTEM H20-NaC1-MgC12
AT
4053
25”
pressed in Harned’s rule,16 I n Table VI1 values are given for the quantities
-0.1
c
= [log (Y*A(B)/Y*A(A))
]/I
QBA
= [log (Y*B(A)/Y*B(B))
1/I
and
-0.5
0
&AB
0.5
t.0
YM,S04
Figure 8. Activity coefficients of MgCll in MgSOa:
+, estimate from two-component data.
estimates varies from 3 to 8% in yf. At I = 6, however, the error varies from 11 to 56%. I n general, the systems investigated here follow well the linear relationship between log Y&:A and YB as ex-
where Y&A(B) is the activity coefficient of component A in a pure solution of component B (YB = 1) and Y ~ A ( A ) is the activity coefficient of component A in a pure solution of component A (YB = 0), with analogous definitions for the quantities involved in QBA. These quantities thus represent a straight-line approximation for the variation of log yk with y using the end points to define the straight line. This approximation is exact only for the system MgSOdMgC12-H20. The deviations from the straight line in are all 1% in yk or less except for log NaZSOa, where the deviation is 3% at I = 6.
Acknowledgment. We express our appreciation to J. S. Johnson, K. A. Kraus, and R. J. Raridon for helpful discussions. (16) H. S. Harned and B. B. Owen, “The Physical Chemistry of Electrolytic Solutions,” 3rd ed, Reinhold Publishing Corp., New York, N. Y., 1968, Chapter 14.
Isopiestic Measurements on the System Water-Sodium Chloride-Magnesium Chloride at 25 by R. F. Platfordl Marine E C O ~ O Laboratory, Q~ Fkheries Research Board of Canada, Dartmouth, Nova Scotia, Canada
(Received M a y 27,1968)
Activity coefficients for the salts in the system H20-NaC1-MgC12 at 25” were derived from isopiestic measurements. The isopiestic data were treated by both the methods of McKay and Perring and of Scatchard, and the results agree well with each other; at ionic strengths up to 3 they agree with those calculated from emf measurements. At constant ionic strength the activity coefficient of each salt was increased by increasing proportions of the other salt. The Harned’s rule coefficients at ionic strengths of 1, 3, and 6, respectively, were -0.016, -0.011, and -0.009 for NaCl and -0.006, -0.014, and -0.014 for MgClz.
Introduetion Activity coefficients of the salts in several ternary systems consisting of aqueous mixtures of 1-1 and 2-1 salts have been calculated from isopiestic data using the McKay-Perring method or some form of the cross differentiation expressions.2-6 This paper is the third in a series of isopiestic studies on seawater analogs, the
other two systems being H20-NaC1-R’IgS046 and HzONaC1-Na2S04.7 These isopiestic results can be com(1) Canada Centre for Inland Waters, Burlington, Ontario, Canada. (2) H. A. C. McKay and J. K. Perring, Trans. Faradau Soc., 49, 163
(1953). (3) R. A. Robinson and V. E. Bower, J . Res. Nat. Bur. Stand., A, 69, 19 (1966). Volume 72?Number 18 November 1968
R. F. PLATFORD
4054 pared with activity coefficients derived from emf measurements made in aqueous mixtures of NaCl and n!sgci2.8,9
+0.01,1
I
I
I
I
I
I
I
,
7
Experimental Section (1) Reagents. Sodium chloride was precipitated with HCl and was fused at 850" in a platinum dish, Magnesium chloride was recrystallized from water and was dried at 50" under water-pump vacuum to give MgC12.6H20. Isopiestic comparisons of the osmotic coefficients of the two salts agreed within 0.5% with the values quoted by Robinson and Stokes.1° (2) Procedure. Seven solutions were equilibrated at 25" in each run, for times varying from 3 days for the most concentrated solutions to 7 days for the least concentrated ~olutions.8~~ Equilibrium concentrations were determined by weighing the dried salts into the vapor pressure dishes, adding water, and then reweighing the dishes containing the solutions after equilibration. Solutions containing MgClg 6H20 were corrected for contribution of water, and all weights were corrected to in UUCUO. The concentration of saturated NaCl at 25" was taken to be 6.1443 m.I1 0
Figure 1. The integral in eq 2 and 3.
The Scatchard treatment is simplified1*if the osmotic coefficient, 4, of the mixed solution can be expressed as (YA
+ 114
= 2yA4A0
+
Y B h n
+A
(4)
YE)
(5)
where A
+
POYAYB
-
P~MAYB(YA
in which
Results The isopiestic results were treated by two methods. (1). Robinson2 has shown that if for a given set of measurements on a mixed solution
R
=
1-
UZB
- ~XB'
(1)
then the activity coefficients calculated by the NIcKayPerring treatment are log Y A = log FA
+ log R +
The isopiestic ratios are shown in Table I as a function of solution composition, and the integral in eq 2 and 3 is shown in Figure 1. The activity coefficients calculated from eq 2 and 3 are given in Table 11. The uncertainty in the log y values is about .t0.004, most of which is due to the uncertainty in the integral term shown in Figure 1. (2) The second method was an alternate treatment by Scatchard,12 which has been recently applied to several system^.'^-^^ By using the Debye-Huckel expression as a guide in the low-concentration region, Scatchard eliminated the uncertain extrapolation to m = 0, which is needed to evaluate the McKay-Perring integral term. The Journal of Physical Chemistry
and = b1212
+
b131S
(7)
For some of the systems treated by this method, certain of the bjk coefficients in eq 6 and 7 disappear. For example, in the three systems H20-NaC1-KC1,14 l 3 the coH z O - K C ~ - C ~ Cand ~ ~ , Hz0-HC104-LiC104, ~~ efficients ba3, bI2, and bI3 are zero, and in the system H20-HC104-NaC104,13 b12 is zero. The deviation function A is plotted in Figure 2 for the H20-ATaCl-MgC12 data. The curves are skewed because 01 is finite. The standard deviation in the quantity 4coalod - 4 o b s d is 0.002 and is not significantly increased by putting bo3 and b12 equal to zero. The coefficients in eq 6 and 7 for H20-NaC1-R/IgC12 are16bo' = 0.0464, bo2 = -0.00296, bo3 = 0, bL2 = 0, and (4) R. A. Robinson and V. E. Bower, J . Res. Nat. Bur. Stand., A , 69, 439 (1965). (5) R. A. Robinson and V. E. Bower, ibid., A , 70, 313 (1966). (6) R. F. Platford, Can. J . Chem., 45, 821 (1967). (7) R. F. Platford, J . Chem. Eng. Data, 13, 46 (1968). (8) R. D. Lanier, J . Phys. Chem., 69, 3992 (1966). (9) J. N. Butler and R. Huston, ibid., 71, 4479 (1967). (10) R. A. Robinson and R. H. Stokes, "Electrolyte Solutions," Butterworth and Co. Ltd., London, 1965, Appendix 8.10. (11) G. Scatchard, W. J. Hamer, and S. E. Wood, J . Amer. Chem. SOC.,60, 3061 (1938). (12) G. Scatchard, ibid., 83, 2636 (1961). (13) R. M . Rush and J. S.Johnson, J . Phys. Chem., 72, 767 (1968). (14) R. M. Rush and R. A. Robinson, J . Tenn. Acad. Sci., 43, 22 (1968). (15) R. A. Robinson and A. K. Covington, J . Res. Nut. Bur. Stand A , 72, 239 (1968).
ISOPIESTIC MEASUREMENTS ON THE SYSTEM H20-NaCl-MgC12
AT
4055
25" ~~
~~
Table I : Isopiestic Compositions for the Ternary System H20-NaC1-MgC12 Set
I
R
IIB
0.1115 0.1213 0.1262 0.1714 0.1835 0.2111 0.2403
0 0.1506 0.2138 0.6421 0.7423 0.8768 1.o
1.o 0.9942 0,9895 0.9585 0.9656 0.9399 0 9277
7
2
0.1777 0.2028 0.2518 0.3076 0.3287 0 I3744
0 0.2334 0.5576 0.8007 0.8716 1.0
1.o 0.9925 0.9782 0.9626 0.9581 0.9493
3
0.2958 0.3071 0,3235 0.3717 0.4896 0.5383 0.6264
0 0.0644 0.1596 0.3826 0.7526 0.8594 1.o
1.0 0.9953 0.9936 0.9840 0.9685 0.9636 0.9442
0.5467 0.6658 0.8141 0.9718 1.1074 1.1337
0 0.3388 0.6290 0.8428 0.9742 1.0
1.o 0.9887 0.9799 0.9724 0.9627 0.9646
0.5797 0.6921 0.7990 0.9216 0.9714 1.0513 1.1457
0 0.3261 0.5508 0.7477 0.8163 0.9089 1.o
1.o 1.0005 1.0012 1.0045 1.0083 1.0106 1.0121
0.7064 0.7633 0.8085 0.9444 1.1631 1.1852 1.4172
0 0.1501 0.2539 0.5045 0.7815 0.8072 1.0
1.o 1,0006 1.0007 1.0003 0 9970 0.9993 0.9970
1
4
5
6
I
Set
(+BO
bo212 (-1/,bw
+
IIB
R
3.6190 3.8922 4.3219 4,9056 5.0586 5.3859 5.4417
0 0.2139 0.4913 0.7889 0.8543 0,9801 1.0
1.0 1.0411 1.1100 1.2182 1,2489 1.3176 1.3301
1.o
8
1.1417 1,2276 1,5885 1,6732 1.8380 2.0030 2.1249
0 0.1530 0.6095 0.6867 0.8179 0.9300 1.0
1.o 1.0071 1,0337 1.0391 1.0150 1.0655 1.0746
14
4.2487 4.5204 5.2085 5.6203 5.8781 5.9985 6.1788
0 0.1970 0.5995 0.7891 0.8929 0.9377 1.o
1.0 1,0426 1.1649 1.2486 1.3057 1.3335 1.3753
9
1.6913 2.0489 2.3840 2.7500 2.9555
0 0.4088 0.6813 0.9016 1.o
1.o 1,0375 1.0759 1.1199 1.1446
15
0 0.1868 0.3676 0.6065 0.8943 0,9633 1.o
1.o 1,0406 1.0900 1.1758 1,3209 1,3662 1.3917
10
1.9671 2.0776 2.4550 2.6670 2.8974 3.2132 3.3447
0 0.1306 0.4832 0.6392 0.7803 0.9429 1.0
1.o 1.0130 1.0565 1.0841 1.1132 1.1582 1.1762
4.5139 4.7847 5.0738 5.5101 6.1815 6.3743 6.4872
16
4.9365 5.1038 5.2342 6.1043 6.6267 6.6790 6.9522
0 0,1193 0.2046 0.6727 0.8860 0.9059 1.0
1.o 1,0286 1,0506 1.2185 1.3374 1.3511 1,4202
2.5460 2.7947 2.9795 3.5130 3.8875 4.0163 4.1157
0 0.2366 0.3842 0.7249 0.9057 0.9608 1.o
1.0 1.0332 1,0577 1.1367 1.1970 1.2201 1.2372
17
3 2639 3.4090 4.1522 4 5936 4 6346 4.9039 5.0217
0 0.1241 0.6192 0.8347 0.8502 0.9580
1:il 1.0207 1.1386 1.2195 1.2250 1.2774 1.2999
6.1443 6.3368 6.4697 7.1332 7.2352 7.4004 7.6749 7.7090 0.7676 7.8892 8.0144 8.0214 8.2653
0 0.1133 0.1970 0.5471 0.5995 0.6723 0.7891 0,8008 0 8260 0.8708 0.9171 0.9191 1.0
1.0 1.0278 1.0535 1.1857 1.2127 1,2506 1,3222 1,3293 1.3476 1.3794 1.4160 1.4173 1.4868
11
12
I
+ 1 + boll +
b'a13)yB
I
13
0 0.1967 0.4612 0.5747 0,7895 0.9448
I
- ~+AO
Set
1.0496 1.1576 1.3425 1.4408 1,6689 1,8881 1* 9797
= -0.000644. Only solutions having ionic strengths between 1 and 6 were used in evaluating these coefficients. (This excluded all data in sets 1-6 and 17.) If bo3 and b12 are zero, the activity coefficients of the two salts in the mixture are given by the two expressions'e =
R
1.0 1.0057 0.1062 1.0223 1,0392 1.0537 1.0604
b13
2 In (TA/TA')
IIB
+
+
- 2b1313)yB2
(2 / a b ' 3 1 3 ) ~ ~ a (8)
1.o
I
and
In
(TBIYBO) = (%A' - +Bo - 1 + bo'l bo212
( - l/,b0212
- b l 3 1 3 ) YA
+
+
+ 2bla13)yA2-
(9) The mean activity coefficients calculated from the (2/8b'31a)yA3
(16) I am grateful to Dr. R. M. Rush of the Oak Ridge National Laboratory for calculating these coefficients. The author has made the YB values consistent with those of M. H. Lietzke and R. W. Stoughton, J. Phys. Chem., 66, 508 (1962), which were used by Rush.
Volume 7.2, Number 12 November 1968
4056
R. F. PLATFORD
Table 11: Mean Activity Coefficients in the System HzO(w)-NaCl(A)-MgClz(B) a t 25"
-
Log y-A -2@
M-Pa
0 0.2 0.4 0.6 0.8 1.o
-0.182 -0.181 -0.180 -0.178 -0.177 -0.176
-0.182 -0.179 -0.176 -0.173 -0.169 -0.166
0 0.2 0.4 0.6 0.8 1.0
-0.146 -0.141 -0.136 -0.131 -0.126 -0.120
-0.146 -0.141 -0.135 -0.128 -0.121 -0.113
0 0.2 0.4 0.6 0.8 1.0
-0.006 0.000 0.007 0.016 0 027 0.037
-0.006 -0.002 0.006 0.018 0 032 0.049
I
a Present work, McKay-Perring treatment. ments, Butler, et aL9
LOP YE-
Bd
M-Pa
Sb
1=1 -0.182
-0.183
-0.168
-0.168
-0.322 -0.323 -0.324 -0.326 -0.327 -0.328
-0.322 -0.323 -0.324 -0.326 -0.327 -0.328
1 = 3 -0.146
-0.147
-0.115
-0.114
-0.219 -0.224 -0.229 -0.234 -0.240 -0.246
-0.203 -0.211 -0.220 -0.228 -0.237 -0.246
I = 6 -0.006
-0.006
0.030
-0.009
LC
Sb
Present work, Scatchard treatment.
0 094 0.078 0.063 0.047 0.032 0.018
0.104 0.091 0.078 0.063 0.043 0.018
Emf measurements, Lanier.8
d
Emf measure-
~
~-
Table I11 : Harned's Rule Coefficients for H20-NaC1-MgC12 I = O
1 3 1
1 - 3
-0.026"
-0.016 -0.019 -0.016 -0.0146
-0.011 -0.011 -0.012 -0.0104
O.OIOa
-0.006
0.01425
-0.012 -0.006" -0.0137"
-0,014 -0.016 -0.016" -0.0159a
1=6
Ref
-0.009 -0.007 0.0004 -0.0060
This work 17 9 8
-0.014 -0.017 -0.002" -0.0148"
This work 17 9 8
a12
-0.0238"
a21
Q
YA
Figure 2. The deviation function in eq 4, plotted a t three ionic strengths. A = (768 l)$ - 2y,+Ao - y&Eo.
+
isopiestic measurements are given in Table I1 along with the YA values measured by the emf methods. The Harned's rule coefficients are given in Table 111, and ytr values are plot,ted in Figure 3. Some preliminary values by Wu, et aZ.,17 are included in Table 111.
Discussion The agreement between the two methods of treating The Journal of Physical Chemistry
Calculated indirectly.
the isopiestic results is good; the average variation in yt' is 0.009, of which about 0.003 is due to the uncertainty in the McKay-Perring integral term. Because of this uncertainty, the results treated by the Scatchard method are considered the more reliable and are those plotted in Figures 3 and 4 and given in Table 111. The subscripts referring to the two salts are "mixed" to make the coefficients in Harned's equation consistent with those of the other workers quoted in Table 111. At I = 1 and 3, log ytr values of the author agree with the log yAt' values of Lanier and Butler within 0.002, and with both the log y ~ and ~ 'log y ~ of~Wu, ' within (17) Y . C. Wu, R. M. Rush, and G. Scatchard, personal cornmunice tion.
ISOPIESTIC MEASUREMENTS ON THE SYSTEM H20-NaCl-MgC1,
AT
4057
25"
i Figure 4. Harned's rule coefficients for H20-NaCl-MgC12 as a function of ionic strength. Figure 3. Mean activity coefficients in aqueous mixtures of NaCl(A) and MgCb(B) as a function of ionic strength: - - - -, activity coefficients in binary systems; -- , trace activity coefficients.
0.005. However, at I = 6 there are differences among the various results of about 0.01 in log yt', and there is a difference (0.05) between Butler's value for log y ~ and ~ ' the isopiestic values, which may be greater than experimental error and for which the author can offer no explanation. Nly results agree with Lanier's actual experimental results at I = 6 (see Figure 3, ref 8), and show that there is probably a small quadratic term needed in Harned's equation at I = 6. The Harned coefficients in Table I11 and Figure 4 were calculated from log (~O/T'')/Iand do not take into account any quadratic terms. The author did this in the interest of simplifying the comparison among the various values. The finite slope of the plot of 1/2(2a12 ael)us. I is simply confirmationa that there are additional square terms required to complete Harned's rule for this system. The finite value of the ordinate in Figure 4 indicates that the excess free energy of mixing is also finite.4 It is given approximately by
+
AGE' = -2.3RTI2(2al2
+
a21)/8
(10)
At I = 1, 3, and 6, AGE = 6.6, 55, and 190 cal/kg of water, respectively. These relatively large values are consistent with those for the other alkaline earths represented by M in the series H20-NaC1-MC12. The AGE a t any given I were found to increase with the de-
creasing atomic weight of $1. (At I = 1 and for M = Ba,*Ca14and Mg, AGE = -2, 4, and 6.6, respectively.) If this generality holds for all members of the series, AGE for M = Sr should be between -2 and 4 at I = 1.
Acknowledgments. I wish to thank Drs. R. A. Robinson, R. M. Rush, and Y. C. Wu for supplying me with preprints of some of their work and for giving me preliminary experimental data on pertinent systems. I am also grateful to B. R. Kerman for modifying the program used in computing the McKay-Perring coefficients.
Molalities of NaCl and MgC12, respectively, in the mixed solution Activity coefficients of NaCl and MgC12, respectively, in the mixed solution above Activity coefficient of M A m NaCl solution or MB m MgCl2 solution in isopiestic equilibrium with the mixed solution MA/(mA f 1 . 5 m ~ ) 1 . 5 M ~ / ( m ~1.5m~) 1.5mB/(mA 1.5m~) mA/(mA 3mB) = mA/I = 1 - YB Osmotic coefficient of M A m NaCl Osmotic and activity coefficients, respectively, of NaCl solution having the same ionic strength, f, as the mixed solution Activity coefficient of an infinitesimally small concentration of NaCl in a solution of MgC12 -In (Uw)/[O.o18(2mA f h B ) ]
+
+ +
Volume 7.9, Number 13 November 1968
