ARVINS. QUISTAND WILLIAML. MARSHALL
2100 3 together represent the formation of one layer of adsorbed water but the quantity of water involved is the weight equivalent of two chemisorbed monolayers. Deviations from these ideal values for AH, in the case of
samples A, B, G, and H are attributed to surface heterogeneities resulting from their small crystallite size and resulting interstices between these small crystallites in the primary particles.
Electrical Conductances of Aqueous Sodium Bromide Solutions from 0 to 800"and at Pressures to 4000 Bars1 by Arvin S. Quist and William L. Marshall Reactor Chemistry Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 57850 (Received November 3, 1967)
The electrical conductances of dilute (0.002-0.015 m) NaBr solutions were measured from 0 to 800" and to 4000 bars pressure. Isothermal limiting equivalent conductances were calculated from these measurements and were found to be linear functions of the solvent density. At temperatures of 400" and above, at constant solvent density, Ao(NaBr)was independent of the temperature; moreover, the value of the limiting equivalent conductances extrapolated to zero solvent density (1880 om2ohm-' equiv-1) was very close to those obtained previously for other 1: 1 electrolytes, indicating that perhaps all 1:1electrolytes may have nearly the same value of limiting equivalent conductance under these conditions. Equilibrium constants for the ionization of NaBr were calculated from the data at high temperatures where NaBr behaves as a weak electrolyte. By considering hydration to be an essential part of the dissociation process, isothermal equilibrium constants were obtained that were independent of solvent density.
Introduction Several researches in recent years have indicated that aqueous electrolyte solutions at high temperatures and pressures, particularly in the supercritical region, exhibit a simplicity in behavior not found in their room temperature counterparts. For example, it has been observed that isothermal limiting equivalent conductances of KHS04,2 NaClj3 and HBr4 are linear functions of solvent density a t 100-800". Moreover, a t temperatures of 400-800", A i s for a particular electrolyte appeared to be independent of temperature (at constant solvent density). It was also observed that at temperatures of 400" and above, when A0 is plotted against solvent density and the linear relationship extrapolated to zero density, the limiting equivalent conductances at zero density for KHS04 (under conditions where it behaved as a 1:1 electrolyte),2NaCIj3and HBr4 were all near 1800 f 80 om2ohm-' equiv-'. The present paper contains the results of measurements of the electrical conductances of dilute (0.0020.015 m) NaBr solutions from 0 to 800" and to 4000 bars pressure. From these measurements, limiting equivalent conductances of NaBr were obtained at integral temperatures and densities. Sodium bromide b d ~ v e s as a progressively weaker electrolyte with increasing temperature; consequently, at temperatures of 400" The Journal of Physical Chemistry
and above, ionization constants could be calculated from the data. To our knowledge, these are the first conductance measurements on this electrolyte a t elevated temperatures and pressures.
Experimental Section An earlier paper3 contains a complete description of the equipment and procedures used for these measurements. The most recent model of the conductance cell (no pressure seals in the high-temperature region) was used exclusively. All solutions were prepared from reagent grade sodium bromide (J. T. Baker Co., Phillipsburg, N. J.) and conductivity water (obtained from a quartz distillation unit). To provide additional verification of the concentrations of these solutions, their conductances were measured at 25.00 f 0.01" in a glass conductance cell, and these values agreed with previously reported conductances of NaBr solutions. With the use of the high-temperature high-pressure cell, conductance measurements were made to 800" and 4000 bars on five solutions of NaBr, 0.002010, 0.005000, (1) Research sponsored by the U. S. Atomic Energy Commission under contract with Union Carbide Gorp, (2) A. s. Quist and w. L. Marshall, J . P ~ U S . Chem., 70, 3714 (1966). (3) A. s. Quist and w. L. Marshall, ibid., 72,884 (1968). (4) A. S. Quist and W. L. Marshall, ibid., 72, 1536 (1968).
ELECTRICAL CONDUCTANCES OF AQUEOUS SODIUM BROMIDE SOLUTIONS 0.007000, 0.01000, and 0.01496 m. Three different inner electrodes were used for these measurements. Their cell constants were 1.96,0.510, and 0.489 cm-l as determined with 0.01 and 0.1 demal KCl solutions at 25.00 * 0.01'.
2101
800
0.0l000rnolol' NoBr
Results and Discussion The measured conductances were converted to specific conductances and equivalent conductances by the methods described earlier.3 An example of isothermal specific conductances for 0.01000 m NaBr solutions as a function of pressure is shown in Figure 1 at the temperatures of the measurements. The curve where individual points are not shown represents averages of two or more separate runs at approximately the same temperature and ordinarily with the use of different inner electrodes for each run. Isobaric specific conductances of 0.01000 ?n NaBr solutions as a function of temperature are shown in Figure 2. The graphs for the other concentrations of NaBr are similar in shape to those for the 0.01 m solution. Figure 3 gives isothermal equivalent conductances of 0,01000 m NaBr as a function of solvent density. The other concentrations of NaBr exhibit similar behavior, except that the density at which the nzaximum in equivalent conductance occurs increases with increasing solution concentration. For 0.002010 m NaBr the maximum occurs near 0.55 g ~ m - and ~ , for the 0.01496 m solution it is near 0.65 g ~ m - ~ This . behavior was previously observed with the NaCl solutionsa and indicates that there is increasing association of the sodium and bromide ions with increasing temperature and decreasing solvent density. From graphs such as those in Figure 3, equivalent conductances were obtained at integral densities. When these values were plotted against temperature (at constant density), equivalent conductances at integral temperatures and densities were obtained by interpolation and extrapolation. These equivalent conductances for the
1
0
200
400
800
600
TEMPERATURE ('C),
Figure 2. Isobaric variation of specific conductances of 0.01000 m NaBr solutions with temperature a t pressures from 500 to 4000 bars.
I
I
I
I
I
0.8
1.0
I3
800
T 600
-3 k N
S 400 4
200
" 0.2
0.4
0.6 DENSITY
((I
cnr3)
Figure 3. Equivalent conductances of 0.01000 m NaBr solutions as a function of density at several temperatures.
0.01000 molal NoBr I
five concentrations of NaBr are given in Tables I-V. The values in parentheses represent conductances at saturation vapor pressure at that temperature. Calculation of Limiting Equivalent Conductances. From the conductances given in Tables I-V, limiting equivalent conductances were calculated by the several methods described previously.s At low temperatures and high densities, the Robinson-Stokes equation,6 the Fuoss-Onsager equation,eand the Shedlovsky equation (including an ionization constant)' gave essentially "
0
IO00
2000
3000
4000
6000
PRESSURE (bars1
Figure 1. Specific conductances of 0.01000 m NaBr solutions as a function of pressure at several temperatures.
(5) R. A. Robinson and R. H. Stokes, J . Am. Chem. SOC.,76, 1991 (1954). (6) R.M. Fuoss, L. Onsager, and J. F. Skinner, J. Phys. Chem., 69, 2581 (1965). (7) T. Shedlovsky, J . Franklin Inst., 225,739 (1938). Volume 78, Number 6 June 1968
2102
ARVINS. QUISTAND WILLIAML. MARSHALL
Table I: The Equivalent Conductances (cmz ohm-' equiv-1) of 0.002010 m NaBr Solutions at Integral Temperatures and Densities Density,
Temp, 0.30
OC
100 150 200 250 300 350 400 450 500 550 600 650 700 750 800
0.35
0.40
0.45
0.50
0.55
0.60
g
---
om-:
0.65
0.70
0.75
0.80
0.85
0.90
7
0.95
1.00
(347)
(940)
320 240 185 150 120 100 90
860 780 710 650 590 550 505 480
560 470 400 350 310 280 265
1000 945 890 850 810 775 740 710
1055 1030 1000 970 935 900 850 815
1075 1060 1040 1010 985 960 925 890
1070 1060 1045 1025 1005 984 960 935 910
1035 1030 1020 1005 987 968 950 928 908
995 990 980 970 955 935 912
905 925 936 940 936 930 915 898 878
850 874 884 888 886 876 858
628 695 740 766 778 778
(653) 741 795 823 835 835 828
328 438 532 596 633
580 642 686 710 728
Table 11: The Equivalent Conductances (cmz ohm-' equiv-l) of 0.005000 m NaBr Solutions a t Integral Temperatures and Densities Density, g o
Temp, OC
100 150 200 250 300 350 400 450 500 550 600 650 700 750 800
0.30
0.35
0.40
0.45
0.50
0.55
0.60
0.65
r 0.70
(900)
260 190 145 120 95 80 70
435 350 290 255 230 210 200
710 620 550 500 450 410 380 360
860 790 735 690 645 605 570 545
950 910 880 840 800 760 720 670
990 965 935 910 880 845 810 770
1012 1000 982 960 940 915 888 860 830
990 980 968 952 935 916 898 875 855
962 956 945 930 912 894 872
0.75
868 892 905 908 904 895 882 864 840
n 0.80
824 850 865 870 864 852 832
0.85
0.90
(635) 718 774 806 820 820 810
610 675 720 746 762 764
8 0.95
8 1.00
(342)
323 427 518 582 618
564 627 670 695 712
Table 111: The Equivalent Conductances (cmz ohm-' equiv-') of 0.007000 m NaBr Solutions at Integral Temperatures and Densities Temp,
OC
400 450 500 550 600 650 700 750 800
Density, 0.35
360 255 220 200 185 170
0.40
485 430 385 350 320 300
0.45
655 610 560 520 490 460
g
om-'
-
0.50
0.55
0.60
0.65
0.70
0.75
0.80
0.85
0.90
0.95
968 955 940 922 904 884 863 840 815
940 930 920 907 890 870 850
894 894 886 874 856 837 814
852 855 848 834 814
806 805 796
756 755
820 775 735 690 650 600
970 955 935 915 895 870 840 815 780
704
940 920 890 860 820 780 740 705
the same limiting equivalent conductances. However, factorily. These limits are about the same as were previously observed with the NaCl data.3 a t densities of 0.70 g cm-3 and below, the RobinsonStokes equation did not represent the data as well as Limiting equivalent conductances for NaBr are given the other two equations, and below O.GO-O.G5 g ~ m - ~in Table VI. The standard errors associated with the A,)s in Table VI are less than 1% at densities of 0.65g only the Shedlovsky equation fitted the data satisThe Journal of Physical Chemistry
ELECTRICAL CONDUCTANCES OF AQUEOUS SODIUM BROMIDE SOLUTIONS
2103
Table IV: The Equivalent Conductances (cmz ohm-' equiv-") of 0.01000 m NaBr Solutions at Integral Temperatures and Densities Temp, 'C
100 150 200 250 300 350 400 450 500 550 600 650 700 750 800
0.30
0.35
Density, g om-a
_ _ _ I
0.40
0.45
0.50
0.55
0.60
0.65
0.70
(855)
225 160 125 100 80 65 55
480 360 280 230 200 180 160 145
610 520 450 390 350 315 285 265
760 680 620 570 530 490 455 425
840 805 770 730 690 645 600 560
905 880 850 815 780 745 705 660
935 925 906 885 860 835 805 775 740
940 930 915 898 875 852 830 805 776
912 908 900 885 868 845 822
0.75
838 864 877 877 866 852 832 810 785
0.80
800 823 837 840 832 820 796
0.85
(616) 697 750 782 796 795 784
0.90
595 659 705 733 746 746
0.95
1.00
(337)
320 420 506 568 605
550 613 655 682 697
Table V : The Equivalent Conductances (cmz ohm-' equiv-I) of 0.01496 m NaBr Solutions a t Integral Temperatures and Densities -Density, g crn-L----
Temp, O C
100 150 200 250 300 350 400 450 500 550 600 650 700 750 800
0.30
0.35
0.40
0.45
0.50
0.65
0.60
0.65
0.70
(840)
200 140 100 75 60 45 40
440 325 245 195 165 140 130 120
560 465 390 340 300 270 245 230
700 630 570 520 480 440 400 370
790 755 710 670 630 585 540 485
850 825 795 765 730 690 640 600
905 890 870 845 816 786 760 725 690
906 898 884 862 840 818 792 765 735
890 884 874 860 840 818 790
0.75
815 840 855 855 848 832 815 794 768
0.80
784 805 818 822 816 800 775
0.85
(605) 685 737 768' 782 780 770
0.90
583 645 692 720 735 734
-
0.95
1.00
(330)
314 413 498 558 595
542 603 645 670 687
Table VI : Limiting Equivalent Conductances (cmz ohm-' equiv-1) of NaBr a t Integral Temperatures and Densities OC
100 150 200 250 300 350 400 450 500 550 600
650 700 750 800
-
Density, g om-*
Temp,
0.36
0.40
0.45
0.50
0.55
0.60
0.65
0.70
0.75
0.80
0.85
0.90
0.95
(359)
(1005)
1100 1100 1200 1200 1300 1100 1400
1250 1290 1400 1450 1400 1500 1500 1500
1280 1270 1250 1270 1250 1275 1350 1450
1260 1250 1250 1230 1220 1210 1190 1230
1220 1220 1200 1180 1160 1160 1150 1140
1175 1170 1155 1140 1125 1110 1090 1075 1060
1115 1110 1105 1090 1075 1060 1050 1030 1020
1065 1060 1050 1040 1030 1010 990
958 978 990 995 995 995 980 965 950
900 920 931 936 935 928 915
(684) 777 834 862 875 877 873
655 725 772 798 811 813
602 667 714 738 758
-
1.00
339 453 552 619 657
Volume 78, Number 6 June 1068
ARVIN S. QUISTAND WILLIAML. MARSHALL
2104 and above. Below this density, the uncertainty in the limiting equivalent conductances increases with decreasing density and with increasing temperature. Figure 4 shows the linear relationships observed when isothermal values of Ao(NaBr) are plotted against solvent density. The limiting equivalent conductances of NaBr at constant density increase steadily with temperature, reaching maximum values near 400-500". Thereafter, there is a slow decrease in these values with increasing temperature. This apparent decrease is probably a result of the limitations of the data. When NaBr behaved as a strong electrolyte, reliable limiting equivalent conductances could be obtained when the data Over the concentration range o~002-0~015 were extrapolated to infinite dilution. However, at high temperatures and low densities where NaBr behaved as a weak electrolyte, the Ao's obtained by the extrapolation procedures became increasingly unreliable, even when using the Shedlovsky eq~ation~which includes the effects of ionic association. The limiting equivalent conductances for NaC13 were obtained from data at lower concentrations (0.001 m ) and, consequently, did not show this decrease until temperatures of 600-700" were reached. Lacking the data on NaBr solutions at concentrations below 0.002 m, we have assumed that the calculated limiting equivalent conductances (at constant density) stili would be independent of temperature in the region 400-800". This behavior would be represented by the line shown in Figure 4 as drawn through the no's a t 400-500". The relationship as a function of density (d) is described by the linear equation Ao(NaBr)
=
1880 - 1180d
(1)
A similar relationship in the temperature region 400800" was observed for KHS04 (considered as a 1: 1 electrolyte),2 NaCl,3 and HBr;4 these equations are given as Ao(NaC1) = 1876 - 1160d Ao(KHS04)
=
1740 - llOOd
Ao(HBr) = 1840 - 560d
Pa) (2b) (2c)
This similarity in behavior for these electrolytes indicates that perhaps above 400" all 1:l electrolytes would have a value for the A. at zero density of approximately 1800-1900 cm2ohm-' equiv-'. It also appears that this is the maximum value for 1:1 electrolytes, since all the data indicate that the limiting equivalent conductance (at constant density) does not increase for ternperatures above 400". As mentioned previ~usly,~ the smaller dependency on density for HBr (eq 2c) may be related to the extra mobility of the hydrogen ion and its decrease with decreasing solvent density. Furthermore, the value of the slope (560) for HBr is almost exactly one-half the value for the several 1: 1 salts. It is The Journal of Physical Chemistry
-
2000
..
!g ,500
; "E
moo
5B
500
0 0.40
0.50
0.60
0.70
0.80
0.90
1.00
DENSITY(e cm-3) Figure 4. Limiting equivalent conductances of NaBr as a function of density at temperatures to 800".
interesting to compare the limiting equivalent conductances for NaBr with those previously observed for NaC1. At high densities, where reliable comparisons can be made, it appears that in general Ao(NaBr) is about 2% less than Ao(;"iSaC1), Calculation of the Ionixation of NaBr, The ionization equilibrium for NaBr in aqueous solutions can be represented by the equationss,9 NaBr(H2O)j
+ kH2O
KO
=
K/u'H,o
log K = log K"
+ k log
(3c) UH~O
(3d)
where KO is the complete ionization constant including hydration and K is the conventional ionization constant. The integers j , m, and n represent hydration numbers of NaBr, Na+, and Br-, respectively; IC is the net change in hydration number when one molecule of NaBr ionizes. Values of the conventional ionization constant for NaBr were calculated from the experimental data by using the Shedlovsky method.7 This method provides a value of K simultaneously with A0 and is satisfactory as long as the K's are greater than about However, as noted previously, this method was not satisfactory for our data at low densities and at high temperatures. Therefore, to calculate K's over the complete density range at 400-800", eq 1 was used to obtain a value of Ao(NaBr), and the Shedlovsky equations' were used to calculate K's. Table VI1 contains the results of these calculations, where negative logarithms of the K's are given at in-
s.,
(8) W.L.Marshall and A. 8. Quist, PTOC.Natl. Acad. Sci. U. 58, 901 (1967). (9) A. S. Quist and W. L. Marshall, J . Phys. Chem., 72, 1545 (1968).
ELECTRICAL CONDUCTANCES OF AQUEOUS SODIUM BROMIDE SOLUTIONS ~
~
~
2105
~~
Table VI1 : Negative Logarithm of the Conventional Equilibrium Constant, K , for the Dissociation of NaBr into Naf and Br-; Standard State is the Hypothetical 1 M Solution Temp, OC
400 450 500 550 600 650 700 750 800
------0.30
4.44 4.70 4.93 5.12 5.30 5.49 5.60
-----
Density,
g cm-3--
7
I _ _ -
0.35
0.40
0.45
0.50
0.55
0.60
0.65
0.70
0.75
3.84 4.04 4.25 4.37 4.47 4.55 4.61
3.15 3.33 3.49 3.62 3.73 3.82 3.90 3.96
2.68 2.84 2.98 3.08 3.17 3.25 3.33 3.40
2.30 2.39 2.50 2.60 2.69 2.79 2.88 2.99
1.92 2.02 2.12 2.22 2.32 2.42 2.52 2.62
1.46 1.55 1.67 1.78 1.89 1.99 2.09 2.18 2.28
1.03 1.14 1.29 1.45 1.58 1.70 1.80 1.90 2.00
0.56 0.72 0.91 1.11 1.29 1.45 1.60
0.41 0.26 0.58 0.88 1.12 1.31 1.48
tegral temperatures and densities. Concentrations in the standard state are a t unit molarity at the particular temperature and density. The average standard error associated with the values in Table VI1 is approximately 0.03 pK unit, with the greatest uncertainties occurring a t 0.30 g cm-3 and also a t the highest densities at 600800". These conventional ionization constants for NaBr are approximately 25-60% larger (about 0.1-0.2 pK unit more positive) than the constants previously obtained for NaCL3 This is consistent with what might be predicted upon consideration of the halogen ion sizes. Since the bromide ion is larger than the chloride ion, the force of attraction between the sodium ion and the bromide ion would be less than that between the sodium ion and the chloride ion. The ionization constants for NaBr are also considerably larger (particularly at the lowest densities) than those previously calculated for HBr.4 With the concept of a complete equilibrium constant (KO) independent of density,899 an isothermal plot of log K us. log CHaO (where C H a O is the molar concentration of water) should give a straight line with slope k (eq 3d). The results of this type of plot for some of the NaBr data are given in Figure 5, for temperatures from 400 to 800". The slopes of these lines varied randomly from 9.76 to 9.94, with the average value being 9.85 f 0.05. Since this value of k appears to be independent of temperature from 400 to 800", it may represent the net change in primary hydration numbers, as proposed for the NaCl eq~ilibrium.~A value of k of 10.2 was calculated for NaCl from 400 to 800".
.oa I
-6
4.2
80.35 1
DENSITY (g cm-3) 0.55 0.65 I l l
ox
0.40 0.45 1 I
I
I
1.3
1.4
1
4.5 log C H ~(moles/literl O
0.85
I
4.6
J
i.7
Figure 5. Log K (molar units) for the equilibrium NaBr Ft Na+ Br- ns a function of the logarithm of the molar concentration of water a t temperatures from 400 to 800'.
+
With a value of k of 9.85, eq 3d was used, along with the data in Table VI1 and Figure 5, to calculate values of log KO. At 400, 500, 600, 700, and 800", the calculated values of log KO were - 16.37, - 16.61, - 16.86, - 17.09, and - 17.28, respectively. A plot of log KO vs. 1/T gives a slight curvature. However, the points a t 500, 600, and 700" can be represented approximately by a straight line, the slope of which gives a AEv of -7.5 kea1 (as compared to -5.7 kcal for NaCP). Acknowledgment. It is a pleasure to acknowledge the technical assistance of Wiley Jennings in making the conductance measurements.
Volume 78,Number 6 June 1968
