3714
ARVINS. QUIST
deviate to the low side from measured electrical transference numbers a t higher sodium chloride solution concentrations. I n general, fair agreement is found between the transference numbers calculated from ioninterchange data and membrane transference numbers
AND
WILLIAM L. MARSHALL
obtained by direct measurement for our experimental conditions of the membrane cell. Acknowledgment. The authors are indebted to the National Research Council, Ottawa, Ontario, Canada, for financial support.
Electrical Conductances of Aqueous Solutions at High Temperatures and Pressures.
111. The Conductances of Potassium Bisulfate Solutions
from 0 to 700"and at Pressures to 4000 Bars1
by Arvin S. Quist and William L. Marshall Reactor Chemistry Dioiswn, Oak Ridge National Laboratory, Oak Ridge, Tennessee 91880 (Received June 27, 1966)
The electrical conductances of dilute aqueous potassium bisulfate solutions have been measured from 0 to 700" and at pressures to 4000 bars. From these measurements, the second ionization constant of sulfuric acid was calculated a t temperatures to 300" and a t densities to 1.0 g em+. At temperatures above approximately 400", KHS04 behaves as a uni-univalent electrolyte, dissociating into K + and HSOI- ions only. I n this region, limiting equivalent conductances were obtained and dissociation constants for the equiHSOo- were calculated. KHSOo behaves as a weaker electrolibrium KHSOl & K + lyte as temperature increases (at constant solution density) and as solution density decreases (at constant temperature).
+
Introduction Earlier papers in this series presented the results of conductance measurements on aqueous K2S042and H2SOh3solutions at temperatures from 0 to 800" and a t pressures to 4000 bars. As part of a continuing program a t this laboratory studying the behavior of aqueous solutions at high temperatures and pressures, conductance measurements mere made on potassium bisulfate solutions in the same ranges of temperature and pressure. These measurements were carried to very low concentrations (0.00007 m) in an effort to determine the lowest practical concentration range that could be studied with the present conductance cell. From the The Journal of Physical Chemistru
measurements, the second ionization constant of H2SO was calculated a t temperatures from 100 to 300" and a t solution densities to 1.0 g Values reported herein for this constant are considered to be more reliable than those calculated previously from the measurements on H2S00abecause of the better reproducibility of the KHSOl measurements. From the present (1) Research sponsored by the U. S. Atomic Energy Commission under contract with Union Carbide Corp. (2) A, S. Quist, E. U. Franck, H. R. Jolley, and W. L. Marshall, J .
Phys. Chem., 67, 2453 (1963). (3) A. S. Quist, W. L. Marshall, and H. R. Jolley, ibid., 69, 2726
(1965).
ELECTRICAL CONDUCTASCE OF POTASSIUM BISULFATE SOLUTIONS
data. it appears that KHS04 behaves as a uni-univalent electrolyte (dissociation into K + and HSOe- only) at densities below 0.8 g ~ m at- 400”, ~ and at 450-700” at all densities obtained with the present apparatus. Above 0.8 g cm-3 at 400” and at all the densities at lower temperatures, there is detectable dissociation of the bisulfate ion. Where KHSO? behaved as a uniunivalent electrolyte, limiting equivalent conductances were obtained by extrapolating the experimental data to zero concentration by several methods.
0
3715
200
400
600
BOO
TEMPERATURE ( T I
Experimental Section The conductance cell and the associated equipment have been deqcribed previously.2-4 Stock solutions of KHS04 (approximately 0.5 and 0.1 nz) were prepared from conductivity water and reagent grade salt (J. T. Baker Chemical Co., Phillipsburg, S. J.). The hydrogen ion concentration of these stock solutions was determined by titration (using weight burets) with a sodium hydroxide solution (Fischer Scientific Co., Fairlawn, N. J.) that had been standardized against potassium acid phthalate (Baker Analyzed reagent, primary standard). The molality of the KHSOl solutions was considered to be equal to the molality of the hydrogen ion. To verify this assumption, the potassium ion concentration iyas determined by flame spectrophotometry and mas found to be equal to the hydrogen ion concentration within the limits of accuracy set, by the spectrophotometric method. From these stock solutions, weight buret techniques were used to prepare six solutions of KHSO, (0.0000737, 0.000226, 0.000432, 0.000817, 0.00240, and 0.00505 nz) for the conductance measurements. The 0.0000737 in solution was too dilute to give suitably reproducible results. The 0.000226 and 0.000432 m solutions gave reasonably reproducible measurements (=t3Yo or better), but the uncertainty in the correction for “background” conductance (usually called solvent conductance) was large enough to limit the usefulness of the measurements with these lowest concentrations. Under normal conditions (room temperature, atmospheric pressure, glass conductance cells), the background conductance is that of pure solvent, and amounts to a very small fraction of the total conductance of the Polution. However, conductance measurements at high temperatures and pressures require the use of all-metal containers (stainless steel pressure tubing, platinum-iridium-lined conductance cell), and impurities (or corrosion products) from these contribute to the “background conductance.” Estimates of the “background conductance” of the present system were obtained from many measurements on the conductance of pure water over all the experimental conditions of
Figure 1. “Solvent correction” for conductance measurements in aqueous solution a t high temperatures and pressures. Specific conductance as a function of temperature at several pressures.
temperature and pressure. These estimates are shown in Figure 1. At 600”, these values are about 30% of the total conductance of the 0.000432 m KHS04 solution. An estimated uncertainty of 20% in the background conductance at this temperature leads to a possible uncertainty in the corrected conductance value of about 6%. This was considered to be too large to use for the evaluation of limiting equivalent conductances. (However, at 300” and below, the background conductance is less than 14% of the conductance of 0.000432 m KHS04. The estimated uncertainty of 20% in the background conductance gives an estimated uncertainty in the corrected value of only 3%. Consequently, the conductances of 0.000432 m KHSO4 were used in the calculation of the second ionization constant of sulfuric acid at 300” and below as described in a following section.) Three different inner electrode assemblies were used throughout the series of measurements. Their cell constants, as determined with 0.01 demal KCl solutions at 25.00 f 0.01”, were 0.239, 0.285, and 0.291 cm-l. Because of the geometry of the conductance cell, the changes in cell constant with temperature and pressure are negligible (less than 0.25%). The experimental procedure that was followed has been described earlier2! with the exception that the high-pressure tubing was connected only to the bottom of the conductance cell. Each experiment was begun by bringing the conductance cell and its contents to a uniform predetermined temperature. When the conductance cell was heated, thermal expansion of the solution inside the cell caused an increase in the pressure of the system. During this period, the valves between the conductance cell and the solution reservoir remained open to ensure that the (4) E. U. Franck, J. E. Savolainen, and W. L . Marshall, Rea. Sci. Instr., 33, 115 (1962).
Volume 70. Number 11
iyovember 1966
3716
pressure inside the conductance cell did not reach a value high enough to rupture the cell. The initial pressure on the solution was such that when the operating temperature was reached, the pressure in the cell had increased enough so that the contents of the cell were at a density of approximately 0.5 g or higher. After the operating temperature was attained, conductance measurements were made at increasing pressures to the maximum of 4000 bars. Measurements then were made at decreasing pressures until densities near 0.2 g ~ 1 1 1 were 1~ reached (these low densities, of course, were only obtained above the critical temperature), and finally measurements were made at increasing pressures untiI the initial pressure value was reached. The measured values were usually the same on both increasing and decreasing the pressure. As with the sulfuric acid solutions, reproducible measurements on potassium bisulfate solutions were most difficult to obtain in the temperature range 100-300". The conversion of the experimental data (pressure and conductance readings) to specific conductances, equivalent conductances, and densities was carried out by the methods described p r e v i ~ u s l y . ~ ~ ~
Results and Discussion Figures 2-4 show isotherms of experimentally determined specific conductances of the KHSO, solutions, corrected for solvent conductance, as a function of pressure at temperatures from 0 to 700". From enlargements of these figures, specific conductances at integral pressures were obtained by interpolation. Examples of the type of graphs obtained when isobaric specific conductances are plotted against temperature are shown in Figure 5 for 0.00505 rn KHS04. Similar behavior is observed with the lower concentrations of KHS04, except that the maximum in the specific conductance near 100" is gradually shifted toward higher temperatures as the concentration is decreased. These graphs are similar to those obtained previously for H2S04,3but differ considerably from the K2S04measthis difference urements2 As mentioned previo~sly,~ from the behavior of KzSO~is due to the properties of the bisulfate ion. The specific conductances of K2S04 solutions are nearly independent of pressure a t temperatures of 200" and be lo^. However, in the same range of temperature, increasing the pressure on KHSO, solutions causes a relatively large increase in conductance. This increase is due to greater dissociation of the bisulfate ion with increasing pressure. From 0 to loo", the specific conductance of KHSO, solutions increases rapidly with increasing temperature because the viscosity of water decreases sharply over the same temperature interval, permitting greater moT h e Journal of Physical Chemistry
ARVINS. QUIST
440
AND
WILLIAM L. MARSHALL
I I
I20 io0
Y
40 20
0
0
(000
2000 3000 PRESSURE (bars)
4000
5000
Figure 2. Specific conductances of 0.0008174 m KHSOl solutions a.s a function of pressure a t several temperatures.
t
I
250
P --'8 200 3
150
Y
00
50 0
0
1000
2000 3000 PRESSURE (bars)
4000
5000
Figure 3. Specific conductances of 0.002401 m KHSO4 solutions as a function of pressure a t several temperatures.
' 600 0°
0
500
"0
-2
400
'I
200
100 C
0
io00
Zoo0 3300 PRESSWIE (bors)
4000
5000
Figure 4. Specific conductances of 0.005049 m KHSOa solutions as a function of pressure a t several temperatures.
bility of the ions. The viscosity of water continues to decrease as the temperature is increased, but the bisulfate ion becomes a weaker acid as the temperature is
ELECTRICAL CONDUCTANCE OF POTASSIUM BISULFATE SOLUTIONS
I
I
1
I I
3717
1.04
1.14
DENSITY l p cm-') 0 90 0.76
0.65
0005049 molal KHS04 Lo
0
600
400
6
e
E
7
-
r
E
2 200
400
200 0
0
200
400 600 TEMPERATURE I'CI
800
Figure 5. Isobaric variation of specific conductances of 0.005049 m KHSO, solutions with temperature at pressures from 500 to 4000 bars.
increased, thus giving fewer ions in solution. The increased mobility of the ions is thus offset by a decreased number of ions in solution, and a maximum in the graph of conductance us. temperature is reached. A direct comparison of KzS04, KHSO,, and HzS04 solutions of approximately equal molalities is shown in Figure 6. At 400°, the specific conductance of 0.005 112 KHS04 has decreased until it is approximately equal to the specific conductance of a KpS04 solution approximately one-half as concentrated. At higher temperatures, the conductances of the two solutions remain approximately equal. The near equality in conductances for these two solutions of different molal concentrations indicates that their "equivalent concentrations" are nearly equal. The 0.002199 nz KzS04 solution contains approximately 0.0044 equiv/1000 g of solution. Even if hydrolysis of the sulfate ion occurred
504'-
+ HpO
HSOd-
+ OH-
the number of ionic equivalents would remain constant. However, if the bisulfate ion in the 0.005 m KHSO, solution is undissociated, this solution then contains only 0.005 equiv, and consequently its conductance would be close to that of the 0.002199 m solution. This comparison then leads to the conclusion that at temperatures of 400" and above, even at 4000 bars, there is no detectable dissociation of the bisulfate ion in this solution. In Figure 6, the greater conductance of H2S04 as compared to the KHSO4 solution is due to the "extra mobility" of the hydrogen ion as compared to the potassium ion. This difference begins to decrease above 500" as a consequence of the decrease in the first ionization constant of sulfuric acid with increasing temperature. Since a difference does persist up to 700", this indicates that at least up to 700" there is some "extra mobility'' to the hydrogen ion. Isothermal molar conductances of the KHSO4 solu-
l
01 200
0
PRESSJRE=4000 bars
, 400 TEMPERATURE
,
I 600
8CO
loci
Figure 6. Comparison of the specific conductances of KISO~,KHSOa, and HlSOa solutions as a function of temperature at a pressure of 4000 bars. 1600
1400
I
I
I
-
1000
E
'g
800
N
5
600
