A. S. QUIST, W. L. MARSHALL, AND H. R. JOLLEY
2726
Electrical Conductances of Aqueous Solutions at High Temperature and Pressure., 11. The Conductances and Ionization Constants of Sulfuric Acid-Water Solutions from 0 to 800"and at Pressures up to 4000 Bars'''
by Arvin S. Quist, William L. Marshall, and H. R. Jolley3 Reactor Chemistry Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee
(Received March 8, 1966)
The electrical conductances of dilute aqueous sulfuric acid solutions have been measured at temperatures from 0 to 800" a t pressures to 4000 bars. Molar conductances were calculated from which, by several methods, limiting equivalent conductances of HzS04 as a function of temperature and density were obtained. The second ionization constant of HzS04was calculated at temperatures up to 300", and the first ionization constant was calculated between 400 and 800". Estimates were made of the standard heat of ionization, AH", for the first ionization process between 400 and 800" at pressures of 1000, 2000, 3000, and 4000 bars.
Introduction In a continuing study on the properties of aqueous electrolyte solutions at high temperatures and pressures, the electrical conductances of dilute sulfuric acid solutions were measured at temperatures from 0 to 800" and at pressures from 1 to 4000 bars. Earlier papers in this series presented a description of the conductance cell4 and the conductance measurements on &So4 solutions.6 From the present measurements on Hi304 solutions, the second ionization constant was calculated at temperatures from 100 to 300" and at densities up to 1.0 g. ~ r n . - ~ .Above 300" this constant became too small to be calculated accurately. The first ionization constant of HzS04 was calculated a t densities below 0.8 g. ~ m . -a t~400", and up to 800" at all experimentally attainable densities. Other calculations include estimations of the change in hydration numbers for the ionizaiion processes, the heat of ionization (for the first ionization step), and limiting equivalent conductances at iuemperatures above 400". Experimental Apparatus. The conductance cell and associated equipment described p r e v i o ~ s l ywere ~ ~ ~ used with some modification. The 0.125-in. 0.d. high pressure tubing was replaced by higher strength, 100,000The Journal of Physical Chembtry
p.s.i. tubing. This tubing, in contact with sulfuric acid solution only a t 25", was made from 316 stainless steel, 0.250 in. o.d., 0.030 in. i d . (Superior Tube Co., Norristown, Pa.). The valves that were exposed to dilute sulfuric acid also were constructed of 316 stainless steel for use to 100,000 p.s.i. (Autoclave Engineers, Erie, Pa., Model lOOV-1003), but modified to use 0.25in. 0.d. instead of the designed 0.31411. 0.d. tubing. The normally supplied 18-4-1 valve tips were replaced by tips made of Stellite 6 (Haynes-Stellite Co., Kokomo, Ind.). Although there was no evidence that the solution contained in the separator unit5 was contaminated by water leaking around the close-fit floating piston, this piston was modified by the addition of a neoprene "quad" ring (Minnesota Rubber Co., Minneapolis, Minn.). The piston was also electroplated very lightly (approximately 0.0003 in. thick) with chromium to lessen the possibility of galling. (1) Research sponsored by the U. S. Atomic Energy Commission under contract with the Union Carbide Corporation. (2) Presented in part at the 146th National Meeting of the American Chemical Society, Denver, Colo., Jan. 1964. (3). Summer Participant, 1963, Department of Chemistry, Loyola University, New Orleans, La. (4) E. U. Franck, J. E. Savolainen, and W. L. Marshall, Rev. Sci. Instr., 33, 115 (1962). (5) A. S. Quist, E. U. Franck, H. R. Jolley, and W. L. Marshall, J . Phys. Chem., 67, 2453 (1963).
CONDUCTANCES OF AQUEOUS SOLUTIONS AT HIGHTEMPERATURE AND PRESSURE
Materials. The conductivity water was prepared in the manner described previ~usly.~Stock solutions of sulfuric acid were prepared from sulfuric acid collected from a quartz distillation unit. These stock solutions were standardized with a sodium hydroxide solution (Fisher Scientific Go., Fairlawn, N. J.) that had been standardized against potassium acid phthalate (Baker analyzed reagent, primary standard). From the sulfuric acid stock solutions three concentrations (0.002424, 0.004893, and 0.009855 m) were prepared for the conductance measurements by using weight burets. A 0.0005 m solution was also prepared, but its concentration was too low to give suitably reproducible results. Cell Constants. Two inner electrode assemblies were used throughout the series of measurements. The cell constants, determined a t 25.00 f 0.01” by using 0.01 Demal KC1 solutions, were 0.286 and 0.270 cm. -I, respectively. Accuracy of Measurements. The earlier measurements on KzS04were estimated to be precise to within =kl-2%. However, for sulfuric acid solutions, possible corrosion in the tubing and valves increased the maximum uncertainty in the measurements to an estimated f4-50/,. Reproducible measurements were most difficult $0 obtain in the temperature range 100300”, where the highest conductances were observed. Procedure. Because of the corrosive nature of HzS04 solutions, the procedure previously described6 was modified. A schematic drawing of the essential high-pressure equipment is shown in Figure 1. Pressures to 1000 bars were generated by a hand-turned pressurizer and measured on a calibrated Heise bourdon tube gauge. Pressures from 1000 to 4000 bars were produced by the air-driven hydraulic pump and the intensifier system and were measured by a calibrated strain gauge. By changing the tubing connections, solution could be added (pressurization) to the conductance cell from either the top or bottom and subsequently removed (depressurization) from the opposite end. Consequently, the cell was now a “flow-through” type, in contrast to the previous design wherein tubing was connected only to the bottom. This new arrangement permitted more effective flushing of the cell at, the temperature of the experiment. At temperatures below 400°, the solution usually was introduced through the top connection and removed from the bottom, but a t higher temperatures the opposite method was used. Although flushing the cell from the top probably was the most effective method, at the higher temperatures there was greater probability of cracking the alundum tube by thermal shock when room temperature solution was introduced into the
AIR 1.3 bo,$
OIL 4WbaIS
OIL
2727
OIL
I
.
AIR-DRIVEN
HYDRAULIG P U W
WD-TURNED
PISTON PRESSURIZER
-
To ATMOSPHERE
Figure 1. Schematic drawing of equipment for conductance measurements at high pressures.
red-hot cell. (The alundum insulating tube, a part of the inner electrode assembly, enters the top of the cell.) The conductance cell, high pressure tubing, and separator unit were always rinsed thoroughly with solution before each run. After reaching the desired temperature, the system was again flushed by flowing solution through the cell (by alternate pressurization and depressurization). With the present arrangement, the separator unit containing the solution reservoir could be isolated from the rest of the system by closing the proper valves, and then could be refilled easily with fresh solution for continuing the experiment. The data taken for each run were temperature, conductance, and pressure in bars (to 1000 bars with bourdon gauge) or millivolts (1000 to 4000 bars with strain gauge). A digital computer (IBM-7090) was used to convert strain gauge readings to bars and to correct resistances both for the effect of frequency and for lead resistance. Solvent conductances a t the experimental temperatures and pressures were interpolated by the computer from previously determined solvent conductances. Since all solutions were very dilute, their densities were assumed to be that of pure water and were determined (with the computer) by a nonlinear interpolation of Sharp’s6table of specific volumes a t integral temperatures and pressures. This compilation, based mainly on the data of Kennedy, et uZ.,’-~I gives values a t the highest pressures slightly (6) W. E. Sharp, “The Thermodynamic Functions for Water in the Range -10 to 1000° and 1 to 250,000Bars,” University of California Radiation Laboratory Report UCRL7118 (1962). (7) G.C.Kennedy, Am. J. Sci.,248, 540 (1950). (8) G.C. Kennedy, ibid., 255, 724 (1957). (9) G. C. Kennedy, W. L. Knight, and W. T. Holser, ibid., 256,
590 (1958). (10) W. T. Holser and G. C.Kennedy, ibid., 256, 744 (1958). (11) W. T. Holser and G. C.Kennedy, %id., 257, 71 (1959).
Volume 69,Number 8 August 1066
A. S.QUIST,W. L. MARSHALL, AND H. R. JOLLEY
2728
450 molal H2k04
/.002:24
0.009855 molol H2S04
400 1400
350
"0 c
300
?I 1
E E
-
250 200
L
i5Q io0
50 0 0
2000 3000 PRESSURE (bars)
1000
4000
5000
Figure 2. Specific conductances of 0.002424 m HzS04 solutions as a function of pressure a t several temperatures.
0
1000
2000 3000 PRESSURE (bars)
4000
5000
Figure 4. Specific conductances of 0.009855 m HzSO~ solutions as a function of pressure a t several temperatures.
0.004893 molal H2S04
400
860
0.002424 molal H2S04 1 Y)
0
0 600
I
500
7s 200
400
-c .-, Y
c
-
E
0
IE
-
300
-
Y)
100
-c
300 0 0
200
200
400
600
800
1000
TEMPERATURE ("C) 100
Figure 5. Specific conductances of 0.002424 m HzS04 solutions as a function of temperature a t several pressures.
0
0
1000
2000
3000
4000
5000
PRESSURE (bars)
Results and Discussion
2-4 as a function of pressure for each temperature. The curves where individual points are not shown represent averages of two or more different runs a t that particular temperature. For clarity of presentation, the individual points were not given. From enlargements of these figures, specific conductances a t integral pressures were obtained by interpolation. Isobaric specific conductances plotted against temperature are shown in Figures 5-7. The results for 0.004893 m HzS04 a t temperatures to 100" are in good agreement (within 1%) with the measurements of Franck and HartmanlZ but are somewhat higher (approximately 7%) than their measurements near 200". The graphs
Specific conductances of the HzSOa solutions, corrected for solvent conductance, are shown in Figures
(12) D. Hartman, Thesis, Institut filr physikalische Chemie und Elektrochemie, Technische Hochschule, Harlsruhe, Germany, 1964.
Figure 3. Speciic conductances of 0.004893 m &So4 solutions as a function of pressure a t several temperatures.
different from those used previ~usly,~ based also on Kennedy's data. The output from the computer provided a printed record and also magnetic tape input for an automatic plotter (California Computer Products, Inc., Anaheim, Calif.). This plotter drew graphs of specific and equivalent conductances as a function of both density and pressure for each temperature and solution concentration.
Ths Journal of PhynicaE Chemistry
CONDUCTANCES OF AQUEOUS SOLUTIONS AT HIGHTEMPERATURE AND PRESSURE
800
I 1% 0.004893mold1 H2S04 /
\
I
I
I
Table I : Negative Logarithm of the Second Ionization Constant of H2S04, -Log K2"; Standard State Is the Hypothetical 1 M Solution
I
Temp.,
'C.
0
200
400 600 TEMPERATURE ( " C )
800
1000
Figure 6. Specific conductances of 0.004893 m &SO4 solutions as a function of temperature a t several pressures.
1200
-aoo
v)
0 x
7 E c
'E c
* 400 0 0
200
400
600
800
2729
1000
TEMPERATURE ("GI
Figure 7. Specific conductances of 0.009855 m H2S04 solutions as a function of temperature a t several pressures.
for sulfuric acid are considerably different from those obtained previously for K2S04. For K2S04 solutions at temperatures of 200" and below, the isothermal specific conductance is nearly independent of pressure. In contrast, the specific conductances of HzS04 increases markedly with increasing pressure. This behavior of H2SO4is believed to result predominantly from increasing ionization of the bisulfate ion with increasing pressure (see Table I). The increased ionization is presumably due to the enhanced hydration of the ions caused by increasing pressure.la#l4 Another striking difference between these graphs (Figures 5-7) and those for K2S04appears in the position and shape of the maximum of the curves. With KzS04 this maximum lies near 300", whereas with H2so4 the maximum is close to 100'. The difference is believed to be due also to the behavior of HSO4- in the H2S04 solutions. As the temperature increases from 0 to loo", the conductance increases rapidly due to a rapid decrease in the viscosity of water. Therefore, the mobilities of the separate ions increase rapidly.
100 150 200 250 300
Saturation vapor pressure
3.10 4.09
...
0.75
0.80
...... ...... . . . . . .
...... ... 4.09
Density, g. om. -\ 0.85 0.90 0.95 1.0
... ... ... ... 4.03
...
...
3.85 3.85 3.91
... ... 3.56 3.65 3.73
2.60 2.83 3.13 3.35 3.58
With KzS04 the conductance increases until temperatures near 300" are reached. At higher temperatures, the decreasing dielectric constant of water, caused both by increasing temperature and decreasing density, permits association between ions and begins to offset the effect of decreasing viscosity; therefore, conductance decreases. For H2S04 solutions, the dissociation constant for HSO4- decreases with increasing temperature. Near 100" its rate of decrease with increasing temperature begins to counteract the increase in conductance of ions due to decreasing viscosity. Although a plateau (conductance vs. temperature) occurs between 200 and 400" with H2S04(where the bisulfate ion dissociation is very small), the conductance begins to decrease more rapidly with increasing temperature a t temperatures above 400" (at constant pressure) than is observed for K2S04. This difference appears due to increasing association between Hf and HS04ions with increasing temperature which occurs to a greater extent than any association between the ions in K2S04 solutions. A direct comparison of K2S04 and H2S04 solutions of approximately equal molal concentration is shown in Figure 8. The molar conductances of the H2S04solutions as a function of density are shown in Figures 9 to 11, and smoothed values are tabulated a t integral temperatures and densities in Tables I1 to IV. At temperatures of 200" and below, the effect of increasing density on increasing the dissociation of the bisulfate ion is readily apparent. At constant density a t temperatures above 400", the decrease in the first ionization constant of H ~ s o 4with increasing temperature can be noted by comparing the graphs with those for KPso4.5 (13) S. D. Ham-, "Physico-Chemical Effects of Pressure,'' Academic Press, New York, N. Y., 1957,pp. 137-159. (14) 8. D. Hamann in "High Pressure Physics and Chemistry," Vol. 11, R. 5. Bradley, Ed., Academic Press, New York, N. Y., 1963,Chapter 7, ii.
A. S. QUIST, W. L. MARSHALL, AND H. R. JOLLEY
2730
~
~~
Table 11: The Molar Conductances (cm.z ohm-' mole-') of 0.002424 m HzS04 Solutions a t Integral Temperatures and Densitiee Temp., O C .
0 25 100 150 200 250 300 350 400 450 500 550 600 650 700 750 800
Density, g. 0.4
580 500 380 280 180 130 100 90 80
0.45
800 680 540 420 310 240 190 160 120
0.5
980 890 780 640 500 400 320 250 200
0.55
1130 1050 940 810 690 580 490 380 300
0.6
1230 1180 1120 1030 920 800 690 570 450
0.65
0.7
1310 1310 1290 1250 1200 1130 1060 1000
1290 1280 1240 1160 1060 960 860 740 620
0.75
1270 1290 1310 1300 1270 1220 1150 1120 1070
0.8
1230 1280 1300 1300 1270 1220 1140
0.85
1200 1250 1270 1280 1260 1250
0.9
1110 1150 1180 1200 1220
0.95
1120 1160 1180 1190 1190
1.0
460 720 1170 1210 1220 1210 1190
Table 111: The Molar Conductances (cm.z ohm-' mole-') of 0.004893 m HzSO, Solutions a t Integral Temperatures and Densities Temp., OC.
0 25 100 150 200 250 300 350 400 450 500 550 600 650 700 750 800
Deneity, g . om. - 8
,
0.4
480 350 230 150 100 90 80 70 60
0.45
650 520 390 280 200 170 150 130 100
0.5
800 720 600 480 370 300 240 200 160
0.55
940 870 770 660 560 480 390 310 260
0.6
1080 1020 940 860 760 680 590 490 390
0.65
1160 1140 1080 1010 930 850 760 660 540
Calculation of Limiting Equivalent Conductances. For evaluating the limiting equivalent conductance of an electrolyte from measured equivalent conductances for HzS04 [A(equivalent) = h(mo1ar) or I/zh(molar) depending upon treatment either as a 1-1 or 1-2 electrolyte, respectively], all the available procedures depend on extrapolating the conductance (or some function of conductance) vs. concentration (or some function of concentration) curves to zero concentration. The several methods used below 300" were unsatisfactory for HzS04, probably because incomplete ionization of HSOI- gave extrapolated limiting conThe Journal of Physical Chemistry
0.7
1200 1210 1200 1170 1130 1060 1000 940
0.75
1160 1210 1240 1240 1220 1180 1130 1080 1020
0.8
1140 1200 1240 1240 1240 1200 1140
0.85
1130 1190 1230 1240 1240 1220
0.9
1050 1100 1130 1170 1200
0.95
1060 1090 1120 1130 1150
1.0
470 680 1010 1080 1110 1120 1110
ductances too low assuming complete ionization to H+ and S042- ions, but too high for ionization only to H+ and HS04-. At 300 and 400" a t respective densities of 0.75 and 0.80 (or below) g. ~ m . - ~ and , at higher temperatures, when the dissociation of HS04- is negligible, sulfuric acid can be considered a uni-univalent electrolyte. Under these conditions, several extrapolation procedures were used with varying degrees of success. The simplest procedure assumes that the Onsager limiting law16 is obeyed and involves merely (16) L. Onsager, Physik. Z., 28, 277 (1927).
273 1
CONDUCTANCES OF AQUEOUSSOLUTIONS AT HIGHTEMPERATURE AND PRESSURE
Table IV:
The Molar Conductances (cm.2 ohm-’ mole-’) of 0.009855 m HtSO4 Solutions at Integral Temperatures and Densities
Temp., OC.
Density, g. om. --I 0.4
0 25 100 150 200 250 300 350 400 450 500 550 600 650 700 750 800
0.5
0.45
340 240 160 90 60 50 40 40 40
510 390 260 200 140 120 100 90 80
680 570 440 340 260 210 170 150 120
0.6
0.55
820 740 620 500 400 330 270 220 200
980 900 800 700 600 520 440 360 300
0.65
1120 1050 960 850 730 660 580 520 460
DENSITY (g.cm-3)
1.14
4.04
0.90
0.76
0.65
600
!n
-0 400 -6
0.75
0.7
1190 1200 1150 1070 970 870 800 760
1140 1200 1230 1190 1120 1040 950 860 780
0.8
1130 1190 1220 1190 1130 1050 960
0.85
1110 1170 1210 1200 1150 1090
0.9
1020 1060 1100 1140 1180
0.95
1030 1060 1100 1120 1140
1.0
410 580 910 1000 1060 1080 1090
(where in this case E and J are empirical parameters) to solve for A,, E , and J using A-values from three or more concentrations. The limiting Onsager slope, S, was calculated from dielectric constants and viscosities given elsewhere.1*,19 The Owen method worked better than the first two procedures, and for an unsymmetrical electrolyte (such as K2S04)was better than any other procedure. However, when both E and S can be calculated, the Fuoss-Onsager method of extrapolating the quantity A Sc’/’ - Ec log c us. c to zero concentration gave perhaps the best values for Where H2S04 behaved as a weak uni-univalent electrolyte, the best method for obtaining A,, was in which A. and presumably that of Shedlovsky,21,22 the ionization constant are determined simultaneously. At solution densities below 0.6 g. ~ m . -and ~ temperatures above 550”, H2S04 behaved as a very weak electrolyte. Thus conductances were not available a t sufficiently low concentrations for reliable use of the previous methods for extrapolation to accurate novalues. Estimates of the limiting conductances in
+
E
r I
x
200
0 0
1
I
I
I
400 600 TEMPERATURE(’C )
200
800
Figure 8. Comparieon of the spec& conductances of K2SO~ and HzSOa solutions as a function of temperature; pressure = 4000 bars.
extrapolating .A us. (molarity)’/’ to zero concentration. This was successful only when H2S04 behaved as a strong uni-univdent electrolyte. Similarly, plots of A us. (molarity) ‘/’/(I (moIarity)’”) (an empirical extension to the limiting law, assuming the Bd parameter in the equation given by Robinson and Stokes16 was constant at 1.0) gave only slightly larger & values. A third procedure (also used in the evaluation of the KzS04 data), suggested originally by Owen,17 made use of the Fuoss-Onsager conductance equation
+
+
A == A, - S C ” ~ EClog c
+ JC
(16) R. A. Robinson and R. H. Stokes, J. Am. C h . Soc., 76, 1991 (1954). (17) B. B. Owen, ibid., 61, 1393 (1939). (18) A. S. Quiet and W. L. Marshall, J. Phys. Chem., in press. (19) E.U.Franck, Z . physik. Chem. (Frankfurt),8, 107 (1956). (20) R. M. Fuoss and F. Accascina, “Electrolytic Conductance,” Interscience Publishers, Ino., New York, N. Y., 1959. (21) T. Shedlovsky, J. F~onklinInst., 225, 739 (1938). (22) R. M.Fuoss and T. Shedlovsky, J. Am. Chem. Soc., 71, 1496 (1949).
Volume 69,Number 8 August 1966
A. S. QUIST, W. L. MARSHALL, AND H. R. JOLLEY
27 32
0.009855 molal H2S04 t
I
1
I
I
0.2
0.4
1600 4400
1400
1000
-E 1000
800
,"800
E
-EE
E
-2
600
