THERMODYNAMICS OF STRONG ELECTROLYTES I N PROTIUM OXIDE-DEUTERIUM OXIDE MIXTURES. I' HYDROGEW CHLORIDE EVAN NOONAN AND VICTOR K. LA MER Department of Chemistry, Columbia University, New York, New York Received October 18, 1988
I n their pioneer investigation on the dissociation constant of heavy water, Abel, Bratu, and Redlich (1) measured the cell (1)
Dz I DCl(m in DZO) 1 AgC1-Ag
Although correctly treated in principle, the limited amounts of heavy water available at that time rendered measurements difficult. Furthermore, a t the conclusion of their investigation these authors recognized that their results at intermediate deuterium concentrations were uncertain, owing to the fact that the gas bubbled over the electrode differed in deuterium content from that in equilibrium with the solvent (8). The interpretation of the small E.M.F. differences when the atom fraction of deuterium in the solvent, designated as FD or n, is varied requires a higher order of precision than they were able to obtain. We have measured cell I at 25°C. over a wide range of deuterium content with a microcell employing the principle of the Clark rocking electrode (4). This type of cell possesses an advantage for work with heavy water in that it is possible to start with a small volume of pure hydrogen and to establish the exchange equilibrium between the gas phase and the bulk of the solvent of a given deuterium content in a reasonable time by means of the platinized electrode. Under these conditions the same E.M.F.'S are obtained when either pure deuterium or pure hydrogen is the initial gas phase. Furthermore the gas is conserved, the pressure on the closed system can be carefully regulated, and the complete removal of oxygen is effected. Aside from the inherent interest in the thermodynamics of deuterium of cell I is necessary chloride in deuterium oxide, a precise value for for the determination of dissociation constants of acids in deuterium oxide, 1 Presented at the Symposium on IntermolecularAction, held at Brown University, Providence, Rhode Island, December !27-29,1938, under the auspices of the Division of Physical and Inorganic Chemistry of the American Chemical Society.
247
248
EVAN NOONAN AND VICTOR K. LA MER
as well as the dissociation constant of deuterium oxide itself, from cells without transference, using the deuterium gas electrode. By subtracting cell I from the corresponding cell 11,employing protium oxide as the solvent
Hz I HCl(m in HzO) I AgC1-Ag (11) the free energy change of the following process may be determined. 1/2 Hn
+ DCl(m in DzO) = 1/2 Da + HCl(m in HzO)
(1)
Abel, Bratu, and Redlich (1) obtained 3.4 millivolts for the E.M.F. of process 1 when extrapolated to pure deuterium oxide. Their results also indicated that there might be a maximum in the E.M.F. of process I , as written above as a function of the deuterium content of the solvent. A single measurement of Drucker (5), when FJ-, = 0.89, yielded the value 5.4 millivolts, suggesting that this maximum might be greater than was previously suspected (8). Confusion has appeared in the recent literature in a n attempt to reconcile Schwarzenbach, Epprecht, and Erlenmeyer’s (14) value of -2.2 millivolts for a cell with transference with Abel, Bratu, and Redlich’s value of 3.4 millivolts (13). This investigation was undertaken to refine and clarify the knowledge of the behavior of hydrogen chloride in protium oxide-deuterium oxide mixtures. EXPERIMENTAL
Dry hydrogen chloride gas was passed into heavy water until the concentration reached 9 per cent. This stock solution was analyzed gravimetrically at the beginning and end of the research; it remained constant t o 6 parts in 10,000, corresponding to an uncertainty in the E.M.F. of ~ 0 . 0 millivolt. 2 Heavy water was purified by molecular distillation in vucuo from alkali and then from potassium dichromate, organic matter being removed when necessary by heating with alkaline permanganate. Density determinations were made in a combined pycnometer and conductance cell. The specific conductance of the water was less than 2 x lo-‘ mhos. The water was transferred directly from the pycnometer to a small flask and weighed. Deuterium chloride stock solution was added from a micro weight buret. The solution was then boiled i n vacuo to remove oxygen, 1 to 2 per cent of the water being evaporated in the process. Deuterium or hydrogen at atmospheric pressure was admitted to the flask, and the loss of weight determined. Pyrex glass apparatus with interchangeable ground joints was used throughout this investigation, and all parts were carefully cleaned and steamed before use. The double cell illustrated in figure 1 was attached to an electrically driven mechanism which rocked it about the glass joint A as an axis.
THERMODYNAMICS OF ELECTROLYTES IN
&0-D20
249
Each cell had two silver chloride and two hydrogen electrodes. Hydrogen was admitted through the stopcock'B and the connection A, the fixed inner member being connected to a supply of gas. a t constant pressure slightly higher than atmospheric. After the electrodes were in place the cell was filled by connecting the filling flask a t C and a n empty receiving flask a t D, and evacuating the system repeatedly with a Hyvac pump. After all water was evaporated from the electrodes the cell was flushed twice with hydrogen or deuterium and the stopcocks closed under vacuum, so that the solution could be admitted to the silver chloride compartments.
FIQ.1
FIQ.2
FIG.1. The double cell FIG.2. Manostat and gas storage system
After 30 min. this solution was drawn off into a receiving flask, and more solution was run into the cell. The horizontal compartments were half filled, and hydrogen was admitted. The flasks were replaced by caps and the cell transferred to a thermostat. Sixteen milliliters of solution was sufficient to wash the electrodes once and to fill the cell. The limited quantities of heavy water available for washing constitute one of the serious restrictions upon the precision of the results. Scrupulous cleanliness and care in avoiding contamination of the electrodes with films of stopcock grease are essential. Two hydrogen electrodes, consisting of 22 B. & S. gauge platinum wires
250
EVAN NOONAN AND VICTOR K. LA MER
1 cm. long, were sealed through a soft-glass 12/30 standard taper inner member, as detailed. Silver chloride electrodes were deposited on platinum wires sealed through 10/30 standard taper soft-glass joints. The electrode holders were the only parts of the apparatus made of soft glass; their area was small compared to the total glass surface. Two types of silver chloride electrodes were used. The electrolytic type described by Brown (3) yielded highly reproducible results at the temperature of preparation, 25"C., but gave unreliable temperature coefficients, probably owing to strains in the layers of silver and silver chloride. Electrodes of the annealed thermal type described by Rule and La Mer (11) are not quite as reproducible a t 25"C., but yield more consistent temperature coefficients and are simpler to prepare. The electrolytic type electrodes were not washed in the cell, but were soaked overnight in conductivity water before use. The influence of all these variations in electrode technique was within the experimental error, as shown by figure 3 and the accompanying legend. Constant pressure of hydrogen or deuterium was maintained to f 0.2 mm. of mercury by a manostat, which is shown, together with the gas storage system, in figure 2. Contacts sealed in the manometer operated a relay connected to an electrolytic cell, and gas pressure from this cell was transmitted through a mercury seal to the hydrogen system. Excess pressure was released through the capillary tip T. The length of the manometric mercury column can be adjusted over a wide range by distilling mercury from the storage bulb on the vacuum side, or by forcing i t out of the tip. The stopcock B was opened for about 5 sec. between readings to equilibrate the pressure, but was kept closed at other times to prevent distillation of the solvent and to avoid equilibration of all gas in the manometer system. All readings are corrected to 760 mm. of mercury at 0°C. The hydrogen and deuterium were prepared by electrolysis. Each gas was passed over hot copper, the water was frozen out, and the gas was bubbled through an inclined mercury column into an evacuated 5-liter storage flask. I n this manner the gas can be generated a t atmospherci pressure and collected a t pressures ranging from zero to atmospheric. The inclined tube should be a t least 15 mm. in diameter, and the splash bulb is advisable. After starting, the process proceeds smoothly and requires little attention. The gas was transferred to the manostat system by means of a Toepler pump, P. The storage system was checked from time to time for leaks. The electrical measuring equipment and thermostatic facilities have been described previously (12). The six independent voltages obtained from the double cell were averaged as the final reading. At 25°C. readings were started about 4 hr. after preparation, continued for 6 hr., and checked
THERMODYNAMICS OF ELECTROLYTES I N
HzO-Dso
251
after a 24- to 30-hr. period. Readings over this period agreed to 0.02 millivolt in most cases. To minimize hysteresis, temperature changes were made slowly a t a rate of 5°C. oyer a 2-hr. period. Constant readings were always obtained within 15 min. after reaching constant temperature, except a t 5°C. and IOOC. Three readings a t half-hour intervals were taken at' constant temperature. The rate of attainment of exchange equilibrium between the gas and solvent car lot be estimated from th'e change in E.M.F., since a n unknown time ic, required to saturate the solution with gas. Starting with pure hyd sgen and a solvent containing 64 per cent D, equilibrium was reached min. after the cell was filled and rocking started. The same equilibjr rium values are obtained starting with either pure hydrogen or deuterium, as shown by figure 3 and legend.
.
o
/d
JO
30
10
30
so
70
80
90
/oo
-a/./o7,
FIQ.3. E.M.F. of process 1 plotted ae sfunction of the deuterium content of the eolvent. e, initially pure HIgas and thermal silver chloride electrodes; 0 , initially pure DI gas and electrolytic silver chloride electrodes.
The concentration of hydrogen chloride was reduced to a uniform molal basis by calculating moles of chloride ion per 55.51 gram-atoms of oxygen in the solvent. The vapor pressure of pure deuterium oxide was taken from the data of Miles and Menzies (9). Linear variation of the vapor pressure of the solvent with deuterium content was assumed.* Corrections were made for the light water introduced from the stock solution and for the water evaporated during evacuation. Weights were reduced to weights in vacuo, and corrections were applied for the buoyancy of The changes in vapor pressure with deuterium content will be linear only if the vapor pressure of HDO is the mean of protium oxide and deuterium oxide. Resulte of Stedman (Can. J. Research lSB, 114 (1935)) indicate a sagged curve, but the deviation is certainly within 1 mm. of mercury or f 0 . 0 2 millivolt.
1
252
EVAN NOONAN AND VICTOR K, LA MER
hydrogen or deuterium replacing air in the flask. E.M.F. values in light water at corresponding molalities were interpolated from the data of Harned and Ehlers (7). The subscript n in E,, refers to the fraction of deuterium in the solvent defined as FD = n = As/0.1079; 0 < n < 1. Thus EOis a n E.M.F. in pure water; Eo., a n E.M.F. when F D = 0.4. The superscript zero indicates a molal potential, Le., the E.M.F. has been corrected to a hyppfhetical molal activity of the solute equal to unity. It is impractical to obtain E! by measuring an extensive series of cells at varying acid concentrations and extrapolating to infinite dilution s h i l e the deuterium concentration is kept constant. The difference E l o F, was measured at a concentration of about 0.03 to 0.04 molal. &.?L&found by assuming that the change in interionic activity coefficient with concentration is the same in light and in heavy water, with an allowance for the minor difference in dielectric constants of protium oxide and deuterium oxide. Defining Hz and D) a t 760 mm. as the standard gaseous state, and letting y represent the mean interionic activity coefficient, referred to infinite dilution in protium oxide and deuterium oxide as unity, then
EO = E: - PRT/F In
YHC~(H~O)
Through the equation log y =
-A(M)l/z
we obtain
Values of A in the Debye-Huckel limiting law for protium oxide and deuterium oxide have been calculated from the recent dielectric constant data of Wyman and Ingalls (15), and are presented in table 1. Experimental data at 25°C. are presented in table 2. The E! - E: values are given only for large values of n, Calculations of E! - E: for lower values of n were not made, because of a possible uncertainty in the dielectric constants of solvents containing large amounts of the unsymmetrical HDO. The E.Y.F. of process 1 is plotted in figure 3 as a function of the deuterium content of the solvent; a pronounced maximum occurs at n = 0.75. The extrapolated value in 100 per cent deuterium oxide for E: - E", is 0.00447 volt; the Eo value for cell I is therefore 0.21792, compared to the value of 0.22239 volt given by Harned and Ehlers (7) for cell I1 a t 25OC.
TABLE 1 Values o j A jor protium oxide and deuterium oride A Dt0 -
0.492 0.496
0.489 0.493 0.498 0.502 0.506 0.511 0.516 0.521 0,527
30 35 40 45
0.00024 0.00026 0.00027 0.00031 0.00033 0.00035 0.00038 o.oO041 0.00044
0.500 0.504 0.509
0.514 0.519 0.524 0.530
TABLE 2 Electromotive force oj the cell Ht I (HCl D C l ) , in HIO-DIO I AgC1-Ag a: 96°C. i n protium-deuterium on’de mixtures o j deuterium Fraction n and molality m n
m
0.989 0.986 0.984 0.984 0.982 0.966 0.956 0.955 0.954 0.915 0.915 0.909 0.848 0.848
0.02883 0.03282 0.04607 0.01626 0.02991 0.03287 0.05927 0103190 0.15233 0.03030 0.03378 0.03419 0.03322 0.03826 0.04028 0.04428 0.03341 0.03182 0.02817 0.03158 0.02901 0.03417 0.03239 0.03148 0.03595 0.02899 0.03115 0.02555
0.848
0.848 0.813 0.813 0.739 0.739 0.644 0.523 0.522 0.436 0.268 0.266 0.158 0.008
-
E4 F,
-
E,
FD
0
0.41247 0.40620 0.38984 0.44031 0.41071 0.40614 0.37769 0.40758 0.33204 0.41007 0.40480 0.40423 0.40562 0.39880 0.39632 0.39176 0.40534 0.40770 0.41360 0.40806 0.41218 0.40626 0.40684
n
0.40792 0.40164 0.38532 0.43574 0.40610 0.40148 0.37286 0.40271 0.32722 0.40480 0.39958 0.39890 0.39977 0.39312 0.39047 0.38609 0.39946 0.40180 0.40758 0,40206 0.40636 0.39920 0.40169 0.40360 0.39882 0.40918 0.40691 0.41826
0,40823
0.40181 0.41220 0.40873 0.41831
* In plotting results were corrected t o 0.03 m . 253
Eo
- E.
+o ,00455 0.00456 0.00452 0.00457 0.00461 0.00466 0.00483
0.00487 0.00482* 0.00527 0.00522 0.00533 0.00578 0.00568 0.00585 0.00567 0.00588 0.00590 O.OO602 0.00600 0.00582 0.00506 0.00515 0.00463 0,00299 0.00302 0.00182 O.ooOo5
E:
- E:
0.00461 0.00462 0.00459 0.00461 0.00467 0.00472 0.00491 0.00493 0.00495
254
EVAN NOONAN AND VICTOR K. LA MER
TABLE 3 Temperature coeficient data A#/0.1079
m
BYPBBATUB!
-
Eo
FD
-
Eo 0
FD
1
Eo - b -
‘C.
0.982
0.986
0.02991
0.03282
25 30 36 40 46
0.41071 0.41066 0.41044 0.41004 0.40957
5 10 15
0.40521 0.40579 0.40599 0.40612 0.4062l
0.4O090
0.00431
0.40111 0.40176 0.40181 0.40164
0.00468 0.004p 0.00431 0.00458
0.00436 0.00462
0.37848 0.37858 0.37837 0.37807 0.37769 0.37709 0.37639 0.37545 0.37445
0.37410 0.37403 0.37390 0.37348 0.37288 0.37212 0.37121 0.37015 0.36892
0.00438
0.00444 0.00468 0.00464
0.40651 0.40709 0.40732 0.40753 0.40758 0.40753 0.40718 0.40678
0.40204 0.40251 0.40270
0.00449 0.00458 0.00462
0.45286
0.00463
0.40271 0.40243 0.40199 0.40130
0.00487
20
25 0.956
0.06926
5 10 15
20 25
30 35 40 45 0.955
0.03190
5 10 15
20 25 30 35 40
0.40610 0.40589
0.40550 0.40498 0.40424
0.b-
0.00471 0.00494
O.Oo506 0.00533
0.00452 0.00447 0.00459 0.00483 0.00497 0.00518
0.00530 0.00553
0.00506 0.00525 0.00548
c O.,
0.W 0.00435 0.00473
0.00428
0.00467 0.00491
0.00505 0.00527
0.00540 0.00685 0.00453 0.00482 0.00487 0.00469 0.00493 0.00512 0.00532 0.00555
TABLE 4 Tharmodynamic quantities of db0C. for the process 1/2 Hi D C l ( D i 0 ) 1/2 Di H C l ( H i 0 )
+
0.955 0.956 0.982 0.986 1.O (extrap.)
+
wltr
calmied
Cd. &a.
calorie4
0.00493 0.00491 0.00467 0.00462 0.00447
113.7 113.2 107.7 106.5 103.1
1.OO
184 146 133 137 120
0.87 0.81 0.82 0.75
THERMODYNAMICS OF ELECTROLYTES IN
HaO-DzO
255
Experimental results of cell I at. the various temperatures are given in table 3. At the lower temperatures the data in both light and heavy water are less reliable, and the differeyes correspondingly less certain. The thermodynamic quantities for process 1 listed in table 4 have been evaluated a t 25’C. by numerical differentiation of the data from 15°C. to 45°C. The dependence of AS and AH on the deuterium content of the solvent indicates that a maximum for these quantities will exist similar to AF, as shown in figure 3. The data for l(r E,/T for m = 0.05926 when n = 0 and when n = 0.956 are plotted against 1/T in figure 4. The slope of the resulting curve is a
/o ‘/r
FIQ.4. The temperature dependence of
E.Y.F.
of cells I and I1 an
process 1
plotted as E / T against 1/T.
direct measure of AH for the corresponding cell process. Since both the light and the heavy water data fall on smooth parallel curves, AC, is not zero for the process involving the silver chloride electrode in eithersolvent, &s would be expected. On the other hand, when the sensitive ditrerence function
lo7(&’: - Z ) / T is plotted against 1/T, a straight line results except for the two less certain points a t the lowest temperatures. AC, for the exchange process 1 is
256
EVAN NOONAN AND VICTOR IC. LA MER
accordingly very small if not actually zero, Le., AH is practically independent of temperature. For theoretical purposes the equilibrium constant of the reaction 1/2Hz
+ Df(DzO)
= 1/2D2
+ H+(H20)
(2)
is frequently desired. The free energy change of process 2 differs from that of process 1 by the process Cl-(DzO) = Cl-(HzO)
(3)
representing the difference in free energy of solvation of chloride ions in light and heavy water. This process, however, is inaccessible to experimental determination, a point which will be elaborated in another paper. Gross and Wischin (6) have mistaken process 1 for process 2 in their theoretical treatment. Orr and Butler (10) utilize process 1for the calculation of the constant L of their semi-empirical equation for equilibria in isotopic mixtures, but are obliged to ignore the effect of chloride ions. Abel and Redlich (2) emphasize that the exchange process 1 is not the “normal potential” of the deuterium gas electrode. I n order to ascribe a value for the normal potential of deuterium it i s necessary that the half-cell process proceed in the same solvent, HzO, f o r which the normal potential of Hzi s taken arbitrarily as zero. The specification that the process must be conducted throughout in protium oxide as the solvent is impossible to meet experimentally on account of the rapid exchange of gases with solvent on platinum black as the catalyst. The closest approach would be given by the process 1/2 Dz
+ &O+(HzO)
= 1/2 Hz
+ HzDOf(H20)
(4)
when the concentration of H2DO+is made negligibly small. On the basis of process 4 Abel and Redlich compute a normal potential for deuterium which is approximately 44 millivolts less noble than hydrogen. We also subscribe to their view that little is to be gained by attempting to define a normal potential of the deuterium electrode against the hydrogen electrode. If silver bromide electrodes and hydrobromic acid had been used in cell I the following process could be obtained
+ DBr(D20) = 1/2 De + HBr(H20)
1/2 Hz
(5)
The free energy of this process would differ from that of process 2 by the difference in the free energy of sdvation of bromide and chloride ions in the two solvents. A somewhat more complicated process has been measured by Drucker (5). (A)
Dz I KDSOa(O.ll5C in Dz0) I Hg2S04-Hg
(B)
Hz I KHS04(0.115Cin HzO) 1 HgzS04-Hg
E E
= 0.7627 volt = 0.7527 volt
THERMODYNAMICS OF ELECTROLYTES I S
&O-DzO
257
The net process for cell A minus cell B is 1/2 Dz + KHSOa(H.0) = 1/2 Hz
+ KDSOd(Dz0)
E
= 0.0100 volt (6)
Taking the second dissociation constant of sulfuric acid as 2 X lo-*, the hydrogen-ion concentration in a solution of potassium hydrogen sulfate 0.115C in HzO is 0.059C. From the empirical curve of Rule and La Mer (12) the dissociation constant of DSOa- is estimated as 2.5 times less than that of HS04- or 8 X Ap’plying the mass law, the deuterium-ion concentration in a solution of potassium deuterium sulfate 0.115C in deuterium oxide is 0.035C. After considering the contribution to the E . Y . F . difference of cells , 4 and B due to the concentration of hydrogen and deuterium ions, respectively, the E.M.F. of the combination still has a different sign from the E.M.F. of process 1 as a result of the specific differences in the free energy of solvation of chloride, sulfate, and potassium ions. SUMMARY
1. The cell without transference
Dz DC1
Dz0 min
Hz HC1
1 AgC1-Ag
HzOI
has been studied at 25°C. over a wide range of deuterium content. The Eo value at 100 per cent deuterium oxide is 0.21792 & 0.00005 volt, or 4.47 millivolts less than for hydrogen chloride in protium oxide. 2. The free energy change of the process 1/2 H z
+ DCl(m in DzO) = 1/2 Dz + HCl(m in H 2 0 )
(1)
is a complicated function of the deuterium content of the solvent, passing through a maximum at a deuterium fraction 0.75, corresponding to an E.M.F. 6.0 millivolts lower than Eoin protium oxide. 3. Thermodynamic quantities for process 1 at high deuterium concentrations have been evaluated from temperature coefficient data. 4. With the rocking electrode described, equilibrium between the gas phase and solvent is achieved rapidly, starting with either pure deuterium or hydrogen. (1)
(2) (3) (4) (5)
REFERENCES ABEL,BRATU,AND REDLICH: Z . physik. Chem. Al73, 353 (1935). ABELAND REDLICH: Z . Elektrochem. 44, 204-5 (1938); cf. reference 1. BROWN:J. Am. Chem. SOC.66,646 (1934). CLARK: Determination of Hydrogen Ions. 3rd edition, p. 295. The Williams & Wilkins Co., Baltimore (1928). DR*CKER:Trans. Faraday SOC.33, 660 (1937).
258
EVAN NOONAN AND VICTOR K, LA MER
(6) GROSSAND WISCEIN:Trans. Faraday SOC.32, 879 (1936). (7) HARNED AND EHLERS: J. Am. Chem. SOC.64, 1350 (1932);66,2179 (1933). (8) KORMAN AND LA MER: J. Am. Chem. SOC.68, 1396, 1399 (1936). (9) MILESAND MENZIES:J. Am. Chem. SOC.68, 1067 (1936). (10) ORBAND BUTLER: J. Chem. SOC.1957, 330. (11) RULEAND LA MER: J. Am. Chem. SOC.68,2339 (1936); cf. SMITE,E.R., AND TAYLOR, J. K.: J. Research Natl. Bur. Standards a0, 837 (1938). (12) RULEAND LAMER: J. Am. Chem. SOC.60,1974 (1938). (13) SCHWARZENBACH: 2.Elektrochem. 44,46 (1938); 44,302 (1938). (14) SHWARZENBACH, EPPRECHT, AND ERLENMEYER: Helv. Chim. Acta 19, 1292 (1936). (15) WYMANAND INQALLB: J. Am. Chem. Soc. 60, 1182 (1938).
