1186
ROBERT GARY,ROGERG. BATES,AND R. A. ROBINSOX
Thermodynamics of Solutions of Deuterium Chloride in
Heavy Water from 5 to 50"
by Robert Gary, Roger G. Bates, and R. A. Robinson National Bureau of Standards, Washington, D . C.
(Receiued December 1411963)
The standard e.m.f. of the cell Pt ; Dz(g) a t 1atm., DC1 in DzO,AgCl; Ag has been determined from 5 to 50'. At 2.5' the standard e.m.f. is lower by 9.78 mv. (on the molality scale) or 4.31 mv. (on the inole fraction scale) than the standard e.m.f. of the corresponding cell with a hydrogen electrode and a solution of hydrochloric acid in ordinary water. ThermoHCl(in HzO) = dynamic quantities have been calculated for the reaction l/zDz(g) 1/2Ha(g) f DCl(in DaO). At 2 3 O , A G O is 418 joules mole-', A H O k -611 joules-', and AXo is - 3.5 joules deg. -l mole-', when all four substances are in the standard state on the mole fraction scale. The mean ionic activity coefficient and relative partial molal enthalpy of DC1 a t molalities from 0.01 to 0.05 in heavy water have been obtained and are compared with those for HC1 in HzO. The activity coefficient of DC1 in D20is slightly smaller than that of HC1 in HzO a t the same molality; a t m = 0.05, t = 2 5 O , the difference in log yi is 0.0022.
+
Introduction The standard e.m.f. of the cell
+
Pt; Dz(g) a t 1 atm., DCl(m) in D,O, AgCl; Ag
(I)
together with the known standard e.1n.f. of the corresponding cell with a hydrogen electrode in a solution of hydrochloric acid in ordinary water furnishes a measure of the change in free energy of the reaction '/zDz(g)
+ HCl(aq)
=
'/zHz(g)
+ DCl(in DzO)
It is also of fundamental importance to the determination of dissociation constants and other thermodynamic properties of weak acids in deuterium oxide by means of the Harned-Ehlers cell' as well as to any effort to give meaning to pD measurements in deuterium oxide. The silver-silver chloride electrode has had wide application in the determination of thermodynamic data for solutions in ordinary water.2 In addition, this electrode has found use in establishing pH standard~.~ In 1933 Abel, Bratu, and Redlich4 used this electrode in solvents consisting of mixtures of light and heavy water, but only one measurement was made in a solvent containing inore than 90 mole % of DzO. It should be noted that these authors defined the T h e Journal of Physical Chemistry
acid concentration, m', as moles of solute in 55.51 moles of (Hz0 DzO). In the present paper concentrations are expressed in moles per kilogram of solvent, designated m. Noonan and La Mer6 made a inore extensive study of cell I using solvents of compositions approaching pure deuterium oxide ; some measurements were made oyer a range of temperatures. They also expressed acid concentrations in terms of a reduced molality m', that is, as moles of solute in 33.51 moles of solvent. Renewed interest in the properties of acids and bases in heavy water has underscored the need for an operational scale for measuring conventional deuterium ion activities and, consequently, for pD standards with which to establish such a scale. As a first step, the standard e.1n.f. of cell I must be determined. ~~~~
(1) H. S. Harned and It. W. Ehlers. J . Am. Chem. Soc., 54, 1350
(1932). (2) H. 8 . Harned and B. B. Owen, "Physical Chemistry of Elertrolytic Solutions," 3rd Ed., IXeinhold Publishing Corp., New York,
N. Y., 1958. (3) See R . G . Bates, J . Rcs .Vatl. B u r S t d . , 66A, 179 (1962). (4) E. Abel, E. Bratu, and 0. Itedlich. 2 . P h y s i k . Chem. (Leipzig), 173A, 353 (1935). (5) E. Noonan and V. K. La Mer, J . P h y s . Chem., 43, 247 (1939).
THERMODYNAMICS OF I~EUTERIUM CHLORIDE SOLUTIONS IN HEAVY WATER
Deuterium gas is now available in comparatively large quantity. The measurement of the e.m.f. of cells of type I is relatively easy and we have now made a fresh study of the problem. This paper reports measurements of cell I a t temperatures of 3 , 15, 25, 35, 45, and 50" for five concentrations of deuterium chloride from 0.01 to 0.05 m. The data have been used to derive the standard electromotive force of cell I and the activity coefficients of deuterium chloride a t these temperatures, as well as the relative partial molal enthalpy of DCI in DzO a t 25". The difference between the standard electromotive force of cell I and that of the corresponding cell in ordinary water has been found to be 9.78 mv. a t 25". The data are shown to be consistent with the earlier data of Noonan and La Xer5 when the same method of calculation is used
Experimental Materials. The heavy water had a density of 1.10416 g. ml. -l a t 25', indicating an isotopic purity of 99.7 mole 70.6Its specific conductance was 3 X ohm-' em--* a t 25'. The stock solution of deuterium chloride (about 0.05 m) was prepared by bubbling dry HCI gas, generated by adding concentrated HzS04 to bromide-free NaCl, into heavy water. The amount of hydrogen added in this way was less than 0.1 mole % of the deuterium present. Preparation of the Cells. The cells were of Pyrex glass throughout, except for Teflon stopcocks. The design was similar to that of Harned and his co-workers' and used by workers iLnthis laboratory, except for the following features. Presaturation of the deuteriuiii gas by portions of the same solution as that in the electrode compartments was achieved by a threestage saturator with IZ sintered glass disperser in the middle stage. The glass joints were specially constructed with two seating surfaces separated by a groove 5 nim. wide to protect the solution from contamination by grease or by water from the therniostat. The deuterium electrodes were partially inimersed in the solution, the upper half being exposed to the deuterium above the solution. The deuterium gas was stated by the suppliers to contain a t least 99.7 mole % of Dz; before entry into the saturators and the cell it was passed through a Deoxo purifier to remove traces of oxygen. The silver-silver chloride electrodes were of the thermal-electrolytic type prepared according to the recommendation of Bates.* Before the cells were filled, the electrodes were thoroughly washed and soaked in ordinary water and inserted into the empty cell vessels, which had been flushed with helium. The cells were then evacu-
1187
ated and the vacuum maintained for about 30 inin to dry the electrodes, after which the cells mere filled with deuterium gas. The cell solutions, deaerated and saturated with deuterium, were forced into the cell vessels by deuterium pressure, the cell being vented while the solution entered. Preliminary experiments with hydrogen and solutions in ordinary water showed that this technique gives stable, reproducible results in agreement with data obtained earlier in this laboratory. The cell solutions were prepared by weight (vacuum corrections were applied) by dilution of the stock solution. The solutions were made up in air, transferred by pressure to helium-filled flasks, weighed, boiled a t room temperature under vacuum, saturated with deuterium gas, and weighed again. The concentration of the solution was corrected for the loss of heavy water on boiling. The use of helium-filled flasks simplified the vacuum correction, since helium and deuterium have nearly identical densities.
Results The e.m.f. of cell I a t five molalities is recorded in Table I. The first measurements were made with a cell containing 0.02003 m DC1, and some instability of e m f . was found a t 55". Therefore, 50' was chosen as the highest temperature a t which measurements of the other four solutions were made. The value in parentheses (at 50") in Table I is an interpolated one. For purpose of comparison two cells with hydrogen electrodes and containing exactly 0.01 m HCl in ordinary water were measured; the e.1n.f. values are also given in Table I. The standard e m f . of the deuterium oxide cell (on the molality scale) was found by extrapolating to zero concentration the function
E,"
= E f 212 log m - 21c
A (mdo)'"
1
+ Ba*(mdo)1'2 (1)
where k is written for (RT In 1 0 ) l F . The ion-size parameter,g a*, was put equal to 4.3 8. Values of Ado"' and Bdg1'*,the constants of the Debye-Huckel equation, were calculated with the dielectric con(6) I. Kirshenbaum, "l'hysical Properties and Analysis of Heavy Water," H. C. Vrey and G. M. Murphy, Ed., McGraw-Hill Book Co., Inc., New York, N. Y . , 1951, p. 17. (7) See H. S. Harned and J. 0. Morrison, Am. J.Sci., 33, 161 (1937). (8) R. G. Bates, "Determinatlon of pH," John Wiley and Sons, Inc., New York, N. Y . . 1984, p. 282. (9) For their data in ordinary water, R. G. Bates and V. E. Bower [J.Res. FufZ. Bur. Std.. 53, 283 (1954)l put a* = 4.3 A . at 0 to 30' and 5.0 A. at 35 to 55'. If we put a* = 5.0 1.at 5Q0,the present data for heavy water give an extrapolated E," = 0.19312 v. a t thi.; temperature instead of 0.19310 v. with u* = 4.3 1.
Volume 68, n'umber 5
M a y , 1.964
1188
ROBERT GARY,ROGERG. BATES,AND R. A. ROBINSON
Table I : Electromotive Force" of the Cell P t ; Dz(g) a t 1 atm., DCl(m) in DzO, AgC1; Ag from 5 to 50' 50
15'
250
350
450
50"
0.48081 0.41911 0.40080 0.38777 0.37765 0.45962 0.5232 0.3429
0.45305 0.42031 0,40135 0 :38784 0,37739 0,46222 0,5319 0.3448
0.45458 0.42071 0.40110 0.38721 0.37639 0.46425 0.5413 0.3467
0.45547 0.42048 0.40027 0.38580 0 I37473 0.46571 0.5513 0.3488
0.45573 0.41964 0.39881 0.38394 0.37267 0.46656 0.5622 0.3604
0.45562 (0.41901) 0.39783 0.38280 0.37120 0.46684 0.5678 0.3513
m
0.010015 0.02003 0.02999 0 04001 0.04998 0.01000~ I
Ado'/' Bdo'/z
Electromotive force in volts.
Table I1 : Standard Electromotive Force of the Cell P t ; Dz(g) a t 1 atm., DCl(m) in D20, AgC1, Ag from 5 to 50' Em" (DzO),
u,
E m o (HzO),
OC.
V.
mv.
V.
5 15 25
0.22528 0.21931 0.21266 0.20532 0,19733 0.19310
0.03 0.04 0.04 0.03 0.02 0.02
0.23420 0.22862 0,22244 0.21574 0,20839 0.20456
35 45
50
--Emo. mv.
--EN',
8.92 9.31 9.78 10.42 11.06 11.46
3.81 4.02 4.31 4.76 5.22 5.53
+ 2k log my,
m = 0.01
together with the activity coefficient data of Bates and Bower,@which are in good agreement with the earlier data of Harned and Ehlers.12 Values of this standard e.ni.f. on the molality scale are also given in Table I1 together with the difference in standard e.1n.f. between the ordinary water and the heavy water cells on both the molality (m) and mole fraction ( N ) scales
AEO
Eo(D,O) - EO(Hz0)
The difference in standard e.1n.f. (on the inole fraction scale) can be expressed as a function of the temperature by the equation
--ENo
= 3.74 f (11.40 X 10-s)t f
(4.87 The Journal of Phy8&%l Chemistry
0.5736 0.3523
x
10-4)ta
where t is in degrees Celsius and A E N o is in millivolts. Alternatively
- AEN'
=
36.96 - 0.2546T
(2)
+ (4.87
x
10-4p
(3)
where T is in degrees Kelvin. Since AGO = - FAEA7O , where AGO is the free energy change of the reaction '/2DZ(g)
+ HC1 (in HzO)
--c
'/zHz(g)
+ DC1 (in DzO)
we can now calculate thermodynamic functions for this reaction
mv.
The standard e.m.f. of the cell with ordinary water as solvent was calculated using the equation
Emo= E
0.41821
These results refer to the cell P t ; Hz(g) at 1atm., HCl(O.01 m) in HzO, AgCl; Bg.
stants given by Malmbergio and the density data given by Chang and Tung." Values of these constants are shown a t the bottom of Table I. Table I1 gives the extrapolated values of the standard electromotive force on the molality scale, together with the standard deviation.
t,
55"
AGO
3566.4
- 24.57T + 0.04699T2
A H o = 3566.4 - 0.04699T2 ASo
=
24.57 - 0.09398T
(4)
(5) (6)
(7)
ACpo = -0.09398T
At 25", AC," = -28 joules deg.-l mole-l. Values of the other functions are given in Table 111, which also includes the change in electrostatic free energy, Table I11 : Thermodynamic Functions" for the Reaction HCl(in HzO) = l/SHz(g) DCl(in DzO) '/zDz(g)
+
+
t, oc.
AGO
AH"
ASo
AGel
5 15 25 35 45 50
368 388 418 457 50 6 534
- 69 - 335 -611 - 896 - 1190 1331
-1.6 -2.5 -3.5 -4.4 -5.3 -5.8
27 34 42 49 56 63
-
AGO and AH" are expressed in joules mole-' and AS" in joules deg.-l mole-l.
(10) C. G.Malmberg, J. Rcs. Natl. Bur. Std., 60, 609 (1958). (11) T. L. Chang and L. H. Tung, Chinese J. Thus., 7 , 230 (1949). (12) H. S. Harned and R. W, Ehlers, J . Am. Chem. SOC.,55, 2179 (1933).
1189
THERMODYNAMICS OF DEUTERIUM CHLORIDE SOLUTIONS IN HEAVY WATER
Table IV : Activity Coefficients of DCl in DzO Solutions" 112
0.01 0.02 0.03 0.04 0.05
15'
6'
0,0440 0,0580 0.0674 0.0746 0.0795
0.0446 0.0591 0.0687 0,0757 0,0810
25"
25ab
350
450
0,0454 0.0603 0,0701 0.0772 0,0827
0.0436 0.0578 0,0675 0,0747 0,0805
0.0464 0.0615 0.0714 0.0788 0,0847
0.0474 0.0626 0.0729 0.0805 0,0867
a The negative logarithm of the molal activity coefficient is tabulated. mole-'.
calculaFd by the Barn equation with r H = r D = rc1 = 2 A. corresponding to the removal of hydrogen and chloride ions from ordinary water followed by the introduction of deuterium and chloride ions into heavy water. It will be observed that this change in electrostatic free energy is only about one-tenth of the total free energy change.
Discussion We have recalcu1a)ted the data of Noonan and La Mer6 at 25 " by converting their values of E to absolute volts and their values of m' to moles per kilogram of solvent (m). Our calculations give the following results : m
E E (calcd )
0 01465 0 43588 0 43597
0 02596 0 40805 0 40810
0 04150 0 38545 0 38539
The values labeled E (calcd.) were obtained from the data of the present investigation. The results for 0.02955 m DCl (or 0.03282 m') are as follows: E E (calcd.)
5 O
15'
25O
0 40103 0 40145
0 40189 0 40199
0 40177 0 40180
and for 0.02695 m DC1 (or 0.02991 m') : 25
E E (calcd.)
'
0 40623 0 40629
35O
45O
0 40563 0 40562
0 40437 0 40432
With the one exception of the cell at 5", the agreement is excellent, the average difference being only 0.06 mv. Abel, Bratu, and Redlich4 found ,an e.ni.f. of 0.3492 v. for the cell Pt; 98.4 mole yo Dz, 0.09007 712 DC1 in 97.0 mole yo DzO, AgCl; Ag at 21". Froin our data we calculate an e.m.f. 0.4 mv. lower than theirs but some of this difference can be accounted for by the appreciable amount of hydrogen in their cell. The values of A G O and related thermodynamic quantities in Table I11 are all based on AE,' values, that is, they refer to transfers between HC1 (in HzOi)
* These values
50'
0.0479 0,0634 0.0736 0.0813 0.0878
refer to HCl in H20 at 25".
t2
(250)C
290 410 470 520 630 In joules
and DC1 (in DzO) when each is in its standard state on the mole fraction scale. The free energy on the molality scale will be different by
where w designates molecular weight. l 3 This quantity becomes, on insertion of the appropriate numerical values, 1.7652' joules inole-'; thus, the values of A H " and AC," are the same on each scale but AGO becomes larger, e.g., 944 joules mole-' at 25' on the molality scale compared wit,h 418 on the mole fraction scale. Likewise, the entropy change is more negative by 1.8 joules deg.-' mole-' a t all temperatures, e.g., -5.3 joules deg.-' mole-' a t 25" on the molality scale compared with -3.5 on the mole fraction scale. This discussion of scales of reference is pertinent to the work of Noonan and La Mer who employed neither the mole fraction scale nor the molality scale in its conventional sense. It can be shown that the free energy change on their scale is indeed the free energy change on the mole fraction scale, and this is true for the associated thermodynamic quantities. Our values (at 25") of AGO = 418 joules i n o k l , A H " = -611 joules mole-', and AS" = -3.5 joules deg.-] mole-' compare with their values of AGO = 431 joules A H " = -502 joules mole-l, and AS" = -3.1 joules deg.-lniole-'. The activity coefficient of DC1 in DzO is given in Table IV, where the values a t 25" are compared with the corresponding values for HC1 in H20. The value of the relative partial molal enthalpy of DC1 in DzO,is given in the last column of the table. There is a difference of 0.002 to 0.003 in log yk, and it is of interest to note that this difference is less dependent on the dielectric constants of ordinary and heavy water than on the difference in the densities
zz,
(13) R. A. Robinson and R. H. Stokes, "Electrolyte Solutions," 2nd Ed., Butterworths, London, 1959, pp. 31 and 352.
Volume 68, Number 6 M a y , 1964
J. C. SHEPPARD
1190
of the two solvents. Thus the A constant of the Debye-Huckel equation is 0.5115 mole-l’z 1.’’’ for ordinary water a t 25’ and 0.5151 for heavy water,
whereas Ado”z is 0.5108 for ordina-y water and 0.5413 for heavy water. The value of for DC1 in DzO is about 30% higher than for HC1 in H20.9v12
z,
The Kinetics of Reduction of Neptunium(V1) by Vanadium (111) in Perchloric Acid’
by J. C. Sheppard Hanford Laboratories, General Electric Company, Richland, Washington
(Received September 13,1963)
The rate law for the reduction of neptunium(V1) by vanadium(II1) in perchloric acid obeys the expression, rate = [Np(VI)][V(III)]fk k’/[H+]]. At 25’ and a t an ionic strength of 2.0, the values for k and k‘ are 6.3 f 1.2 M-l sec.-l and 20.3 f 0.5 sec.-l, respectively. The corresponding energies and entropies of activation are 18.6 f 1 kcal./ mole and 5 e.u. for the hydrogen ion concentration independent path and 22 f 4 kcal./ mole and 19 e.u. for the hydrogen ion concentration dependent path.
+
The study of the kinetics of reduction of neptunium(VI) by vanadium(II1) in perchloric acid provides an opportunity to compare results obtained for other reactions involving the reduction of neptunium(V1) . 2 , 3 Since neptunium(V1) is isostructural with plutonium(VI), it is also of interest to compare the rates and kinetics of reduction of these ions with a common reducing agent, vanadium(II1). Preparation of Reagents. All reagents used in this investigation, unless specified otherwise, were reagent grade. Sodium perchlorate solutions were prepared by addition of an equivalent amount of perchloric acid to a sodium carbonate slurry. Perchloric acid solutions of vanadium(II1) and vanadium(1V) were prepared in the following ways. Vanadium pentoxide, formed by the ignition of ammonium metavanadate, was suspended in 1 M perchloric acid and electrolyzed until vanadium(II1) was f ~ r m e d . A ~ second preparation involved the dissolution of ammonium metavanadate in hot, dilute sodium hydroxide. The centrifuged solution was acidified with perchloric acid to precipitate the hydrated vanadium pentoxide. The Journal of Physical Chemistry
The oxide was washed several times with dilute perchloric acid and then suspended in 1 M perchloric acid where it was electrolyzed to form vanadium(III).5 Neptunium(V1) stock solutions were prepared by ozone or electrolytic oxidation of neptunium(V) in 1 M perchloric acid. The results of the kinetic experiments were not dependent on the mode of preparation of the reactants. Analytical. The concentrations of vanadium(II1) and vanadium(1V) in perchloric acid solutions were determined spectrophotometrically using a Cary Model 14 spectrophotometer and the molar extinction coefficients found by Appelman and S ~ l l i v a n . ~ Total neptunium concentrations were determined by a(1) Work performed under contract AT-(45-1)-1350 between the General Electric Co. and the U. S.Atomic Energy Commission. (2) (a) J. C. Sullivan, A. J. Zielen, and J. C. Hindman, J . Am. Chem. Soc., 82, 5288 (1960); (b) A. J. Zielen, J. C. Sullivan, and J. C. Hindman, ibid., 80, 5632 (1958). (3) D. Cohen, J. C. Sullivan, and J. C. Hindman, ibid., 76, 352
(1954). (4) S.W. Rabideau, J . Phya. Chem., 62, 414 (1958). (5) E. H. Appelman and J. C. Sullivan, ibid., 66, 442 (1962).
