The ionization constant of heavy water 4D,O) in the temperature range 298 8s 523 K
DAVID WILLIAM SHOESMITH
A N DWOON LEE
Research C/ietili.strj B~.atzcll, I.P'/~ifeshell N~rcleclr. Research Esrablishti~et~t, Pitmi~a, !Vczn., Caiznda ROE ILO Received June 7, 1976
DAVID WILLIAM SHOESEVIITH and woo^ LEE. Can. 9. Chem. 54, 3553 (1976).
The ionization constant of liquid D 2 0 has been measured over the temperature range 298 to 523 K using an aqueous electrolyte concentratioil cell. Values for the standard free energy, enthalpy, entropy, and heat capacity of ionization have been calculated. The results are com- pared to similar results for liquid W20.
DAVID WILLIA~? SHOES~IITH et woo^ LEE. Czn. J. Chem. 54, 3553 (1976).
On a mesure la constante d'ionisation du D:O liquide B des tempCratures allant de 298
B
523 K utilisant une celluleB
concentration d'electrolyte aqueux. 011 a calcule les valeurs pour les energies libres, les enthalpies, les entropies et les capacites calorifiques standards. On compare ces rCsultats avec des rCsultats similaires obtenus pour I'eau liquide.[Traduit par le journal]
Introduction t o obtain the ionization constant of D 2 0 , along In the ('ANDU-pHWl nuclear reactor, D 2 0 the saturation VapoUr pressure CUrle,
LIPt o is used both as a moderator and a coolant. In the 523 K.
coolant circuit the D 2 0 is maintained a t temper- atures between 523 and 573 K . T o minimise corrosion and the spread of radioactive corrosion products in the coolant circuit, strict control of thc chen~ical conditions is necessary. At present a large amount of the required chemical informa- tion is obtained from experiments performed with light water systems under similar conditions.
T o establish a firmer basis for the c a l c u l a t i o ~ ~ of the most favourable chemical conditions for reactor operation it is necessary to obtain an accurate knolbledge of the physical chemical properties of D 2 0 and h o ~ v they ditl'er from those of H 2 0 a t temperatures up t o 573 I<.
One essential parameter is the ionization constant. This has been extensively measured for H 2 0 (1-13) up to 1000 "C. Thc accuracy of thcsc measurements has been assessed recently by Mepler and Wooley (14) and by Sheeton et
(11.(1 1). The ionization constant for D 2 0 has been measured a number of times a t 298 K (15-20) but only two studies (16, 19) have investigated the temperature dependence of pK,,, and then only over a narrow temperature range.
The present work emplo>s the high temper- ature aqueous electrolyte concentration cell,
Pt /D~,DCl(ti?l),KCl(t7~z) / / K C ~ ( ~ I ~ ) , N ~ O D ( ~ I I ~ ) , D ~ /Pt 'Canadian Deuteriuin Uranium - Pressurized Heavy
Water.
Experimental
Eqlripnzen
r
The electrolyte concentration cell used in this study was the same as described previously by MacDonald, Butler, and Owen (10). The cell temperature was controlled by immersion in a n oil bath. The temperature was followed in both cell compartments and in the bulk of the oil fluid, using chromel-alumel t l p e K thermal couples and a multi-point Leeds and Northrup Speedornax Recorder precalibrated for temperature measurement. The recorder calibration allowed resolution to t 0 . 5 K. Resolution to
k0.1 K was achieved using a potentiometer.
All potential measurements were made with a Dana Model 5330 Digital Voltineter capable of 1 yV resolution.
Potentials were recorded after they had become constant to within 0.1 mV for at least 15 min.
Cizemicals
The D l 0 Mas supplied by AECL Cominercral Products and was 99.78 I O.OJ', D:O. Its specific conductance was 0.57 ohm c n ~ at 23 "C. NaOD (40', in D:O) and DC1 (38(, in D28) here supplied by ICN P11armaceut1- cals. The KC1 was supplied by Fisher (Certified ACS).
Proced1ir.e
The experiiliental procedure was essentially the same as previously reported (10).
The DCI and NaOD solutions vrere made up by volume and the exact concentration determined by titration against standard HC1 or NaOH solution. The concentration used in the calculations was based on a large number of titrations with an overall reproducibiiity of approximately 0.1
- i l.
1 o estiniate the degree of mixing of solutions from the two conlpartn~ents after experiments at elevated temper- atures, the contents of each compartinent were titrated
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3554 CAN. J. CHEM.
after each run. The concentrations were between 5 and 20', different from the original values. However, most of this mixing occurred on cooling which was uncontrolled and consequently fairly rapid between 523 and 373 K.
The potential became erratic on c o o l i ~ ~ g and the porous Teflon junction began to leak. Usually the titration was not performed until -16 h after conipletion of the experiment, allouing plenty of time for mixing through the faulty junction. That leakage was not occurring during the actual experiment was indicated by the stability of the measured potential at elevated temperatures, and its reproducibility over a series of separate experiments.
Above 473 K leaky junctions could be detected by a rapid drift in the measured potential. Potential values were used only if this drift was less than 0.1 to 0.3 mV over the 15 min period during which values were recorded. To minimize this effect no more than two values were re- corded at temperatures >473 K during any individual run.
Results
The potential difference bctwccn the electrodes in the two compartments is related to activities by
FT
here E
=cell potential,
ci, =activity of species i, T
=temperature in K , and s ~ ~ b s c r i p t s 1 and 2 refer t o the outer (DCI) and the inner (NaOD) compartments, respectively. E, is the junction potential. Hence the following expression can be written for pKD20,
where
-y,are activity coefficients. The molalities
nlD+and
t170,-are calculated from the molar concentrations a t 298 I< using the published densities for KC1 solutions in D 2 0 (21). In the experiments performed here, KC1 is always present in concentrations in excess of the acid and base concentrations and. consequently, will be the major factor in determin~ng the soiution ionic strength. Values for
concentrationsof KC1 outside the published range (0.05 to 0.3 mol l k l ) are obtained by linear extrapolation. Such an extrapolation is justified on the basis of the linear variation of density with concentration for KC1 in H 2 0 over the concentration range 0.067 t o 1.274 mol 1-I (22).
The liquid junction potential can be estimated by means of the Henderson equation in the approximate form applicable to solutions of
nearly constant cornposition (6), i.e.
where Z,
=lonsc charge The equivalent con- ductances,
A,,for K ' , Na+, C1-, D-, and OD- in D 2 0 are known only a t 298 K (23,30). Values for higher temperatures are generated by two d ~ f f e ~ e n t methods In the first method the known
X,(equivalent conductance) values in H 2 0 for the above Ions are fitted to
expressionsof the LY P'-
The values of the coeficients a, b, and c derived for the H 2 0 systenl and the measured equivalent conductances at 298 K for the ions in DzO are then used to generate a series of values of
X,for each ion in D 2 0 as a function of temperature.
In the second method,
A,values are generated from viscosities
( 7 , )using the relationship
[51 log
Xi" = (1'log
7,+ bi
The coefficients a' and b' are taken from the light water data of Smolyakov and Veselova (25) and applied t o values for the viscosity of D 2 0 as a function of temperature (28). The values de- rived by the two methods differed by 57, a t 298 K and 7y0 at 523 K. The values from eq. 4 are used in calculating E j . Since there are no criteria by which to compare the above two methods, the choice is arbitrary.
The approximate nature of this calculation has only a small effect on the derived values of pKDzo since the liquid junction potential rep- resents only a minor correction t o the measured potential in all cases except for the solution of lowest ionic strength (f
=0.0285). The calculated effect on pKD,o of a + 10Oi change in
X ivalues is small and shows that the change is negligible compared to other errors in the experiments. For
f
=0.0285 the liquid junction potential rises as high as 3 mV. For all other solutions the value of Ej never exceeds 1.3 mV and rarely rises above 0.8 mV.
The activity coefficient term in eq. 2 is cal- c ~ ~ l a t e d using the expression
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SHOESMITI-I AND LEE 3555
given by Harned and Cook (26) and used by Mesmer and co-~3 orkers (6, 11) and MacDonald
et
(11.(10). The coeficlents In eq. 6 are given by
where
E =dielectric constant and
p =density.
In eq. 8,
a0is the ion size paralnetcr and is assumed t o be independent of temperature. A value of 3.6
Xcm is used in the present work. Since the dielectric constants for H 2 0 and D 2 0 differ only slightly
(<1%) between 298 and 373 K , the expression
based on the experimental data for I-T20, meas- ured by Akerlof and Bshry (27), is used t o evaluate
t n , ~ .The densities of 1920 are taken from the tables prepared by Elliott (28).
The cell voltage, as a function of temperature, was recorded for four different concentrations of KC], and pK values calculated as outlined above.2 Data were also recorded for f
=0.0285, but the pKD,, values obtained were erratic. The relatively large value of Ej previously mentioned and the errors incorporated in its calculation lead t o large uncertainties in the value of pK,,,.
Consequently the va!ues for 7
=0.0285 are not used subsequently.
Interpolated values for 225 deg intervals are plotted as a function of ionic strength in Fig. 1.
These plots are extrapolated t o
=0 and the pKD,, values obtained at zero ionic strength are listed in Table 1 and plotted in Fig. 2. Also listed in Table I are the values obtained by Covington
el cil.
(19), and the values for pKDz0 reported by Sweeton
et(11. (1
1).The data of Table 1 were fitted to the expres- sion
2Complete set of the actual experimental data is available, at a nominal charge, from the Depository of Unpublished Data, CISTI, National Research Council of Canada, Ottawa, Canada K I A 0S2.
IONIC STRENGTH I
FIG. 1. Variation of pKD20 with ionic strength as a function of temperature.
TABLE 1. Ionization constant in molal units for DZO extrapolated to zero ionic strength
298 14.957 14.958 14.955
323 14.184 14.178 14.182
348 13.571 13.579
373 13.115 13.111
398 12.746 12.744
423 12.459 12.460
448 12.246 12.246
473 12.096 12.096
498 12.004 12.004
523 11.968 11.967
"Experimental
\slues. --bvalues
calcuiated fro:n eq. 12.CValues from ref. 19.
dvaiues
from ref. 1 1 .The values of the coefficients pl to pj are listed in Table 2 along nith the values derived for H 2 0 by Sueeton
et rrl.(1 I). Equation 12 fits the data with a standard deviation of 0.0012, and values calculated using this expression are also tabulated in Table 1. The difference
is plotted as a function of temperature in Fig. 3.
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3556 C A N . J. CHEM. VOL. 5 4 . 1976
FIG. 2, Variation of pK with tempei.ature. The data for H20 is fro171 ref. 11. T,,,,, indicates the temperature at which pK passes through a minimum. --- indicates extrap- olated values salcuiated from eq. 12.
TABLE 2. Values of the coefficients derived for a fit to eq. I 2
Value
Coefic~enl This work For E l 2 0 from ref. 11 -
p, -35319 -33 091.6
Pz - i04.37 - iOS.15
1'3 0.10287 0.10757
P4 2.612><106 2.358
:<
1 3 6Ps 6 7 1 . 3 670. SO
Discassion
The data are fitted to e q 12 rather than t o an equation of the form
1141 p~
= 1167-'+
127+
~ I ~ Tused by Covington
ei a / .(19) because e q 12 is found t o reprodace more accurately the high temperature thermodynamic data for ioilization reactions (29). Also a fit to e q 12 allows the data f ~ r H 2 0 t o be extrapolated more accurately to higher temperatures (29) and allows a con~pari-
323 373 4 2 3 473 523 573
T (10
F:G. 3. Difference in the pK values for D20 and Hz0 (from the data of Fig. 2) plotted as a f ~ ~ n c t i o n of temper- ature.
son of the thermodj namic parameters for D 2 0 ionization ~ i t h the corresponding values for HzO ( 1 1 ) .
Co~nparison of our pKD,o values with those reported by Covington
ei;I. (19) using the cell
shows excellentagreement for the temperature range in which the data are duplicated (Table 1).
Some idea of the ~~ncertainties associated with pI(Dzo can be gained rising the maximum accuracy i n the measured parameters. Thus the effects, on pKD.,. of (i) a k0.1 m'd in
E ; ( i i )a 0 . 1 5 change
ini ;and (iii) a IOr', variation in the estimated ionic eqirivalent conductances were computed. On the basis s f such estilnates the i~ncertainties in n a y be given as 5;1-0009 at 298 K , rising t o k0.014 at 423
I(and 0.023 a t 523 K .
Expressions for the thermodynamic param- eters for D 2 8 ionizatioi~ are obtained from eq.
12 by the application of standard ~herrnodynamic
relationships. Thus the standard free energy,
enthalpy, entropy and heat capacity of ionization
can be caicuPated from the fo!lowing expressions
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SHOESMITH AND LEE
TABLE 3. Tl~errnod~naniic quantities for the ionization of D20 and Hz0 at 298 K Value
D20
N20 Parameter This work Ref. 19 Ref. 30 (Ref. 11)
-AGO (kJ mol-1) 85.23 85.37 79.87
AHVkJ mol-1) 60.8'7 59.88 60.62 55.82
A S 0 (kJ K-1 m01-1) -0.8175 - 0.8548 -0.8301' -0.8007 ACpO (J K-' n1olF1) -301.9 -229.3 -231.4
P K D ~ O min 11.953 12.356 11.203
Tm1n 528.5 494 518
QCalculated from the A H o of ref. 30 and the AGO o f rcf. 19.
The values for AGO, AN0, and -TASO are compared to similar values in H 2 0 in Fig. 4.
The values calculated from the data of Covington
etal. (19) are also included for compa-' 11son.
Some discrepancy exists between our resuits and those of Covington et al. around the iowest temperature (298 K) used in the present work.
To facilitate this 'comparison the values for 298 K are tabulated in Table 3 and compared to the calorimetric results of Goidberg and Hepier (30). Our value for AN0 agrees within experi- mental error ~irith the calorimetric value but differs by b e h e e n i and 27; from that of Covington t.r
01.We refitted our data to eq. 14 and obtained AHzssO
=59.31 kJ ~nol-I in close agreement with Covington. As expected, the enthalpy vaiue obtained is dependent on the equation chosen to fit the data. Consequently, our value of AH0 - 50.87 cannot be used to rule out the value of Covington. Since eq. 12 has been shown to be the most reliable fit to such data (24) and produces better agreement wit11 the calori- metric value our value would appear tc be more reliable.
Figure 4 shoals that the variation with temper- ature for each thermodynamic parameter changes only slightly on going from
H20to D 2 0 . The divergence of the TASO terms as the temperature increases over the range 273 to 373 I<, and the simultaneous convergence of the AHo terms
suggests that the variations in these parameters account for the change in pK in this temperature range (see Fig. 3)). A A S o is changing more rapidly with temperature than AAHO suggesting that the major influence on ApK in this region is the change in ernlropy of ionization. This n a y be due mainly to changes in solute-solvent
FIG. 4. Variations in the free energy (AGO), enthalpy (AH01 and entropy (- TISO) of ionization wit11 temper- ature; -- D 2 0 (this worlc); --- Hz0 (from the data of ref.
11); @ I 3 2 0 (from the data of ref. 19).
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3558 CAN. J. CHEM.
VOL.
54, 1976-..+ , , , , , j
323 373 4 2 3 473 523 573
T I K I
FIG. 5. Variation in the heat capacity (AC,o) kith temperature; - DiO; ---H20 (from the data of ref. 11).
interactions with increasing temperature, D 2 0 being a more structured liquid a t low temper- atures than H 2 0 . This effect has been discussed in dctail by Larson and Hcpler (31) and to a lesser extent by Laughton and Robertson (32).
The heat capacitl passes through a maxiinurn at -370 K , Fig. 5. The variation
will;iernper- ature is very similar t o that of H28. The heat capacity is more negative for D 2 0 than H 2 0 at the lower temperatures (27) as cxpected.
T o assess the reliability of these C,O values, corifirmation is required from iridependent meas- urcmcnts. Hopcf~r!ly this will be forthconling from calorimetric experiments now
111p r ~ g r e s s . ~
Also included in Tabie 3 are estimates from eq. 12 of the minimum pKD,? valuc attainable and the ten~perature at which
itis attained. The value of TI,,,, is 9.5" greater than the value in HzO, and ( P K ~ ~ ~ ~ ~ ! ~ ) isgrcatcr than (pKR,o,,in) by 0.74.
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