R. GARY,R. G. BATES,ASD R. A. ROBINSON
3806
Second Dissociation Constant of Deuteriophosphoric Acid in Deuterium Oxide from 5 to 50". Standardization of a pD Scale
by Robert Gary, Roger G. Bates, and R. A. Robinson National Bureau o.f Standards, Washington, D . C.
(Received June 36, 1964)
The second dissociation constant of deuteriophosphoric acid in deuterium oxide has been determined from electromotive force measurements of a cell without liquid junction from 5 to 50'. Thermodynamic quantities for the second dissociation process of this acid have been calculated. Values of -log ( u D - ~ ~ I - and ) the conventional ~ U Dvalues for the equimolal (0.025 m) KDzPOsSazDPOl buffer solutions have been established.
Introduction
Experimental Results
previous reported the standard electromotive force of the deuterium-silver, silver chloride cell from 5 to 50" with deuterium chloride in deuterium oxide as electrolyte. Continuing a program of work on the thermodynamics of electrolytes in deuteriuni oxide, we now present e.m.f. measurements for the cell
Deuterium gas was taken from commercial cylinders; mass spectrometric analysis3 gave a hydrogen content not greater than O.5 atorn %. The Phosphates were XBS Standard Samples 186 I b and 186 IIb. Sodium chloride was a bromide-free preparation used in previous work.4 The deuterium oxide had an isotopic purity of 99.65%; this was reduced by a further 0.075% on the dissolution of the two . phosphates, each at a concentration of 0.025 m. The solutions made by dilution of this stock solution with 99.65% deuterium oxide were proportionally closer to 99.65% in isotopic purity. The cells have already been described.' The measured values of the e.m.f., corrected to 1 atm. of the gas used, are recorded in Table I. Each entry is the mean value given by two cells. The average difference between the e.ni.f. of duplicate cells at all ten temperatures was 0.04 mv. The e.m.f. of each cell was measured in ascending order of temperature at 5' intervals from 5 to 50". I n three instances a final measurement at 25' was made. For the solutions with m = m' = 0.025, m = m' = 0.020, and m = 5m' = 0.025, the final e.m.f. at 25' was lower by 0.03, 0.05, and 0.04 mv., respectively, than that measured at 25" in the course of raising the temperature from 5 to 50'.
P t ; Dz(g) a t 1 atm., KDzP04(m), NazDPO&), NaCl(m'), AgCl; Ag
(I)
at 5" intervals from 5 to 50". From these data we have derived the second dissociation constant of deuteriophosphoric acid over this range of temperature, as well as the partial molal enthalpy, entropy, and heat capacity changes on dissociation. These are compared with the corresponding quantities for the dissociation of the HzP04- ion in ordinary water. I n addition, values of ~ ( U D ~ C I[e ) -log ( U D + ~ C , - ) ~ have been calculated and tabulated for three buffer solutions of equimolal (0.025 m) potassium dideuteriophosphate and disodium deuteriophosphate in solutions of sodium chloride of molalities 0.025, 0.015, and 0.005. A linear extrapolation gave values of p(aDyc1)" for a solution 0.02j m in each of the phosphates but without added chloride. Values of the conventional ~ u D[= -log aD.1 were calculated with the aid of a convent ion for the chloride ion activity coefficient analogous t o that proposed by Bates and Guggenheiin2for solutions in ordinary water. The Journal of Phusical Chemistry
(1) R. Gary, R. G. Bates, and R. A. Robinson, J . Phys. Chem., 6 8 , 1186 (1964).
(2) R. G. Bates and E. A. Guggenheim, Pure A p p l . Chem., 1, 163 (1960).
(3) Analyses by E. E. Hughes, Analysis and Purification Section. (4) V. E. Bower and R. A. Robinson, J . Phys. Chem., 67, 1524 (1963).
38017
THERMODYNAMICS O F DEUTERIOPHOSPHORIC ACIDI N DEUTERIUM OXIDE
~
Table I : Electromotive Force of the Cell P t ; Dz(g)at 1 atm., KDzPO4(m), Na2DP04(m),XaCl(m'), AgC1; Ag (in volts) from 5 to 50' m
50
m'
0.005004 ,010004 ,01500 ,02002 ,02502 .02900 ,02500
200
15'.
10"
40'
350
45"
50'
Table I1 : Second Dissociation Constant of
Values of p(unyc1) were calculated from
( E - E")/lc
+ log mc1- = -log
Deuteriophosphoric Acid in Deuterium Oxide from 5 to 50"
(a~+ycl-) (1)
where k is written for (RT In 1 0 ) j F . By combining eq. 1 with the equation for the second dissociation constant of deuteriophosphoric acid K2
mD-'mDPO4-2 __ _____ "-
X
Y D 'YDPOa-2
YDzPOa-
mD'PO4-
(2)
there results =
30'
,
Discussion
pK2
25"
0.005004 0.77971 0.78481 0.79004 0.79627 0.80054 0 80590 0.81128 0 81675 0 82209 0 82757 ,010004 ,76060 ,7653; ,77021 ,77506 ,77998 ,78497 ,78999 79504 80011 ,80520 ,74897 ,76276 ,75353 ,75809 ,76751 .77229 . '77699 ,01500 78184 78670 ,79156 ,74067 ,74510 ,74964 ,02002 ,75408 ,75868 ,76326 ,76790 77261 77729 ,78197 ,02502 ,73406 ,73838 ,74276 ,74718 ,75162 ,75606 '76064 77432 76518 76977 ,74672 '77484 ,01499 ,75135 ,75610 ,76076 76540 ,77015 77969 78453 ,78916 ,77415 ,77920 ,78422 ,78944 ,004994 .79458 ,79975 ,80504 ,81032 .a587 ,82087
-log ( a ~ + y c ~-- ) log
rnDPO4 -2 ~
-
rnDzPO4-
log
YDPOa -2 YDzPOa-YCI-
(3)
Since the two phosphakes were present at equal molalities and since the last term of eq. 3 can be written5
eq. 3 becomes
Bates and Acrees6used the value d = 4.4 A. for the ((distance of closest approach" in aqueous solutions. This value was also used in the present work, and good linear extrapolations were obtained. Values of the intercept (p&) are given in Table I1 along with the standard deviations (uJ. The data have been fitted by the method of least squares to the equation7 pKz
=
A J T - Az
+ A,T
(6)
where T is the temperature in OK. The values of Ai, A%,and As are given at the bottom of Table 11. The pKz values calculated by eq. 6 are given in column 4. For comparison, values of pK, for phosphoric acid in ordinary water are given in column 5 of Table 11.
5 10 15 20 25 30 35 40 45 50
7 8846 7 8499 7.8233 7.7986 7.7796 7.7667 7.7547 7.7484 7.7433 7.7435
0,0008
7 8837 7.8508 7.8229 7.7994 7.7804 7.7655 7.7546 7.7475 7 7439 7.7437
0007 .0018 ,0014
,0010 0009 ,0018 ,0018 ,0015 ,0015
7.2810 7.2545 7.2324 7.2145 7.2005 7 . I902 7,1834 7.1800 7.1799 7.1828
0.6027 ,5963 ,5905 ,5849 ,5799 ,5753 ,5712 ,5675 ,5640 ,5609
+
a pK9 (calcd.) = A I / T - A S AoT = 2202.11/T - 5.9823 -/0.0213882'. * A = pKz (calcd.) in DzO - pK, in HzO.
They are averaged values from three sets of data5,8," which agree well among themselves. The differences (A) between pKz in lheavy water and in ordinary water, shown in the last column, give the logarithm of the ratio of K2 in ordinary water to K z in deuterium oxide. Rule and La Mer1" give this ratio as 3.62 a t 25'. Our value is 3.80.
Thermodynamic Quiantities From eq. 6 it follows that AH" = 2.3026R(A1 A 3 T 2 ) ,AS" = 2.3026R(Az - 2A3T), and AC," = 2.3026R( -2A3T). Moreover, the temperature at which the dissociation constant will have a maximum value is given by (5) R. G. Bates and S. F. Acree, J . Res. NaTatZ. Bur. Std., 34, 373 (1945). (6) R. G. Bates, ibid., 39, 411 (1947). (7) H. S. Harned and R . A. Robinson, Trans. Faraday Soc.. 36, 973 (1940). (8) A. K. Graybowski, J . Phys. Chem., 62, 555 (1958). (9) F. Ender, W. Teltschik, and K. Schafer, 2. Elektrochem., 61, 775 (1957). (10) C. K. Rule and 1'. K. La Mer, J . Am. Chem. Soc.. 60, 1974 (1938).
Volume 68,,?;umber 1%' December. 1.984
3808
R. GARY,R. G. BATES,AND R. A. ROBINSON
to eliminate the log ycl- term and convert values of A t this temperature the value of the dissociation constant is -log K,,,
=
2dA1A3 - Az
A few values for the enthalpy and entropy changes on dissociation are as follows, corresponding values for ordinary water as solvent being given in parentheses t , oc. A H ' , Gal. mole-' A S o , oal. d e g 9 mole-1 0 25 50
-27 1 ( - 2 6 0) -31 0 ( - 2 9 6) -35 9 ( - 3 4 2 )
2504 (2034) 1376 (987) - 144 (-423)
At 25' ACPo = -58.4 cal. deg.-l mole-' compared with -54.1 cal. deg.-I mole-' for ordinary watw as solvent, T,,, is 47.7" (42.7' for ordinary water) at which temperature -log K,,, = 7.7436 compared with 7.1796 a t 42.7" when the solvent is water.
Establishment of a pD Scale Table I11 gives values of p ( u D y ~ l ) calculated , from the e.m.f. data (Table I) and eq. 1, for three solutions, all containing 0.025 m KD2P04and 0.025 m Xa2DP04 but different concentrations of sodium chloridenamely, 0.025, 0,015, and 0.005 nz. Extrapolation to zero chloride molality by the method of least squares gave the values recorded in the fifth column of Table 111.
-log ( a ~ + y c l -into ) pa^ values. This is equivalent to assigning a value of 4.565 8. to the ion-size parameter c? in the Debye-Hiickel equation a t 25O. We have used a similar convention to convert the p ( a ~ y c l ) values (Table 111, column 5) into paD values. I n this procedure, the equation -log
yc1- =
A (Ido) 1 Bd(Ido)"'
+
(8)
is used with d = 4.565 fi. ; appropriate values of T and E were used to obtain the constants A and B . Values of pa^ calculated in this way are given in column 6 of Table 111. These values have been smoothed by fitting them to the equation
paD (calcd.)
=
7.573 - 0.00764t
+ 0.0000744t2 (9)
where t is the temperature in "C. Values calculated in this way are given in the last column of Table 111. From a consideration of the standard deviation of the data on which the determination of E" was based,l as well as the reproducibility of the e.m.f. data given in Table I, the values of PGAD are estimated to have an uncertainty of about 0.003 unit. Finally, we have studied the response of the glass electrode to solutions in deuterium oxide a t 25". The customary pH cell with a liquid junction (indicated by the vertical line)
I
glass electrode, solution concentrated KCl(aq) ; calomel electrode
~
Table I11 : Standard Reference Values of ~ U for D the Buffer Solutions KDzPOd (0.025 m ) and Na2DP04(0.025 m ) in Deuterium Oxide
- ~ _ P_(anrc 1 , OC.
5
10 15 20 25 30 35 40 45 50
.
1) a
0.025 m'
0.015 m'
0.005 m'
0 m'
7.618 7.583 7.554 7,530 7.509 7.493 7,481 7.472 7.467 7.464
7.624 7.591 7.565 7.541 7.520 7.504 7.491 7.483 7.478 7.473
7.644 7,610 7.580 7.557 7.536 7.519 7.508 7.499 7.492 7.490
7.648 7.615 7.586 7.563 7.542 7.525 7.513 7.505 7.498 7.495
paD P ~ D
7.537 7.504 7.474 7.450 7.428 7.410 7.397 7.388 7.380 7.376
(calod.)
7,537 7.504 7.475 7.450 7.429 7.411 7.397 7.386 7.380 7.377
a S'alues in these four columns are for the respective values of m' (NaC1).
Bates and Guggenheim2used the convention -log yc1-
=
The Journal of Physical Chemistry
A(Ido)' I 2 1 1.51"2
+
(7)
was standardized at 25" by means of the aqueous equimolal (0.025 m) KH2P04-Na2HP04buffer solutionL1 [pH(S) 6.8651. The standardization was checked with a second reference solution,lI 0.008695 m with respect to KH2P04 and 0.03043 m with respect to NazHPOj [pH(S) = 7.4131. The equimolal (0.025 m) phosphate buffer solution in deuterium oxide then gave a nieter reading of 6.982, constant for a t least 3 hr. The PGAD value of this solution, determined by means of cells without liquid junction with the aid of the convention for -log ycl- described above, is 7.429. I t appears, therefore, that meter readings ( L e . , the operational pH) should be increased by 0.447 to yield values of ~ U D . This is somewhat more than the value of 0.408 which has been recommended recently. 1 2 , 1 a I t should be noted, however, that the correction recommended by Long and co-workers was based on (11) R. G. Bates, J . Res. Natl. Bur. Std., 66A, 179 (1962). (12) P. K. Glasoe and F. A. Long, J . P h w . Chern., 64, 188 (1960). (13) P. Salomaa, L. L. Schaleger, and F.A. Long, J . Am. Chem. SOC. 86, l(1964).
3809
RADIOLYSIS OF CRYSTALLINE LITHIUMBROMATE
hydrogen ion concentrations expressed in molarity units, whereas our PUD value is referred to molality units. The two scales of PUD differ by log do, where do is the density of the solvent. In deuterium oxide, D the molality scale is 0.043 unit higher therefore, ~ U on than that on the molarity scale, and the appropriate c~rrection‘~becomes 0.451, in excellent agreement with 0.447 unit which me have found. There is evidence that the glass electrode responds to deuterium ion as efficiently as it responds to hydrogen i0n.~2,~4It is appropriate, therefore, to define the operational pD of a solution X in the same way as the operational pH is daefined
where EX and Es are the e.m.f. values of the pH cell containing the “unknown” and the pD standard, respectively. The conventional ~ u Dvalues of selected reference solutions are identified with pD(S)
for the experimental determination of pD by eq. 10. (14) P. R. Hammond, Chem. Ind. (London), 311 (1962).
Radiolysis of Crystalline Lithium Bromate by Lithium-6 Fission Recoil Particles’
by G. E. Boyd and
T. G. Ward, Jr.
Oak Ridge National Laboratory, Oak Ridge, Tennessee
(Received June 2g71964)
Measurements were made of the decomposition of Br03- ion and the production of oxidizing fragments in crystalline LiBrOa by energetic tritons and a-particles released following neutron capture by 6Li in the Oak Ridge graphite reactor. A strong dependence of the radiolysis on the linear energy transfer (LET) was indicated by the initial 100-e.v. yield for bromate decomposition, Go(-Br03-) = 1.48, which was five times larger than that obtained with 6OCo y-rays. A correspondingly large yield of oxidizing fragnients also wat; observed; this yield and the ease with which these fragments could be removed from the crystals by mild thermal annealing was interpreted as being inconsistent with a “thermal spike” radiolysis mechanism. The observation that ihe yields, Go(- BrOa-) , Go(“Ox”), and Go(Br-), all were approximately five times those observed with y-rays also suggested1 that the mechanism for the radiolysis did not change with increasing LET. A tenfold increase in the dose rate caused no change in the yields either for broniate deconiposition or oxidizing fragment production.
The dependence of radiolytic yields on the linear energy transfer (LET) is well known for liquids and gases although, 8s Yet, there is comparatively little inforlllation on track &‘ects in crystalline, inorganic solids. The alkali metal nitrates have been studied
most extensively in this connection, and yields have (1) Presented before the Division of Physical Chemistry, 146th National Meeting of the American Chemical Society, Denver, Colo., Jan. 19-24, 1964. Research sponsored by the U. S. Atomic Energy Commission under contract with Union Carbide ~ o r p .
Volume 68,Number 12 December, 1964
