THE JOURNAL OF
PHYSICAL CHEMISTRY
Registeed in
U.Is. Patmt Ofice @ Copytight, 1986, ba, the American Chemical Sodeta,
VOLUME 70, NUMBER 7 JULY 15, 1966
Dissociation of Acetic Acid-d, in Deuterium Oxide from 5 to 50" and Related Isotope Effects
by Maya Paabo,Roger G. Bates, and R. A. Robinson National Bureau of Standards, Washington, D. C.
(Received February $3, 1.966)
The dissociation constant of acetic acidd4 (CD3COOD) in deuterium oxide (D20) has been determined by the emf method at ten temperatures from 5 to 50". From the variation of the dissociation constant with temperature, the changes of enthalpy, entropy, and heat capacity have been derived. The four dissociation processes, namely those for ordinary acetic acid in ordinary water, for deuterioacetic acid in ordinary water, and for these two acids in deuterium oxide, are compared.
Introduction The dissociation constant of prot,oacetic acid (CHr COOH) in ordinary water has been determined using both the emf' and conductance2 methods. In addition, the dissociation of protoacetic acid (CHSCOOD) in deuterium oxide3 and the dissociation of deuterioacetic acid (CDaCOOH) in ordinary water4 have been studied recently. The fourth dissociation process in this related series, namely that of deuterioacetic acid (CD3COOD) in deuterium oxide, is the subject of the present study.
The deuterium gas was found by mass spectroscopic examination t o have an isotopic purity of better than 99.5%. The deuterioacetic acid (acetic acid-&) was obtained from two different commercial sources. The first lot was found to contain 0.88 atom % of H; gas chromatographic analysis showed it to consist only of acetic acid, acetic anhydride, and a trace of water. It was used without further purification. The ot,her sample of material was purified by fractional distillation. Gas chromatographic examination of the fraction used revealed no impurities. ~
Procedures and Results The cell used can be represented P t ; D2(g, 1 atm), CD3COOD (ml), CD3COONa (m),NaCl (mJ, AgCl; Ag The emf was measured a t 5" intervals from 5 to 50". The operation of the cell and the preparation of the materials, electrodes, and solutions followed the general procedures already described.
~~~
~~~
(1) H. 9. Harned and R. W. Ehlers, J. Am. Chem. Soc., 54, 1350 (1932); 55, 652 (1933). (2) D.A. MacTnnes and T. Shedlovsky, ibid., 54, 1429 (1932). (3) R. Gary, R. G. Bates, and R. A. Robinson, J . Phys. Chem., 69, 2750 (1965). (4) M. Paabo, R . G. Bates, and R. A. Robinson, ibid., 70, 540 (1966). ( 5 ) R. Gary, R. G. Bates, and R. A. Robinson, ibid., 68, 1186 (1964). (6) R. Gary, R. G. Bates, and R. A. Robinson, ibid., 68, 3800 (1964).
2073
M. PAABO, R. G. BATES,AND R. A. ROBINSON
2074
n 1
=
mz = ma
50
100
15'
200
25'
30"
350
40°
450
50'
0.005261 0.007598 0.01010 0.01326 0.01680 0.02250 0.02637 0.02957 0.02989 0.03273 0.03479 0.03873 0.04330 0.04535 0.05008 0.05268
0.64707 0.63805 0.63128 0.62485 0.61925 0.61234
0.65103 0.64189 0.63504 0.62843 0.62269 0,61562 0.61179
0.65488 0.64564 0.63868 0.63195 0.62607 0.61890 0.61508
0.65881 0.64943 0.64226 0.63543 0.62947 0.62211 0.61825 0.61525 0.61499 0.61273 0.61131 0.60846 0.60572 0.60442 0.60214 0.60080
0.66261 0.65305 0.64585 0.63889 0.63277 0,62534 0.62134 0.61837 0.61806 0.61579 0.61429 0.61144 0.60860 0.60742 0.60494 0.60368
0.66636 0.65672 0.64936 0.64236 0.63606 0.62848 0.62443
0.67021 0.66048
0.67401 0.66416
0.67775
0.68142
...
...
...
... ...
0.64578 0.63941 0.63166 0.62744
0.64910 0.64264 0,63478 0.63061
0.65245 0.64585 0,63786 0.63366
0.65570 0.64904 0,64094 0.63666
...
...
...
...
0.60550 0.60336 0.60204 0.59944 0.59673 0.59571 0.59337 0.59216
0.60875 0.60656 0.60517 0.60248 0.59978 0.59870 0.59632 0.59513
0.61188 0.60969 0.60824 0.60548 0.60276 0.60162 0.59926 0.59806
The measured values of the emf, corrected to 1 atm of deuterium gas, are given in Table I.
Calculations The emf of the cell yields values of the acidity function -log (aD+ycI-)with the aid of the equation -log
(uD+~cI-)
=
(E - E")/k
+ log ma
(1)
where m is molality, E" is the standard emf of the cell,5 and k is written for (RT In 10)/F. Combination of this acidity function with the equation for the dissociation constant (K) of deuterioacetic acid, namely
...
...
...
...
...
...
0.62114 0.61885 0.61723 0.61434 0.61151 0.61027 0.60779 0.60644
0.62419 0.62187 0.62025 0.61727 0.61440 0.61329 0.61063 0.60925
0.62716 0.62479 0.62314 0.62015 0.61720
0.63015 0.62773 0.62602 0.62298 0.62003
0.63306 0,63060 0.62889 0.62581 0.62278
...
...
...
0.61335 0.61198
0.61609 0.61468
0.61878 0.61735
deuterium chloride5 in its own solution a t the same total ionic strength as that of the deuterioacetate buffer solution. As for similar systems studied previously, the term log ( Y C ~ - Y D A ~ / Y A ~ - )proved to be small, and almost horizontal straight-line plots of pK' us. ionic strength were obtained. Extrapolation to zero ionic strength ~
~
~~~
~
Table 11: Dissociation Constants of Acetic Acid in DzO-----PK CDaCOOD CHaCOOD CDaCOOH Obsd Calcda AlpKb in HzO
------pK
Temp, OC
gives
(E
- E") k
+ log + log +ml
mDt
m2
mD+
m3
(3)
I n all of the 16 cells measured, ml = m2 = m3, so that the last term of eq 3 becomes zero if mDt makes a negligible contribution. Adoption of this simplification in procedure would result in values of pK' higher by only about 0.0007 a t each temperature. It was nevertheless deemed worthwhile to make allowance for the small contribution of the mDt term. For this purpose, a sufficient approximation to mD+ was obtained by the equation where
y
~
was l taken as the activity coefficient of
The Journal of Physical Chemistry
0 5 10 15 20 25 30 35 40 45 50
...
...
...
...
5.360 5.348 5.338 5,331 5.328 5.323 5.323 5.326 5.330 5.336
5.360 5.348 5.338 5.330 5.326 5.324 5.324 5.326 5.330 5.337
5.347 5.334 5.324 5.317 5.312 5.310 5.310 5.313 5.317 5.324
0.013 0.014 0.014 0.013 0.014 0.014 0.014 0.013 0.013 0.013
4.795 4.784 4.778 4.774 4.772 4.771 4.773 4.777 4.783 4.790 4.799
AlpKO
... 0.576 0.570 0.564 0.558 0.553 0,551 0.547 0.543 0.540 0.538
+
' Calculated from the equation pK = 1278.92/T - 3.0490 0.013702T. * AlpK = pK(CD3COOD in D20) - pK(CH3COOD in D20). A?pK = pK(CD3COOD in D 2 0 ) - pK(CD3COOH in H20).
was made by the method of least squares. Values of the intercepts (pK) obtained in this way are given in Table 11. The standard deviations (ui) of the intercepts were less than 0.001 a t each temperature.
DISSOCIATION O F ACETIC ACID-&
IN
D20
2075
Table I11 : Thermodynamic Quantities for the Dissociation of Protoacetic Acid and Deuterioacetic Acid in Water and in Deuterium Oxide" CHaCOOH in H20
AH'at
0" 25" 50" AS" a t 0" 25 " 50" AC," a t 25" tmsx ( "C) -Log Kmx
$781 -98 - 1047 -18.8 -22.1 -25.1 - 37 22.4 4.756
CDsCOOH in H20
+735 -69 - 945
-19.2 -22.1 -24.9 - 34 22.9 4.771
CHaCOOD in D20
CDaCOOD in D20
$1192 +275 - 730 -20.2 -23.4 -26.6 - 39 32.0 5.310
+1174 +279 - 695 -20.3 -23.4 -26.6 38 32.4 5.323
Alb
A8
-46
- 18
+29
-4 +35 -0.1 0 0 f l
+lo2 -0.4 0
+0.2 +3
-
...
I
.
.
...
...
+
' AH" in cal mole-'; AS" and ACpoin cal deg-1 mole-'. a Quantities in this column are for the exchange reaction: CD,COOH CHSCOO- = CHSCOOH CDsCOO- in HzO. Quantities in this column are for the exchange reaction: CD,COOD CHsCOO- = CH3COOD CD3COO- in D20.
+
+
+
Discussion The values of pK obtained experimentally were fitted, by the method of least squares, to the equation'
pK
=
AI/!!' -
A2
+ A3T
(4)
(0°C = 273.15"K) giving A1 = 1278.92, A2 = 3.0490, and A B = 0.013702. The pK values calculated from eq 4 are given in the third column of Table 11. For comparison, pK values for protoacetic acid (CHSCOOD) in deuterium oxide3are given in the fourth column. The fifth column of Table I1 gives the difference between the pK values of the two acids in deuterium oxide at each temperature. The difference is, within experimental error, independent of temperature between 5 and 50". As we noted in an earlier paperJ4the difference in the pK values of protoacetic acid and deuterioacetic acid in ordinary water seems to diminish a t 45 and 50". As the pK values in ordinary water were determined by the same method, but in different laboratories, the slight variation in ApK may well be due to minor differences in technique. On the other hand, the comparison in Table I1 of the two forms of acetic acid in deuterium oxide is based on measurements made in the same laboratory. For this reason, we believe that the pK values differ by a constant amount over the temperature range 5 to 50". This constant difference is not displayed by the pK values of deuterioacetic acid in ordinary water and in deuterium oxide, as shown in the last column of Table 11. The decrease from 0.576 a t 5" to 0.538 a t 50" is real and cannot be ascribed to experimental errors. It parallels very closely the decrease from 0.577 a t 5" to 0.537 at 50" found for protoacetic acid in these two solvents.3 Equation 4, together with the numerical values of
AI, A2, and As, permits a calculation of the enthalpy, entropy, and heat capacity changes on the dissociation of deuterioacetic acid (CDaCOOD)in deuterium oxide to be made. We can also calculate the temperature a t which the dissociation constant has its maximum value and the pK value a t this temperature. Data for the four related dissociation processes are compared in Table I11; 1 cal is defined as 4.1840 joules. The pK values of protoacetic acid and deuterioacetic acid are very similar in ordinary water, as they are in deuterium oxide. This similarity extends to some of the other thermodynamic properties. Thus there is little if any difference between the entropy changes on the dissociation of protoacetic acid (CH3COOH) and deuterioacetic acid (CDSCOOH) in water; hence the entropy change for the exchange reaction CDSCOOH
+ CH3COO-
=
CHsCOOH
+ CDxCOO-
(5)
is effectively zero. This is also true for the exchange reaction CDsCOOD
+ CHsCOO-
=
CHSCOOD
+ CD3COO-
(6)
in deuterium oxide. The enthalpy changes are, however, more considerable. For exchange reaction 5 in water, AH" increases from -46 cal mole-' a t 0" to +lo2 cal mole-' a t 50°, whereas for exchange reaction 6 the increase is only from -18 to +35 cal mole-1 over this temperature interval. Correspondingly, the heat capacity change for reaction 5 is larger than that for reaction 6 . ~
~~~
(7) H. S. Harned and R. A. Robinson, Trans. Faraday Soc., 36, 973 (1940).
Volume 70,Number 7 JuEu 1966
M. PAABO, R. G. BATES,AND R. A. ROBINSON
2076
I n all of the work summarized in Tables I1 and 111, concentrations were expressed on the molality (m) scale (moles per kilogram of solvent), and hence all values of K are based on the molal scale as well. This procedure has an arbitrary feature, in that a kilogram of ordinary water contains 55.51 moles of solvent, whereas a kilogram of deuterium oxide contains only 49.93 moles. A better comparison is obtained if dissociation constants expressed on the mole fraction ( N ) scale are used. The conversion is effected by means of the equation pKN
=
pK, - log (O.O01W,)
(7)
where W , denotes the molecular weight of the solvent. Thus, the pKN value is higher by 1.7444 than the pK, when ordinary water is the solvent, while in deuterium oxide it is 1.6983 higher. Table I V summarizes the four sets of pK values on the mole fraction scale. It is evident that ApK (=pK in DzO pK in H20) is lower than it is when the molality scale is used, but it is still significantly large.
Table IV: Values of pK for the Dissociation of Protoacetic Acid and Deuterioacetic Acid in Deuterium Oxide and in Water (Mole Fraction Scale)
Temp,
QC
0 5 10 15 20 25 30 35 40 45 50
---Protoacetic acid--CHaCHICOOD COOH in DzO in Hz0 A
.
..
7.046 7.032 7.022 7.015 7.010 7.008 7.008 7.011 7.015 7.022
6.524 6.514 6.507 6.502 6.500 6.500 6.502 6.506 6.513 6.321 6.531
---Deuterioacetic acid--CD3 CD3COOD COOH in Dz0 in H20 A
...
...
0.532 0.525 0.520 0.515 0.510 0.506 0.502 0.498 0.494 0.491
7.058 7.046 7.036 7.028 7.024 7.022 7.022 7.024 7.028 7.035
6.539 6.525 6.522 6.518 6.516 6.515 6.517 6.521 6.527 6.534 6.543
CH3COOH = H+ CD3COOH
0.530 0.524 0.518 0.512 0.509 0.505 0.501 0.497 0.494 0.492
+ CHsCOO- in HzO
(AG1")
+ CD&OO-
(AG2") (9)
(8)
=
Hf
in H20
CHsCOOD = Df
+ CH3COO- in D20
(AG,")
CDICOOD = D+
+ CD&OO-
(AG~') (11)
in D20
(10)
The question may be asked whether there is a constant difference between the dissociation energies for a given acid in water and deuterium oxide, independent of the nature of the acid. This seems not to be so, as is evident from the following considerations. Take two proto acids designated HA1 and HA2. In water as solvent we have
+ AiHA2 = H + + HA1
...
It is important to inquire to what extent the thermodynamic quantities given in Table 111 are altered by such a change in scale of reference. The change in question is accomplished by decreasing the value of the A2 parameter in eq 4 by 1.7444 when ordinary water is the solvent and by 1.6983 when the solvent is deuterium oxide, without modifying the -41and A B parameters. Consequently, A H " and AC," have the same values regardless of the scale of concentration used. However, AGO at 25" is higher by 2380 cal mole-l in ordinary water and by 2317 cal mole-' in deuterium oxide when the mole fraction scale is used in place of the The Journal of Physical Chemistry
molality scale. Similarly, A s " is lower a t 25" by 7.98 cal deg-l mole-' if water is the solvent and by 7.77 cal deg-l mole-l when the solvent is deuterium oxide. It is clear that there are four dissociation constants corresponding to the dissociation of the two forms of acetic acid in the two solvents. Similarly, there are four changes in Gibbs energy corresponding to the four dissociation processes
=
Hf
A2-
(AGO)
(84
(AG2")
(9%)
(AG,")
(1 0 4
(AG4')
(1W
and in deuterium oxide
+ AiDA2 = D + + A2-
DA1
=
D+
Then if AGIO - AG3" = AG," - aG4'
(12)
the following relationship among the dissociation constants would hold
and the ratio of the dissociation constants of any given acid in the two solvents would be a constant. Unfortunately, it is not known with certainty how this ratio varies with pK(in H20), although there is evidence that the difference, pK(in HzO) - pK(in D20) increases more or less linearly with increase of P K . ~ Consequently, it seems fairly certain that the (8) R. P. Bell, "The Proton in Chemistry," Cornel1 University Press, Ithaca, N. Y., 1959, p 189, Figure 18.
INTERACTION OF WATERAND VARIOUS SILICAPOWDERS
relationship expressed by eq 13 is not generally true. We have confirmed this conclusion from our own measurements. Thus for protoacetic acid in water and in deuterium oxide at 25",ApK = 0.556,but for the second stage in the dissociation of phosphoric acid, ApK = 0.580. If, however, HA1 and HA2 are acids of nearly equal strength, we would expect eq 13 to be closely valid. When AI is CHICOO and A2 is CDaCOO, for example, it might be anticipated that eq 13 would be a very good approximation, though not necessarily exactly true. We have shown in an earlier paper3 that ApK
2077
-
(=pK in DzO pK in HzO) for protoacetic acid ranges from 0.577at 5" to 0.537at 50". It is now found (Table 11) that ApK for deuterioacetic acid in these two solvents ranges from 0.576 at 5" to 0.538 at 50". Although eq 13 holds to a very good approximation in this instance, there is no apparent reason to expect it to be exactly valid. Acknowledgment. The authors acknowledge gratefully the assistance of E. E. Hughes, who performed the mass spectrometric and gas chromatographic analyses, and of Dr. R. T. Leslie, who purified the deuterioacetic acid.
Adsorption Thermodynamics of the Interaction of Water and Various Silica Powders
by Donald E. Meyer and Norman Hackerman Department of Chemistry, The University of T e w s , Austin, T e w s (Received February 8, 1966)
-
Free energies, heats and integral entropies, and enthalpies of adsorption are presented for powdered fused silica (0.056to 13.58m2/g) and powdered crystalline silica (0.11to 5.65 mz/g). A volumetric adsorption system and a microcalorimeter were used. Both crystalline and amorphous silica were mechanically ground and separated by water sedimentation into several particle-size distributions. In addition, one sample of the ground crystalline silica was etched with varying amounts of dilute H F to yield a particle-size distribution. The effect of grinding and etching on the thermodynamic values of adsorption are reported, and the results are discussed on the basis of surface structure related to particle size and etching. Electron micrographs are also presented.
Introduction Many investigators have considered the interaction of water with silica surfaces. Collectively, precision immersion calorimetry,l-3 adsorption st~dies,4$and infrared studies6'7 have indicated that the energetics of water-silica interactions depend upon the presence and density of surface hydroxyl groups. Additional experimental evidence indicated that these surface OH groups participate in still another manner. Immersional heatss-I0 and adsorption free energies'O
normalized to unit surface area were found to vary with particle size for silica powders. Of the explana(1) A. C. Makrides and N. Hackerman, J . Phy3. Chem., 63, 594 (1959). (2) J. W. Whalen, Advances in Chemistry Series, No. 33, American Chemical Society, Washington, D. C., 1961,p 281. (3) M. M. Egorov, V. G. Krasilnikov, and E. A. Sysoev, Dokl, Akad. Nauk SSSR, 108, 103 (1956). (4) N. Hackerman and A. C. Hall, J . Phys. C h m . , 62, 1212 (1958). (5) M.M.Egorov, V. F. Kiselev, and K. G. Krasil'nikov, Rues. J . mys.ma., 33, NO.io,323 (1959).
Volume 70, Number 7 July 1966
