R. GARY,R. G. BATES,AND R. A. ROBINSON
2750
IV. Conclusion
i.e. (klhlEl -
or
klEl(h1
a!>
> hZklE1
+ h2) >
(15)
a!
+
i.e., the reaction must be exothermic (hl hz > 0) and sufficiently so that (15) is satisfied, or the singularity is a stable nodal point, no explosive behavior being possible. Obviously, in an adiabatic system ( I = 0, a! = 0) inequality 15 is satisfied, and explosive behavior will be shown. Again the separatrix which cuts the T axis has a nonzero slope (negative in most cases), and the intermediate concentration will determine if the explosion is to occur. Thus, in a nonchain explosion of this type, vessel coating with materials which affect the value of 2 will alter the explosion limits.
By consideration of the kinetic and energy conservation equations simultaneously, one can deduce a considerable amount of semiquantitative and qualitative information about potentially explosive materials. The restrictive assumptions of both the isothermal chain and purely thermal theories are removed, and the resultant generaliied theory naturally explains phenomena not amenable to explanation by either theory separately. For example, vessel coating, addition of chain carriers and intermediates, etc., all affect the explosion limit explicitly within the framework of the theory. Also, as the separatrix is not parallel to the 2 axis, it may be possible to account for the irreproducibility of results encountered with certain coatings if these coatings produce x concentrations in a region where the slope of the separatrix is large.
Dissociation Constant of Acetic Acid in Deuterium Oxide from 5 to 50". Reference Points for a pD Scale
by Robert Gary, Roger G. Bates, and R. A. Robinson National Bureau of Standards, Washington, D . C. (Received March 19, 1966)
Electromotive force measurements of a cell without liquid junction have been used to determine the dissociation constant of acetic acid in deuterium oxide from 5 to 50". The enthalpy, entropy, and heat capacity changes on dissociation of acetic acid have been calculated. Values of -log (aD+ycl-) and the conventional ~ U Dvalues for the equimolal (0.05 m) acetic acid-sodium acetate buffer solutions have been determined. These provide a second k e d point for standardizing the pD scale, supplementing data for the equimolal mixture of KDzPOl and NkDP04 established in an earlier investigation.
Introduction
P t ; D2(g) a t 1 atm., CHaCOOD (m), The measurement of the second dissociation conCHaCOONa (m), NaCl (m'), AgCl; Ag stant of deuteriophosphoric acid in deuterium oxide a t 5" intervals from 5 to 50". The dissociation conhas been repohed recently,l along with of stant p(aDycl) and paD for equimolal K D ~ ~ o ~ - N ~ ~of Dacetic ~ ~acid ~ has been derived over this tembuffer solutions. (1) R. Gary, R. G. Bates, and R. A. Robinson, J. Phys. Chem., 68, We have now measured the e.m.f. of the cell 3806 (1964). The Journal of Physical Chemistry
DISSOCIATION CONSTANT OF ACETIC ACIDIN DEUTERIUM OXIDE
perature range, and from these results the partial molal enthalpy, entropy, and heat capacity changes on dissociation have been obtained. These quantities are compared with the corresponding changes when the dissociation occurs in ordinary water as solvent. I n addition, values of ~ ( U D Y C I ) [= -log (UD+YCI-) I have been calculated for the equimolal (0.05 m) acetic acid-sodium acetate buffer solution containing sodium chloride at molalities of 0.05, 0.025, and 0.01. A linear extrapolation then gave the limiting values of P(aDyC1)' in the absence of sodium chloride. Values of ~ u D [ =-log aD+]in deuterium oxide were calculated with the aid of a convention consistent with that on which standard pH values in water are based2 but modified to allow for the differences in density and dielectric constant,.
Experimental Results Deuterium gas was taken from commercial cylinders; mass spectrometric analysis3 gave a deuterium content of 99.5 atom %. The deuterium oxide had an isotopic purity of 99.75%; this was reduced to 99.70y0 on dissolution of the acetic acid and sodium carbonate to produce a solution 0.1 m with respect to both acetic acid and sodium acetate. The solutions made by dilution of this stock solution with deuterium oxide were proportionally closer to 99.75% in isotopic purity. Acetic acid was purified by fractional freezing. ' Titration with standard base indicated 100.18 mole % CH,COOH. Sodium carbonate was dried a t 250" for 3 hr. Titration with standard acid indicated a purity of 100.01%. The cells have already been described.* The measured values of the e.m.f., corrected to 1 atm. of the gas used, are given in Table I. Each entry is the mean value given by two cells. The average difference between the e.m.f. of duplicate cells a t all 10 temperatures was 0.04 mv.
Discussion Values of p(~Dycl)were calculated by means of the equation
( E - E")/k -t IOg ml- = -log (aD+ycl-)E P(aDYC1) (1) where k is written for (ET In lO)/F. Values of the standard electrode potential, E", have already been tab~lated.~ The mass law expression for the dissociation constant of acetic acid (DAc = CH3COOD) is
2751
K =
mD +mAr YD +YAK mDAc YDAc
(2)
and, if this is combined with eq. 1, there results the equation
(3)
+
Here mA, = m mD+ and mDAc = m - mD+; for all but the two most dilute solutions it suffices to put mAc- = mDAc = m, and even for these two solutions the introduction of the mD+ term affects only the fourth decimal place of pK. The pK' calculated by eq. 3 proved to be almost independent of concentration, as might be expected since the activity coefficient term in eq. 3, log ( ~ C I - Y D A ~ / Y A ~ - ) , should be small. At each temperature, pK was derived by fitting the values of pK' by the method of least squares to an equation linear in ionic strength; the ionic strength, I , is (m m' mD+). The values of pK so obtained are given in Table I1 along with the standard deviations, ut. These values of pK have been fitted, also by the method of least squares, to the equation5
+ +
pK
=
AJT - A2
+ AST
(4)
where T is the temperature in degrees Kelvin. The values of A,, Az, and A3 are given at the bottom of Table 11, and the values of pK calculated by eq. 4 are found in the fourth column of this table. Values of pK for acetic acid in ordinary water6 are given in the fifth co1umn, and the difference, pK in DzO pK in HzO, in the last column. These differences are not quite so large as those found for the second dissociation constant of phosphoric acid, for example, 0.5562 at 25O, compared with 0.5799 for phosphoric acid. La Mer and Chitturn' found K = 0.55 X (pK = 5.260) for acetic acid in deuterium oxide at 25'. They used conductance measurements and expressed concentrations as molarities. Presumably, therefore, K is in molarity units, so that on the molality scale (2) R. G. Bates and E. A. Guggenheim, Pure AppZ. Chem., 1, 163 (1960). (3) Analysis by E. E. Hughes of the Analysis and Purification Section. (4) R. Gary, R. G. Bates, and R. A. Robinson, J . Phys. Chem., 68, 1186 (1964). (5) H. 5.Harned and R. A. Robinson, T~ans.Faraday SOC.,36, 973 (1940). (6) H. S. Hssned and R. W. Ehlers, J. Am. Chem. SOC.,55, 652 (1933). (7) V. K. La Mer and J. P. Chitturn, ibid., 58, 1642 (1936).
Volume 69, Number 8
August 1966
R. GARY,R. G. BATES, AND R. A. ROBINSON
2752
Table I : Electromotive Force of the Cell P t ; Dz(g) a t 1 atm., DAc (m), NaAc (m),NaCl (m'),AgC1; Ag (in volts) from 5 to 50"" m
m'
50
100
15'
200
0,005 0.01 0.025 0.05 0.10 0.05 0.05
0.005 0.01 0.025 0.05 0,lO 0.01 0.025
0,64734 0,63071 0.60899 0.59251 0,57604 0,63105 0.60907
0.65135 0.63443 0.61229 0.59541 0.57868 0.63476 0.61241
0.65521 0.63810 0.61543 0.59835 0.58134 0.63838 0.61559
0,65922 0.64168 0.61858 0.60122 0.58388 0.64202 0.61887
a
25'
0.66301 0.64534 0.62186 0.60410 0.58639 0.64558 0.62201
50'
30'
350
4OU
450
0.66687 0.64875 0.62493 0.60688 0.58883 0.64912 0.62514
0.67068 0.65224 0.62806 0.60964 0.59132 0.65261 0.62825
0,67447 0.65573 0.63117 0.61248 0.59375 0.65609 0.63129
0.67823 0.65919 0.63418 0.61517 0.59619 0.65950 0.63434
0.68196 0.66275 0.63727 0.61788 0.59856 0.66293 0.63736
AC = CH.,COz.
Table 111 : Enthalpy and Entropy Changes for the Dissociation of Acetic Acid
Table 11: Dissociation Constant of Acetic Acid in Deuterium Oxide from 5 to 50" PA:, obsd.
PK,
PK,
t , "C.
#
