E.M.F.STUDIESIX .AQUEOUSSOLUTIONS AT ELEVATED TEMPERATURES
3043
Electromotive: Force Studies in Aqueous Solutions at Elevated Temperatures.
V.
The Thermodynamic Properties of DC1 Solutions'
by M. H. Lietzke and R. W. Stoughton Chemistry Dizision, Oak Ridge r a t i o n a l Laboratory, Oak Ridge, Tennessee
(Received June 12, 1964)
Rieasureiiients of the e.ni.f. of the cell, Pt-Dz(p)IDCl(mIAgCl, Ag, have been used to determine the thermodynamic properties of DCI solutions in D2O as well as the standard potential of the cell to 225". The standard potential was found to be lower in the deuterated system than in the corresponding protonated system and the difference became greater the higher the tenipierature. Activity coefficient behavior in the two systems is consistent with a lower value of the dielectric constant of DZO a t all temperatures. As judged from the variation of activity coefficients with temperatures and concentration the difference in the dielectric constant values appears to go through a minimum at about 100".
Previous papers in this series have described the determination of the standard potential of the h g , AgCl electrode2 and the thermodynamic properties of HC1 solutions3 to 275". I n the present work, measurements of the e.m.f. of the cell, Pt-D2(p) ID(% (m)'AgC1, Ag, have been used to determine the therniodynamic properties of DC1 solutions in D2O as well as the standard potential of the cell to 225". I n addition, the original e.m.f. data obtairled in €IC1solutions have been used to recalculate the properties of these soht:ons in a manner consistent with that used in the present calculations of the properties of DC1 solutions. Thus a direct comparison can be made of the thermodynamic properties of HC1 and DC1 solutions over a wide range of concentration and temperature. Experimental The experimental apparatus and the preparation of electrodes were the s,ame as described previously. 2 , 4 The e.m.f. measurements were made on DCl solutions (in DzO) of 0.10102, 0.0196, 0.0502, 0.0735, 0.1004, 0.1983, 0.495, and 1.127 m concentration at temperatures of about 25, 60, 90, 125, 150, 175, 200, and 225". The DCl was purchased from hlerck Sharp and Dohriie of Canada Limited in 50-g. ampoules containing 387, by weight DCI solution in DzO. The mass spectcrographic assay of the DCl indicated 97.3yG DCl by weight; because of the rapid exchange of H + with the D,O in the final solution, the isotopic composition of
the DCl under the experimental conditions is determined by that of the D20. The DzO was prepared by twice distilling nominally 99.7% D 2 0 under an atmosphere of nitrogen that had been dried over Mg(C10J2. The first distillation was made from a 1 m DzS04 and 0.5 m KzCr207 solution and the second from 2y0 K M n 0 4 and 0.04 m NaOD. Extreme precautions were taken a t all times to exclude any contamination by HzO. Final mass spectrographic assay of the D 2 0 indicated 99.4% DzO by weight. The Dz gas was obtained in a cylinder from the Y-12 plant of the Suclear Division of Union Carbide Corporation. Mass spectrographic analysis indicated an assay of 99.84% D2by weight. Results and Discussion I n treating the results, the deuterium pressure was calculated by subtracting the vapor pressure of the solution from the observed total pressure, while the vapor pressure of the solution was obtained by taking the vapor pressure of pure D 2 0 5at the tempera(1) Research sponsored by the U. s. Atomic Energy Commission under contract with the Cnion Carbide Corporation. (2) R. S. Greeley, W. T . Smith, Jr., R . W. Stoughton, and M. H. Lietzke, J . P h y s . Chem., 64, 652 (1960). (3) R. S. Greeley, W. T. Smith, Jr., M. H. Lietzke, and R . '. 1 Stoughton, ibid., 64, 1445 (1960). (4) 31. B. Towns, R . S. Greeley, and iM. H. Lietzke, ibid., 64, 1861 (1960). (53 E. H. Riesenfeld and T. L. Chang, 2 . p h y s i k . Chem., 333, 120 (1936).
V o l u m e 68, Number 10 October, l O F 4
3044
M. H. LIETZKEAND R. W. STOUGHTON
Table I : Observed Values of the E.m.f. in Volts for the Cell, Pt-Dz(p) 1 DCl(m) 1 AgCl, Ag, and Deviations" of the E.m.f. Values Calculated from Smoothed Activity Coefficients ----m
26
2,
----
oc.
60
90
126
160
0.4215 -6
176
200
226
0,0102
0,4505 -3
0.4529 0
0.4481 0
0 I4359 5
0.0196
0,4195
7
0.4175 2
0,4092 -3
0,3922 - 13
0.0502
0,3760 22
0,3685 13
0.3552 -1
0.3350 2
0.3161 -2
0.2954 6
0.2718 11
0.2435 -8
0.0735
0,3576 18
0,3478 7
0.3345 10
0.3119 5
0,2923 5
0,2706 11
0.2464 18
0,2164 - 12
0,1004
0.3417 6
0.3315 8
0.3148 - 11
0.2913 - 12
0.2719 -2
0.2499
0.2248 11
0.1940 - 23
0,1983
0.3100 10
0.2974 26
0.2742 - 30
0.2538 26
0.2328 34
0.495
0.2621 -22
0.2451 1
0.2229 -6
0.1915 - 19
0.1677 - 12
1,127
0.2174 7
0,1933 - 13
0.1680 15
8
The deviations are given below each e.m.f. as observed e.m.f. values less the value calculated from smoothed activity coefficients. Thus, a positive deviation indicates that the e.m.f. reported here is algebraically larger. These deviations have been computed on an equal-moles-of-solvent basis (with HC1).
ture of measurement and correcting for the presence of DC1 in solution by Raoult's law. Each e.m.f. value was corrected to 1.00 atm. of deuterium pressure by subtracting (RT/2F) In fD,, where the deuterium fugacity fD, was taken equal to the deuterium pressure in atmospheres. The solubility of AgCl was neglected, and the ionic strength was taken to be equal to the DC1 molality. The corrected e.m.f. values E at each ionic strength were plotted as a function of temperature and the values corrected to the round values of the temperature 25, 60, 90, 125, 150, 175, 200, and 225". The temperature of measurement was usually no more than 1O from the corresponding round temperature. These corrected values are given in Table I. At the higher temperatures, the e.m.f. values were considered unreliable a t the lowest acidities because of hydrolysis of the AgCl and at the highest acidities because of corrosion of the bomb. Hence these values are not given in the table. The e.1~i.f.values for the cell, Pt-Hz(p) IHCl(m) IAgC1, Ag, which were reported in a previous paper in this series,2had been smoothed with respect to temperature variation by the method of least squares. For the purposes of the present study the original data on HCl were replotted and the values of the e.1n.f. a t round temperatures were read from the curves. These The Journal of Physical Chemistry
values, which differ slightly from those smoothed by least squares, are presented in Table Ia. For the purpose of determining the Eo of the cell, values of E o ' ( , defined by eq. I, were calculated for each data point. I n this equation, E is the e.m.f.
at 1 atm. of Dz a t temperature T , m is the molality of the DC1 solution (which equals the ionic strength), F is the Faraday constant, S is the DebyeHuckel limiting slope (at temperature T ) , and A was assigned a constant value of 1.5 in all the present calculations. Multiplication by the square root of the density p of the solvent approximately corrects the molality term to one in volume concentration as required by the Debye-Huckel equation. I n computing the values of Sp", a t temperature T , it is necessary to know the density and dielectric constant of DZO as a function of temperature. Values of the density of DzO from 30 to 250" are given by Heiks, et r ~ l . while ,~ the dielectric constant from 4 to 100" has been measured by Maln~berg.7 Above 100" (6) J. R. Heiks, M. K. Barnett, L. V. Jones, and E. Orban, J . P h y s . Chem., 5 8 , 488 (1964).
E.M.F.STUDIESIN AQUEOUSSOLUTIONS AT ELEVATED TEMPERATURES
3045
Table Ia : Values of the E.m.f. in Volts for the Cell, Pt-Hs(p) 1 HCl(7n)1 AgC1, Ag, and Deviations” of the E.m.f. Values Calculated from Smoothed Activity Coefficients --____
1, oc.----.
_ _ _ . I _ -
160
178
200
0.4578 17
0.4477 20
0.4350 29
0.4171 11
0.3982 -41
0.4108 -6
0,3983 10
0.3855 20
0,3691 25
0.3493 0
0.3252 -3
0.3798 - 12
0.3706 -7
0.3545 8
0.3396 22
0.3212 31
0,2984 19
0.2716 -9
7
0.3584 - 10
0.3473 -7
0.3288 4
0.3131 23
0,2934 32
0.2708 36
0.2452 32
0.1
0.3519 3
0.3486 -- 5
0.3312 -4
0.3112 5
0.2945 25
0.2730 25
0.2460 -5
0,2224 20
0.2
0.3187 11
0.3062 - LO
0.2905 - 16
0.2685 6
0.2497 26
0.2267 35
0,2021 50
0.1747 58
0.5
(3.2721 13
0.2546 - 19
0.2357 -24
0.2085 - 17
0.1870 3
0.1631 27
0.1305 - 14
0.0928 - 44
1.0
0.2335 4
0.2125 __6’
0.1908 -5
0.1620 6
0.1385 9
0.1129
0.0852 4
a
126
25
60
90
0.005
0.4983 3
0.5057 -.4
0 5065 -4
0.0075
0.4778 -1
0.4826 - 11
0.4814 - 11
0,4759 11
0.01
0.4640 3
0.46’75 -4
0.4654 0
0.025
0.4198 10
0.4181 0
0.05
0.3861 9
0 075
01 3662
111
225
I
11
See footnote a, Table I.
the dielectric constant of HzO was used in preference to extrapolating the D2O values, since the experimental values for the two ,solvents tended to merge a t 100” and since different expressions for D20 gave widely different values on extrapolating to higher temperatures (some higher and some lower than the HzO values). The H 2 0 values used were compuied a t each temperature using the equation given by Akerlof and Oshry.8 By the use of the Sernst equation and the assumption that the logarithm of the activity coefficient of DCI can be expressed at each temperature as the sum of a Debye-Huckel term and a linear term in ionic strength Bm (at least to 0.1 m ) , one obtains the rela,tion Eo” = Eo - (2RT/F)Bm. With the further assumption that AC, for the cell reaction is independent of temperature, the temperature-dependent equation for Eo’’ becomes
Eo”
=
a.
+ alT + a2TIn T 2RT -(as/T + F
a4
$- a6 In
T ) m (2)
The values of Eo” in the range 0.0102 to 0.1004 m were
fitted by the method of least squares using eq. 2 to determine the six coefficients uo, al, . . .a5. The three terms involving ao, al, and a2 give the value of Eo for the cell a t any temperature T , while the terms-involving u3,u4,and usgive the linear term B in the expression for the logarithm of the activity coefficient of DC1. I n carrying out the least-squares determination each data point was assigned a weight equal to the reciprocal of the product. of the absolute temperature and the molality (the two independent variables) associated with the point. This scheme of weighting effectively equalized the contribution of each data point to the over-all fit. The values of Eo were calculated both on a molal basis and on an equal-moles-of-solvent basis ( L e . , moles of solute/55.51 moles of solvent rather than 1000 g. of solvent) and are presented in Table 11, while the coefficients for eq. 2 are given in Table 111. The values of Eo” for DCl were also fitted to an equation in which T Zwas used instead of T In T . I n this case the standard error of fit was slightly larger than (7) C. G.Malmberg, J . Res. Natl. Bur. Std., 6 0 , 609 (1958). ( 8 ) G . C. Akerlof and H. J. Oshry, J . A m . Chem. SOC.,7 2 , 2844
(1950).
Volume 68, Number 10
October, 1964.
31. H. LIETZKEBXD
3046
~
Table 11: Values of the Standard Potentials Eo, in v., of the Cells: Ag, AgCl (molal basis)-This work Ref. 9
---Ds-DCl t , "C.
25 50 60 90 125 150 175 200 225
0 2094 (0.1913) 0 1828 0.1531 0 1111 0.0766 0 0386 - 0.0027 -0.0471
0.2127 0.1931
Ds-DC1 (equal-moles-ofsolvent basis)
0.1886 0,1594 0.1180 0.0838 0.0462 0,0053 - 0.0388
Table 111: Parameters of Eq. 2 DC1 (equal-moles-ofDC1 (molal basis)
solvent basis)
HCI
-0.308117 0.0151850 -0.00236052
-0.310350 0.0152514 -0.00236780
- 0,235985 0.0136202 -0.00212092
a5
- 16.4883 113.631 - 5979,35
- 14.7245 101.579 - 5355,82
-4.17975 27,9216 - 1161.13
rfa
1 . 3 x 10-8
1 . 3 x 10-8
1.6 X
a0 a1
a2
a3 a4
a
0.2220 (0.2052) 0.1973 0,1699 0.1313 0.0998 0.0650 0,0274 -0.0131
The Journal o f Physical Chemistry
~~~~~~
Azo (HC1-DC1) in m.v. --(molal basis)---This w o r k Ref. 9
Ref. 9
0,2224 0,2046
12.6 (13.9) 14.5 16.8 20.2 23.2 26.4 30.1 34.0
AEo in m.v. (equal-moles-ofsolvent basis)
9.7 11.5
7.4 8.7 10.5 13.3 16.0 18.8 22.1 25.7
by Gary, Bates, and R o b i n ~ o n . ~I n Table I1 their Eo and AEO (EOHCI- EODC~) values a t 25 and 50" are compared with ours (our calculated values at 50" being enclosed in parentheses). The difference between the two values of Eo for the deuterated system a t each temperature appears to be larger than expected. The difference may in part result from the niethods of smoothing as to temperature and concentration. After the Eo values for the cells had been determinedeq. 3 was used to calculate an activity coefficient value
E
Standard error of fit.
when the T In T term was used (2.6 X us. 1.3 X Since eq. 2 is based on the thermodynamic assumption that AC, is constant while the equation involving T 2is purely empirical and since the standard error of fit is smaller when the T In T term is used, only the coefficients and Eo values obtained in the former case are tabulated. Attempts were also made to fit an equation like ( 2 ) in which quadratic terms in T were added to the expression for Eoand B T ; such expressions would be consistent with a linear dependence of AC, on T . However the least-squares procedure (on a computing machine) would not converge, presumably because the data are not sufficiently precise to evaluate the coefficients of both T In T and T 2terms. For comparison purposes values of Eo" were also computed for HC1 and fitted using eq. 2. The values of Eo so obtained as well as the coefficients of eq. 2 for HCl are also given in Tables I1 and 111. It is interesting to note that the value of Eo for the cell involving DC1 and D20 is lower than that of the corresponding protonated system and that this difference becomes larger the higher the temperature. The standard e.1n.f. of the cell, Pt-D2(p) (DCl(m)IAgC1. Ag, has recently been determined from 5 to 50"
~~~
Hydrogen and us. Deuterium Electrodes
us.
7-----Hz-DCl----This work
0.2146
~
R.W. STOUGHTOX
=
2RT Eo - -1nm F
2RT F
- __In
y
(3)
y for each experimental concentration a t each round temperature to 225" over the entire concentration range 0.0102 to 1.127 m for DC1 and 0.005 to 1.0 m for HC1. These activity coefficients were then fitted by the method of least squares using
where B and C were taken as
B
=
bo/T
+ bl + bz log T
C
=
co/T
+ +
and ~1
CZ
log T
consistent with AC, equal to a constant. The values of the parameters bo, bl. b2, co, cl, and cz which were obtained in the fits t o eq. 4 are given in Table IV. For concentrations below 0.1 m, the parameters in Table I11 should give more nearly correct values for the activity coefficients. Values of the e.m.f. E were calculated from the Eo values and the smoothed values of the activity CO(9) R.Gary, 1186 (1964).
R.G . Bates, and R . A.
Robinson, J . P h u a Chem., 6 8 ,
E.M.F.STUDIE~ I N A q u E o u s SOLUTIONB AT ELEVATED TEMPERATURES
Table IV: Parameters of Eq. 4 Which May Be Used to Calculate the Activity Cmoefficients of DC1 and HCl DC1 (molal basis)
DC1 (equal-moles-ofsolvent baais)
HC1
- 1935.96 39 9021 - 13.4953
- 1637.96 33.7150 -11.3949
1165.04 - 20,7158 6.85004
C2
2505 34 - 51.6705 7.60646
1834.31 -37.7763 12.8003
- 1381.23 25.9846 -8.64215
Uf
2 . 3 X 10-6
2.1
bo
bi bz co c1
x
10-6
8.5
x
10-6
efficients for the explerimental conditions in both DC1 and HC1 solutions by the use of eq. 3 and 4. The algebraic differences between the observed E values and those calculated with the smoothed coefficients are given below the observed E' values in 'Tables I and Ia. By the use of the parameters in Table IV values of ---
1.980 -.960 ,940
25"
I
3047
log y for both HC1 and DC1 (on an equal-moles-ofsolvent basis) 71s. 4; a t 25, 90, and 200" were calculated; these are shown in Fig. 1. As seen in Fig. 1, (a) the activity coefficient of DC1 (in DzO) is lower than that of HCl in H 2 0 a t all temperatures and concentrations; (b) the difference between the two activity coefficients is greater a t 25" and at 200' than at 90"; and (c) for any curve the lower the minimum value of the activity coefficient (us. 4%) the higher the value of m at the minimum. The fact that the DC1 curves a t 25 and 90" lie below the HC1 curves is consistent with a lower dielectric constant for DzO a t each temperature. The fact that the two curves are closer together at 90 than a t 25" is consistent with a smaller difference in dielectric constant at the higher temperature. Interestingly enough, the difference a t 200" is consistent with a greater difference in dielectric constant a t that temperature than at 90". This would imply that values of the two dielectric constants become closer together at about 100" and then diverge again a t the higher temperature with that of DzO always remaining lower than that of HzO. It is to be hoped that accurate measurements may be made of the dielectric constant of D20 above 100" In order to check this suggestion. The partial molal free energy 8, entropy 3, and enthalpy R for either DCl or HC1 may be expressed in terms of the standard values and the parameters in Table IV by the equations
8 - 80
=
Sp'l"G
4.606RT
($+ bl + bz log S - So = 4.606R [-log
+ 1.54;
1
f
m
c1
+(
+
+ cz log T
4G
X
+
b - (TSp"') - (bl bT
,780 ,760 ,740 .720 ,700 .68Ot,
,
0.05 0.1 0.2
, 0.3
+ bz log T + 2.303
-1
-uu 0.4 0.5
0.6 0.7 0.8 0.9 4.0
6 Figure 1. Plots of log y u s . 4%for HCl and DC1 solutions a t 25, 90, and 200".
Volume 68, Number IO
October, 1964
LOUISWATTSCLARK
3048
where S is the value consistent with eq. 4, $.e., on a common logarithm basis. Acknowledgments. The authors wish to express their
sincere appreciation to 511. D. Armstrong, John Byrnes, Walter Stevens, and Ralph Whitfield who performed the experimental e.ni.f. measurements.
The Kinetics of the Decarboxylation of Malonic Acid and Other Acids-
A General Relationship
by Louis Watts Clark Department of Chemistry, Western Carolina College, Cullowhee, North Carolina
(Received J u n e I$, lQG4)
Kinetic data are reported for the following decarboxylation reactions : malonic acid in benzoic acid, pivalic acid, octanoic acid, heptanoic acid, and dl-2-inethylpentanoic acid ; n-butylmalonic acid in hexanoic acid and octanoic acid; n-hexylnialonic acid in o-cresol ; and oxanilic acid in o-cresol, octanoic acid, benzoic acid, and decanol. The activation parameters for these reactions were calculated and compared with corresponding data obtained previously. A general kinetic relationship was indicated.
A plot of enthalpy us. entropy of activation for a series of related reactions often yields a straight line, the slope of which is designated as the isokinetic temperature. This is the temperature at which the rate of reaction is equal for all the reactions conforming to the line. I n the case of the decarboxylation of oxanilic acid in the molten state and in a dozen polar solvents (ethers and amines) the isokinetic temperature determined graphically was found to be 423"K2 For the decarboxylation of malonic acid in the molten state and in 11 polar solvents (acids, cresols, nitro compounds) the isokinetic temperature was found graphically to be 407°11.3 These values corresponded closely to the melting points of the two reactants (oxanilic acid melts a t 150", which is 423"K.,malonic acid a t 135.6",4which is 409°K.) It was subsequently pointed out by a referee that the isokinetic temperatures for these two reaction series, calculated by the method of least squares, were slightly different from those reported, namely, 418°K. for the oxanilic acid reaction and 414°K. for the malonic T h e Journal of Physical Chemistry
acid reaction. These revised values still did not differ appreciably from the melting points of the two reactants. I n view of these circumstances it was decided to perform additional experiments in order to try to establish more accurate values for the two isokinetic temperatures. Accordingly, the following experiments were carried out in this laboratory: (1) The decarboxylation of malonic acid in benzoic acid, pivalic acid, octanoic acid, heptanoic acid, isovaleric acid, and d2-2-niethylpentanoic acid ; ( 2 ) the decarboxylation of n-butylmalonic acid in hexanoic acid and in octanoic acid ; (3) the decarboxylation of n-hexylmalonic acid in o-cresol; and (4) the decarboxylation of oxanilic acid in o-cresol, octanoic acid. benzoic acid, and n-decyl alcohol. The data obtained in this research were com~~~~~
~
(1) 5.L. Friees, E. S. Lewis, and 4.Weissberger, Ed., "Technique of Organic Chemistry," Vol. V I I I , Part I, "Investigations of Rates and Mechanisms of Reactions," 2nd E d . , Interscience Publiohers, I n c . , New York, N. Y . , 1961, p. 207. ( 2 ) L. W. Clark, J . Phys. Chem., 66, 1543 (1962). (3) L. W.Clark, ibid., 67, 526 (1963) (4) T. Salzer, J . Prakt. Chem., 61, 66 (1900).
