be evaluated. rate theoryg kl =
39 1
ACTIVITIESOF AQUEOUS SOLUTIONS OF ALIPHATIC ACIDS
May, 1955
A4ccordingt'o the absolute reaction kT exp h
K -
(+)AH1 *
exp
(F)
(12)
The value of AS2+ should be very small since it represents the entropy change in going from an adsorbed molecule to an activated complex on the surface. Therefore, AS?* was assumed to be zero in this semi-quantitative analysis of 16' and AS1 +. Using the absolute reaction rate theory expression for kz, in equation 5 one obtains
In this equation, k1 is the rate constant; k , Boltzmann's constant; h, Planck's constant ; T , absolute temperature; K , transmission coefficient, R, kT AH2 AS, the gas constant; AH1* and AS, are the heat rate = K - L'B exp exp (13) h and entropy of activation for the adsorption process, respectively. A plot of log k'k,/T vs. The units of k' are molecules/cm.2 if the rate of 1 / T was linear. From the slope of this line the the reaction is measured in molecules cm.-2 see.-'. heat of activation, AH,* was found to be 28.4 Assuming K to be unity, ASz* to equal zero, and under the conditions that rate equals 8.5 X kcal. per mole. see.-'), T = The heat of activation for the desorption of atm. sec.-l (3.2 X loLomole carbon dioxide, AHt*, was determined from the 431' and 6 = 0.5, k' was found to be 20 molecules For V204.34, Aebij found the 0-0 distance log kl/kz(log B ) versus 1/T plot. The slope of the line is equal to -(AHl* - AHz*)/4.57G. This along the octahedron edges to be 2.7 to 3.3 A. yielded a value of 22.2 kcal. per mole for (AH, - He also found that the 0-0 distance was essentially the same in V205as in V204.34. Assuming all the AH2*) ; therefore, AHz* is 6.2 kcal./mole. The entropies of activation for the two reac- oxygen atoms on the surface to be this distance apart, the surface would have approximately l O l 5 tions-absorption and desorption processes-cannot be calculated directly from equation 12 be- surface sites per square em. Since the number of cause the factors in the products klk' and k21c' surface sites is so much greater than k ' , it suggests cannot be separated. However, it is interesting that only very special type sites enter into the reacto note what the magnitude of k' and AS1+ should tion. By knowing k' and AHl*, the entropy of be in terms of the proposed mechanism. In order activation for the adsorption process, AXI was t o do this a value for AS2* has to be assumed. calculated to be -39 cal. deg.-' mole-'. This is on the basis of one gram of catalyst or 240 square (9) S.Glasstone, K.J. Laidler and H. Eyring, "The Theory of Rate meters of surface. Processes," McGraw-Hill Book Co., Ino., New York, N Y., 1941.
(%) *
*
(R ) *
*
*
ACTIVITY COEFFICIENTS OF COMPONENTS I N THE SYSTEMS TVATERACETIC ACID, nrATER-PROPIONIC ACID AND WATER-n.-BUTYRIC ACID AT 2 5 ' 1 B Y ROBERT s. HANSEN, FREDERICK A. MILLER^
AND
SHERRIL D. CHRISTIAN
Institute for Atomic Research and Department of Chemistry, Iowa State College, Ames, Iowa Received October 18, 1064
Activity coefficients of components in the systems water-acetic acid, water-propionic acid and water-n-butyric acid have been determined at 25" from experimental partial ressure measurements. Activity coefficient functions self consistent according to the Gibbs-Duhem equation are obtainel from these data which represent the data in each system over the entire concentration range. The representations appear to be very satisfactory over the entire concentration range for the S J ~ R tems watepacetic acid and water-n-butyric acid, but less satisfactory in the water- ropionic acid systems a t propionic acid mole fractions in excess of 0.3. Activity coefficients for water in fatty acid have gee, inferred from total vapor pressure measurements over the acid-rich portions of the concentration range for the systems water%-valeric acid, water%-caproic acid and watepn-heptglic acid. These results have been combined with the other activity results and solubility measurements to establish the limiting increment per -CH2- group to the specific free energy of fatty acid a t infinite dilution i n water as 870 cal. per mole.
Introduction Activities of aqueous solutions of the lower aliphatic acids valid a t solution freezing temperatures have been obtained from freezing point depression data by Jones and Bury,S and activities of these same systems have been measured at 34.45 O by Giacalone, Accasina and Carnesi4 using a wet bulb thermometer technique. Both investiga(1) Contribution No. 355. Work was performed in the Ames Laboratory of the Atomic Energy Commission. (2) Based in part upon a dissertation submitted b y Frederick A. Miller to the Graduate School, Iowa State College, in partial fulfillment of the requirements for the degree of Doctor of Philosophy, 1953. (3) E.R. Jones and C. R. Bury, Phil. Mag., 4, 481 (1927). (4) A. Giacalone, F. Aooasina and G. Carnesi, Uazr. chim. ital., 71, 109 (1942).
tions were limited to the water-rich portion of the concentration range, and the second piece of work appears to be neither extensive nor highly accurate. The purpose of the present work was to obtain complete activity data for all components of these systems over the entire Concentration range and to obtain the specific free energies of these components at infinite dilution. Experimental Partial pressures of both components in each of the systems water-acetic acid, water-propionic acid and water-nbutyric acid were determined at from 14 to 20 concentrations covering the entire concentration range. Determinations were performed using the apparatus and techniques
392
R. S. HANSEN,F. A. MILLERAND S. D. CHRISTIAN
described by Hansen and Miller.6 The partial pressures were obtained at 25.00 i 0.02". Total pressures were measured a t selected concentrations in the acid-rich portions of the concentration range for the systems water-n-valeric acid, water-n-caproic acid and water-n-heptylic acid, and these pressures were ascribed entirely to water. I n these measurements, a 25- to 100-ml. reservoir containing the sample was connected to a precisionbore mercury manometer and to a vacuum line. The sample wa8 outgassed with shaking for 5-10 minutes, then allowed to come to pressure equilibrium. The flask was 0.02" during the experikept in a water-bath at 25.00 ment, and the manometer and connections between flask and manometer were maintained a t higher temperature by means of heating coils to prevent condensation. When the pressure determination was completed, an aliquot of the sample was removed and water concentration was determined by Karl Fischer titration using the dead-stop endpoint technique. Solubilities of water in organic acids were also determined by Karl Fischer titration of the acid saturated with water. The water used was redistilled from alkaline permanganate solution; the fatty acids were Baker and Adamson reagent grade acetic acid, Eastman Kodak Co. white label propionic, n-butyric, n-valeric and n-heptylic acids, and Eastman practical grade n-caproic acid. The acetic, propionic, butyric and valeric acids were purified by distillation through a 30-plate Oldershaw column a t 10-1 reflux ratios; the caproic and heptylic acids were purified by simple distillation. The fatty acid fractions used had boiling ranges as pllows (corrected to 760 mm.): oacetic acid, 118.20-118.33 ; prspionic acid, 141.44-141.61 ; n-butyric acid, 164.0-164.2 ; n-valeric acid, 188.1-186.4'; ncaproic acid, 203-205'; n-heptylic acid, 223-224'.
Treatment of Data Resolution of experimental total pressure and condensate mole fraction data in terms of component partial pressures and fugacities is complicated in fatty acid systems by the extensive association of fatty acids in the vapor phase. Let PI, Pzand P3be the partial pressures of fatty acid monomer, dimer and trimer in the vapor phase; nl, n2 and n3, the corresponding moles of condensate; P , and n,, the partial pressure and moles of water in condensate; PT, the total pressure, and X A , the experimental mole fraction acid in the condensate (in which all acid is counted as monomer). Evidently
+ 2n2 + 3n3 + 2n2 + 3n3 + n. 121
xA
e
nl
- PI + 2Pz + 3P3 - pI + 2 ~ + 2 3p3 + P,
=
Let K2 and Ka be the equilibrium constants for formation of dimer and trimer from monomer, respectively. Substitution in (1) leads to h'a(3
- 2XA)P13 + KZ(2 - XA)P12+ P1 - XAPT
=0
(2)
which may be solved for PI. Let be the fatty acid fugacity and PA= PI P 2 PD,the total fatty acid partial pressure. Then
+
+
VOl. 59
= In PJPA
(6)
whence fA
=i
p 1
(7)
Monomer pressures were calculated from eq. 2 using equilibrium constants obtained from the work of MacDougall in the case of acetic acidBaand propionic acidBband from the data of Lundin, Harris and Nash7 in the case of n-butyric acid. Constants used for calculations were: for acetic acid, K2 = 1.63 mm.-', K8 = 0.0016 mm.-2; for propionic acid, K2 = 3.92 mm.-', Ka = 0.074 mmmV2;for butyric acid, K z = 1.27 mm.-'. Equilibrium constants in the latter two systems were evaluated by extrapolation of data a t higher temperatures. The progression of these constants is such as to cause some concern for their accuracy. Allen and Caldins have recently summarized work on fatty acid association. Thermodynamic quantities tabulated by these authors led to free energies of dimerization for acetic acid a t 25" ranging from -3.95 to -4.30 kcal., and representing work of four different groups. The work of MacDougall (selected because his experiments were performed at 25") corresponded to a free energy of dimerization of -4.20 kcal. a t 25". On this basis the dimerization constant used is probably correct to within 15%. The situation with respect to propionic acid is much less satisfactory in that the free energy of dimerization calculated from MacDougall's work, -4.8 kcal., differs from that calculated from the work of Taylor and Bruton,g -4.35 kcal., sufficiently that dimerization constants calculated differ by a factor of two. Lundin, Harris and Nash' appear t,o have presented the only da,ta available on the dimerization of butyric acid. The uncertainties in dimerization constants lead to considerably smaller relative uncertainties in activity coefficients. For example, considering dimerization only, the fatty acid activity referred to pure liquid fatty acid as standard state is given by a A = f A - p"I = *1
fx
In the case of propionic acid, for example, the product XAPTwas greater than unity in every observation except a t the most dilute concentration (mole fraction 0.0246 in the liquid phase, XAPT= 0.47). The terms containing Kz are greater than 10 in all but the most dilute systems regardless of the constants taken. When one rearranges and expands eq. 8, there results
If i t is assumed that deviations from ideality are due solely to the indicated associations then
(5) (5) R . 9. Hansen and F. A. Miller, THISJOURNAL,OS, 193 (1054).
(6) (a) F. H. MacDougall, J . Am. Chem. Soc., 68, 2585 (1936); (b) ibid., 63, 3420 (1941). (7) R. E. Lundin, F. E. Harris and L. K. Nash, ibid., 74, 743 (1952). (8) G. Allen and E. F. Caldin, Quart. Rev., 7 , 255 (1953). (9) M. D. Taylor and J. Bruton. J . Am. Chem. Soc., 74, 4151 (1952).
*
-
ACTIVITIESOF AQUEOUS SOLUTIONS OF ALIPHATIC ACIDS
May, 1955
393
1.5
1.0
o.60
t
w/
a\.
H20 IN CsH7COOH
K -o?o
0.0
H0
0.5
IN CH$OOH
0
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.30 - LOO
MOLE FRACTION ACID IN WATER. Fig. 1.-Activity coefficients as functions of concentration in the water-fatty acid systems. I n the systems wateracetic acid, water-propionic acid and water*-butyric acid curves are calculated from function self-consistent according t o the Gibbs-Duhem equation. All points are experimental.
in which the leading term is independent of I
