THERMAL DECOMPOSITION OF ACETICACIDIN T
August, 1962
mentioned with this table. For the latter three salts we h a w used values of BD equal to 180, 130, and 116 in that order. There was no particular reason for choosing these values. The values of vf taken from Bockris and Richards were not accurate enough to use more than one or two figures and most of the values are close to 8 X lowz5. The Einstein temperature was taken to be ODs5 Two sets of experimental values are included because of the rilther large discrepancy in the reported results. TABLEIV CALCIJLATED ENTROPIES OF ASf
Salt
NaCl KC1 KRr KI RbBr RbI
6 ~ 1 8
281 227 177 115-200 :120-135 110-118
ASf
FUSION
ASf
(obsd.), (obsd.), (calcd.), Calcd.1 e.u.18 e.u.20 e.u. obsd.'8
6.3 5.8 7
..
3.9 3.27
6.23 6.01 6.06 6.02 5.77 5.73
5.7 4.8 5.2 4.2 4.6 4.7
0.90 .83 .74
..
1.18 1.44
Calcd./ obsd.ta
0.91 .80 .86 .70 * 80 .82
IV Probably the most important result of this treatment is that it shows that the Coulomb potential, aside from setting the scale on which thermodynamic properties are measured, does not directly influence the motion of an ion, indicating that a (20) A.
S. Dvorkin and hl. A. Bredie:, J. Phus. Chem., 64,
269
(1960).
J PRASE ~ ~
~ 1513~
molten salt can be approximated by a hard sphere fluid in certain cases. This is a result of the fact that the potential imide a uniformly charged sphere ia a constant. Critical constants of fused salts have not yet been measured, and this treatment, provides a straightforward method for estimating these quantities. This theory imposes an artificial order upon the liquid state and this has appeared in the calculation of the entropies of vaporization. With less order, CY could dccrease and this would improve the results. Also, a consideration of the association of the molecules in the vapor phase might lead to better agreement with experiment, It was the purpose of this paper to present a simple non-empirical theory, however, and so this m s not done. The most obvious modification of this treatment is to consider the presence of holes in a molten salt. Salts expand about 20% upon melting and yet the distance between neighboring ions increases by only 1 or 2%. The Lennard-Jones-Devonshire theory has been modified to include holes in the system and this modification begins with eq. 1 by allowing for the case where N e N - is less than the number of lattice sites. This then becomes a lattice statistics problem and this has been treated by means of various approximations.21 Acknowledgment. -The author is indebted to Prof. T. L. Hill for helpful discussions.
+
(21) H. 15. Peek and T. L. H111, J . Chem. Phys , 18, 1262 (1950); G. E. Blomgren, %bid.,84, 1307 (1961).
THE THERMODYNAMICS OF THE THERMAL DECOMPOSITION OF ACETIC ACID I N THE LIQUID PHASE1 BY JAMES A. KNOPP,WILLIAMS. LINNELL,ASD WILLIAMC. CHILD,JR. Department of Chemistry, Carleton College, h70rthj?eldl Minnesota Recdved March $3, 19692
Equilibrium constants for the thermal decomposition of liquid acetic acid into acetic anhydride and water were determined over the temperature range 169-248'. From the temperature dependence of the equilibrium constant, AH0 for the decomposition of two moles of acetic acid was found to be 15.22 f 0.28 kcal., which is in good agreement with the calorimetric valua, when the latter is corrected for heats of mixing. AFO for the reaction was combined with free energies of formation from the literature to give -117.3 kcal./mole as the standard free energy of formation of liquid acetic anhydride a t 25".
The discovery2 that liquid propionic acid is thermodynamically unstable a t temperatures as low as the normal boiling point led us to suspect that acetic acid also is unstable a t corresponding temperatures, even though previous measurements of critical constant^,^ liquid density,* and vapor pressure3-5 a t high temperature failed to reveal any decomposition. The products of the thermal decomposition of propionic acid in the liquid phase are propionic anhydride and wa,ter.2 By analogy, acetic acid would decompose according to the reaction 111 part from the senior honors thesis of J. A. Knopp. ( 2 ) W. C. C'hild, Jr., Ph.D. Thesis, University of Wisoonsin, 1955, a n d later unpubliQhed work. (3) 8. Young, Sei. Proc. R o y . Dublin Soc., 12, 374 (1910). (4) D. R. Stull, Ind. Eng. Chem., 39, 517 (1947). ( 5 ) A. E. Potter, Jr., a n d H. L. Ritter, J . Phys. Chem., 88, 1040
(1) Taken
(1954).
2CHzCOOH = (CHJ30)ZO
+ H20
(1) By measuring the equilibrium constant for this reaction a t several temperatures, one can calculate AFa and AHo for the reaction and eventually the free energy of formation of acetic anhydride, for which there is no value presently available.6 Experimental Purification of Acetic Acid.-Analytical Reagent grade acetic acid was purified by refluxing for about one day with an amount of acetic anhydride calculated to react with the water present. The acid then was subjected to fractional distillation a t atmospheric pressure, and the middle fraction was used in the thermal decomposition experiments. It was found that if even a slight excess of anhydride was used, the acetic acid after fractional distillation contained a low concentration of anhydride. The amount of anhydride added therefore was adjusted to give a final batch of acid (6) J. H. S. Green, Quart. Rev. (London), 15, 125 (1961).
~
1514
Vol. BE
which contained either water and anhydride at mole fractions of about 1 X 10-&and 3 X l O W , respectively, or water a t mole fractions ranging up to 2 X 10-3 (anhydride concentratioii negligible), Determination of these values IS described in the section on analyses. It was necessary to have low initial concentrations of water and anhydride t o :r,void repression of the decomposition rmctisn . Thermal Decomposition.-Although several methods were employed for equilibrating samples of acetic acid a t high temperature and then quenching the samples, only the final method, used for the quantitative data reported here, is described. A4cetic acid (3-4 ml.) was distilled on a vacuum line into a Pyrex sample tube, which was 16 mm. in diameter and 9 cm. in length and had a small thermocouple well along the axis of the tube. At one end of this tube there was a 5-cm. length of capillary tubing leading to a break seal, which could be fractured n-ith the aid of a glass enclosed iron rod and a magnet. After filling, the tube was sealed off from the vacuum line and placed inside an electrically heated, crucible-type furnace with the Ereak seal a t the top. This seal was connected to another section of the vacuum line, which contained a U-trap partially filled with glass beads. After an appropriate equilibration time a t high temperature (see Table I), the break seal was fractured, and the sample quickly distilled into the U-trap, which wa6 maintained a t -196'. I t is estimated that the time required to freeze the entire sample was 10 to 15 sec. Finally, the sample was warmed and distilled into another tube, which was sealed from the line. The sample was held a t -80" until the time of the analysis.
TABLE I RESULTSO F EQUILIBRIUX Temp.,
oc.
168.9 169 1 169.6 196.8 197.1 197.9 215.7 218.9 222.7 224.8 226.0 244.8 245.1 246.5 247.5 247 7 247.8
STUDIES
Equilibration time, hr. X ; , X I O 3 X w X I O a K X IO6 3
3 2 2 2 3 1.5 2 1.5 2 3 1 1 1 1 0.6 1.7
0.94 .95 .94 .82
.-. ta
,855 1.94 2.08 1.69 1.61 1.77 3.03 3.03 2.76 2.82 3.17 2.82
0.77 .80 .81 2.35 2.64 2.40 1.88 2.02 2.53 3.21 3.09 2.87 2.97 3.59 3.59 3.08 3.64
0.73 0.76 0.76 1.94 1.99 2.07 3.67 4.24 4.32 5.24 5.51 8.80 9.10 10.05 10.26 9.88 10.40
log Kobsd. -10..
%,iod.
0,000 ,019 ,009 - ,017 - ,012 - ,007 - .017 ,001 - ,039 ,015 ,022 - ,021 ,009 ,021 .016 - ,003 ,019
-
Temperatures were measured with an iron-constantan thermocouple calibrated a t the melting points of benzoic acid, tin, and cadmium. Thermocouple e.m.f.'s were measured with a Leeds and Xorthrup KO.7552 potentiometer. To prevent a temperature drop off a t the top of the sample tube, heater windings were more closely spaced a t the top than a t the bottom of the furnace. The temperature of the upper sample tube, which contained a relatively small quantity of vapor, was held no more than 5" above the temperature of the liquid. The latter temperature was maintained constant to 1 0 . 2 ' with the help of a proportional controller. The uncertainty in the reported temperatures is estimated a t 1 0 . 4 ' . Analyses for Acetic Anhydride and Water .-The ultraviolet spectrum of a previously heated sample of acetic acid exhibited a strong absorbance relative to pure acetic acid in the region, 250-280 mp. The shape of the spectrum was identical to that of acetic anhydride in acetic acid. After a small amount of anhrdrous sulfuric acid in acetic acid was added to the sampfe, the absorbance dropped to zero. These observations wcre taken to support the hypothesis that the products of the thermal decomposition are acetic anhydride and water.
The mole fraction of snhj diide mas determined by measur111g the absorbance of the sample at oiie or iriore of ths following wave lengths: 256, 260, and 268 nzM. The absorbance values were converted to mole fractions by use of Beer's law plots. The standard Bolutions used for the Beer's law data were made b adding from a microburet known volumes of acetic anhydriJe to a weighed quantity of acid in a glassstoppered, 1-cm. spectrophotometer cell. The mhydride contained 1.7% water (as determined by the method of Bruckenstein7), which was taken into account in the calculations. A Beckman DU spectrophotometer was employed for all absorbance measurements. The uncertainty in the values for the mole fraction of anhydride is estimated as &2%. To determine the mole fraction of water, it was necessary only to find the amount of water remaining in a sample after the addition of a small amount of anhydrous sulfuric or perrhloric acid in acetic acid, which causes rapid reaction of anhydride with water a t room temperature. The mole fraction of the excess water then was added to the mole fraction of anhydride, determined previously, to give the mole fraction of the total water present. The excess water was measured by a spectrophotometric titration with acetic anhydride in the presence of the acid catalyst.7 This operation was carried out in a drybox during humid weather. In those cases in which the original acetic acid contained slight excess of acetic anhydride, the result of the titration mas a negative quantity of water, which was treated in the calculations exactly as in the other cases. The maximum uncertaintv in the mole fraction of total water varies from =k3 to zk5%i,, because the excess water is a varying fraction of the total, and because the drybox operation was not always successful in preventing absorption of atmospheric moisture.
Results and Discussion The results of seventeen experiments in the temperature range 169-248' are given in Table I. Equilibrium constants for the decompositioii of acetic acid were calculated according to the equation
where X,,, X,q, and X,, represent the mole fractions of acetic anhydride, water, and acetic acid, respectively. Although the ratio of mater to anhydride varied considerably from experiment to experiment, the measured equilibrium constant was independent of this ratio. The results of a set of four experiments a t --174O, conducted during the humid summer months, TTere discarded in favor of the three listed experiments a t 1 6 9 O , which were performed during the dry winter period. These measurements at the lowest temperatures, where the extent of decomposition is relatively slight, are the most susceptible to errors from the absorption of moisture from the air during the water titration. The equilibrium constants calculated from the first experiments were about 20% larger than those predicted from the final plot of log K vs. l / T , and the discrepancy is attributed to this cause. I n addition, the results of an experiment at 197' and one at 248' were omitted, because the calculated equilibrium constants differed from those read from the log R plot by 12 and 23%) respectively, considerably more than the estimated maximum raiidom error. Since there is a vapor phase in the sample tube, it is possible that the experimentally determined equilibrium constant might differ significantly from (7) S. Bruokenstein, Anal. Chem , 31, 1757 (1959).
the true constant for the liquid phase. To iiirwti- is 13.96 kral. a t 30". In order t o make u comparison gate this possibility, the Henry's law canstants for between the two values of AN, oiie must take into water in acetie acid and acetic anhydride in acetic account not only the different temperatures but acid were calculated, by the method described be- also the different standard states used. Kistialow, for a temperature of 24j0, a t which the fraction kowsky, et ai., employed the pure liquids as the of the sample in the vapor phase is greatest. TTsing standard states. Our standard states for enthalpy these values, the known vapor pressure of acetic are, far water and acetic anhydride, the irifiliitely acid a t 245', and the volumes of liquid and vapor dilute solution in acetic acid, and for acetic acid, phases in a typical experiment a t 245O, the differ- the pure liquid. Thus the two AH'S should differ b s ence belweeii equilibrium constants determined the sum of the heats of mixing of water and acetic. with and without a vapor phase was calculated and acid, and acetic anhydride and acetic acid, to form found to be negligible. To confirm this conclusion, the infinitely dilute solutions in acetic acid. Either the amount oE sample used in the experiment a t of these heat,s of mixing is related to partial molar 245.1' (see Table I) was adjusted so that the ratio enthalpies by the equation of vapor volume to liquid volume was approxiAHmix= R2" - RzA (5) mately oine-fifth that of the other experiments near this temperature. The resulting equilibrium con- in which AHmi, is the heat cf mixing per mole of stant, was not out of line with the others. solute (water or anhydride), H2*is the partial molar I1 is hcslieved that the equilihrium constants ob- enthalpy of the solute at infinite dilution, and RJA tained are thermodynamic constants. That is, the is the molar enthalpy of the pure solute. mole fractions are equal to actii7ities1prorided that To obtain the heat of mixing of water in infinitely the proper choice ol standard states is made. The dilute acetic acid, several methods of calculation equilibrium systcm at all temperatures consists of and sources of data have been used. The first a very dilute solution of water and acetic anhydride calculation is based on data of Keily and in acetic acid. One therefore reasonably can ex- Hume,1° who measured the decrease in temperapect water and acetic anhydride t o obey Henry's ture on adding small quantities of water to a fixed law and acetic acid to obey Raoult's law. This amount of acetic acid. From Fig. 3 of their paper, fact suggests that the standard states for water (bT/dV,), was evaluated for use in the equationla and acetic anhydride be chosen as the hypothetical states in which the fugacities of the two components are equal to their Henrp's law constants. The standard state for acetic acid is logically the pure liquid. With this choice, the activities of the to yield the desired heat of mixing. Here (by/ three components approach the respective mole bVw)mis the rate of change of temperature with fractions in the very dilute solutions. volume of water added to a fixed quantity of acetic A straight line was fitted to the values of log K acid, evaluated at infinite dilution, Rl, and d, are and 1/T by the method of least squares. The result the molar weight and density of water, and C, is is the sum of the heat capacities of the solution and the calorimeter. The calculated heat of mixing is log K r: -3326 5 / T 1.385 ( 3 ) 1030 caI. per mole of water. The deviations between calculated and observed A second value for this heat of mixing was obvalues of log K are included in Table I. The aver- tained from the activity coefficients for the system age deviation
[email protected] log unit, which corresponds water-acetic acid a t two temperatures, by use of' to a deviation in K of f 3.2%, well within the esli- the equation mated error. Extrapolation of eq. 3 to the normal boiling point of acetic acid, 118.l0, yields a value of K of 7.6 X 10-8. Absolutely pure acetic acid therefore should decompose to the extent of 0.028 % at the boiling poinh, if held a t this temperature for a where yw* is the activity coefficient, based on sufficiently long time. Recently Bruckenstein8 has Raoult's law, for water in an infinitely dilute solunoticed that after the careful purification of acetic tion of water in acetic acid. The two values of acid, the last step of which involves fractional dis- yn* employed are 2.71 at 25.Ool1 and 1.91 at t illation, very small and approximately equimolar 99.0°.1z On the assumption that the heat of niixamounts of anhydride and water are present. ing is independent of temperature, the resulting From eg. 3 one obtains the thermodynamic value is 1040 cal./mole. quantities, AHo = 15.22 =t0.28 kcal., and AXo = An attempt was made t o obtain a third value 6.3 =I= 0.6 e.u. for the decomposition of two moles of from the heats of dilution for this system measured acetic acid. The uncertainties were obtained from by Payn and Perrnanl3 over the temperature range the 90% confidence level in the least squares treat- 20-70'. However, it was found that the scatter in ment. From calorimetric measurements, Kistia- the data precluded accurate extrapolatioiis to inkowsky and co-workersg found that AH for the finite dilution. An approximate value of 700 cal./ reaction (10) H. J. Keilv and I). N. Hume, Anal. Chem., 28, 1294 (1956). (11) R. 8.Hansen, F. -4.Miller, and S.D. Christian, J . Phys Chem , 2CHoCOOH(l) = (CH,C'O)aO(l) T-I20(1) (4) 69, 391 (1955)
+
+
(8) S Rruckenstein private eommnniration. (9) J 8. Conn G T7 Iii-tiahowsky H I\ Koberts,andF. 4 S m i t h . . I . A m , Chem. So< , 64, 174: (1912)
(12) J. hIarek, Co27. Caech. Chem. Commun., 21, 269 (1956) ( I ? ) R C . Payn and E. P Peiinan, Tians FaTnday Sac., (1029).
as,
590
1516
J. A, KNOPP,TY. S.LINNELL,AND W, C, CHILD,JB.
mole at 25' mas obtained. It was noted that the heats of mixing increase with temperature, contrary to the general rule that solutions approach ideal behavior more closely as the temperature increases. The first two results therefore are regarded as the most reliable, and the final value selerted for this heat of mixing is 1030 cnl. pcr mole of water. The corresponding heat of mixing for acctic anhydride in acetic acid was estimated from the temperature decreases observed by Greathouse and co-workers14on mixing the anhydride with the acid. The method of calculation was identical to that employed in first calculation of the heat of mixing of water and acetic acid, and the resulting value is 430 cal. per mole of acetic anhydride. The error in this value may he as large as 2075, because the temperature changes mere small and the heat capacity of the calorimeter was not given. Addition of the two heats of mixing to the AH determined by Kistiakowsky, et uL19 gives 15.4 kcal. as the value of AHo a t 30' for the decomposition reaction, based on the standard states employed in this research. The correction t o Kistiakowsky's value is particularly large because both solutes in this system exhibit significant positive deviations from Raoult's law. It is not possible to convert accurately the above value of AHo to 210°, the average temperature of the thermal decomposition experiments, because only AC, for reaction 4 a t 30' can be obtained from literature values. Using 40.2,1629.5,16and 18.0L6cal./deg. mole for the heat capacities a t 30' of acetic anhydride, acetic acid, and water, respectively, AC, is found to be -0.8 cal./deg. AHo at 210' would therefore be smaller than ANo a t 30' by about 0.1 kcal. The heats of mixing also would if anything be smaller a t the higher temperature. It would seem that in any case the variation of AHo with temperature is slight. This conclusion is further supported by the fact that log K for the thermal decomposition is a linear function of 1/T, within experimental error. Therefore, the agreement between the AHo obtained from this research, 15.2 kcal., and the calorimetric value seems satisfactory. On the assumption that AHo and ASo for the decomposition reaction do not vary with temperature, one can readily calculate AFO for the reaction a t 25" and from this the standard free energy of formation of acetic anhydride a t 25', since the free energies of formation of acetic acid and water are known. The calculated AFO a t 25' is 13.3 kcal. Since this value refers to the standard states employed in this research, it must be corrected to the usual standard states, the pure liquids. This again involves a correction for water and one for acetic anhydride and requires a knowledge of k2/p2A, the ratio of the Henry's law constant for (14) L. H. Greathouse, H. J. Janssen. a n d C. H. IIaydel, A d . Chem., 88,357(1956). (15) W. M. Philip. Proc. I d a n Aead. S c i . , 9A,109 (1939). (16) F. D. Rossini, et at., "Seleoted Values of Chemical Thermodynamic Properties," CirouIar 5QQ, w&tmnal Bupeau of Standards, Washington, D. C., 1952.
Vol. 66
the solute in acetic acid to the vapor pressure of the pure solute. Since this ratio is equal t>oy2*, the activity coefficient already discussed, it can be found readily. yw* is 2.71 at 25', as discussed earlier. This value leads directly to AF for the process,
FIzO(1, v.13.
k,, 25')
--ic
HzO (1, V.P. = pwA,25')
(8) which is the desired result. The left side of this equation refers to water in a hypothetical state in which it exerts a vapor pressure equal to the Henry's law constant, while the right side refers to pure water exerting its real vapor pressuie. The calculated AF for the process is -690 cal. yan* a t 25' must be calculated from the value at 99.0', which is 2.21.12 The calculation is m_ade by Ese of eq. 7 applied to acetic anhydride; H a n A Ha=" for this calculation already has been obtained. The result is yan* = 2.55 a t 25', and the correction to the free energy change accompanying the decomposition reaction is -560 cal. Addition of these two corrections to the experimentally determined AF' gives 12.2 kcal. as the standard free energy change for the reaction a t 25' when the standard states for reactant and products are the pure liquids. This value now can be combined with the standard free energies of formation of water and acetic acid, -56.716 and -93.16 kcal./mole, respectively, to give - 117.3 kcal./mole as the standard free energy of formation of liquid acetic anhydride at 25". By use of the above corrected AFO for the reaction a t 25' and the known9 AHo, ASo is found to be 5.9 e.u., based on the conventionaI standard states. This value in turn is combined with the standard entropies of water and acetic acid, 16.716and 38.26 e.u./mole, respectively, to give 65.6 e.u./mole for the standard entropy of acetic anhydride a t 25'. A comparison of the magnitudes of the AH" and TAXo terms for the decomposition shows that AH" is by far the more important. This means that the slight instability of acetic acid can be related primarily to bond energies. The TASo contribution, although small, decreases the stability. Kistiakowsky and co-.cvorker~,~ in their study of the heats of hydrolysis of acetic and methyl-substituted acetic anhydrides, found no correlation between AH and increasing methyl substitution ( L e . , increasing positive inductive effect of the substituent). An investigation of the thermal decomposition of several substituted acetic acids is planned to determine whether a trend becomes apparent when the TAS" contribution is included. Acknowledgment.-Financial support from the Research Corporation, the Petroleum Research Fund of the American Chemical Society, and the National Science Foundation is gratefully acknowledged. We are indebted to Dr. Robert Kolenkow and Mr. Arthur Hay for the design and construction of the proportional temperature controller used in this research.
