Ind. Eng. Chem. Res. 1995,34, 1327-1331
1327
Densities of Acetic Acid + Water Mixtures at High Temperatures and Concentrations Tongfan Sun, Danith Ly, and Amyn S . Teja* Fluid Properties Research Institute and School of Chemical Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332-0100
The densities of acetic acid-water mixtures were measured a t temperatures between 290 and 460 K and concentrations ranging from 25 wt % acetic acid to 100 wt % acetic acid. The data were correlated with a polynomial function in temperature and concentration and were extrapolated to low temperatures for comparison with literature data. The data were also correlated using two association models and a model based on the generalized corresponding states principle (GCSP). Although the association models provide more information on the structure of the solutions, the GCSP method required much less information and could apparently be extrapolated over a significant range of temperatures.
Introduction Acetic acid-water mixtures are widely used in the manufacture of products such as acetate plastics, acetic anhydride, esters, and aspirin. Accurate values of their thermodynamic and transport properties are therefore of considerable industrial interest. Thermophysical properties of acetic acid-water mixtures are also of interest from a fundamental point of view, since these mixtures exhibit behavior not usually observed in nonpolar fluids. Schrier et al. (1964) have suggested that the acid associates in an extended open form (shown in Figure 1)in aqueous solutions, with nonpolar groups in maximum contact with each other and in minimum contact with water. This open-form association is apparently stable in aqueous solutions, whereas a cyclic form is more stable in nonaqueous solutions and in gaseous mixtures. As part of a study of the thermophysical properties of aqueous electrolyte systems, we have measured the density, viscosity, thermal conductivity, and critical properties of acetic acid-water mixtures over a wide range of temperatures and concentrations. Densities of these mixtures have also been reported by Apelblat and Manzurola (1987) and by Melzer et al. (1989), but their data are limited to low temperatures and low concentrations. The present work reports density data at much higher temperatures and concentrations. Several models for the densities of mixtures were also examined for their ability to correlate data for this system.
for temperature measurement. A high-pressure pump was used to pressurize the system in order to suppress boiling. Additional details of the apparatus and experimental procedure are given by Lee et al. (1990). Reagent grade acetic acid with a specified purity of 99.7 mol % was purchased from Fisher Scientific Co. and used without further purification. Doubly distilled water was used to prepare the aqueous mixtures.
Results and Discussion Table 1lists the measured densities of six acetic acidwater mixtures containing 25,50, 75,84,92, 100 wt % acetic acid, respectively. The data are also shown graphically in Figure 2. Temperatures in the experiments ranged from 290 to 460 K. Above 370 K, the system pressure was varied from 0.2 to 1MPa in order to suppress boiling. Two measurements were made at each temperature, and the averages are reported in Table 1. The reproducibility of the density data was found to be f0.1% and the accuracy was estimated to be f0.25%. The accuracy of the temperature measurement was estimated to be f O . l K. The density data were correlated as a function of temperature and mole fraction of acetic acid as follows: @kg m-3 = A,
+ A,T/K + A2p/K2+ A3p/K3 (1)
with
+ 1950.54~- 1 0 5 4 . 3 2 ~+~1 7 4 . 0 1 9 ~ ~ A, = 4.1946 - 10.5253~+ 3 . 1 5 9 2 2 ~ ~
A, = 534.613 Experimental Section Densities were measured using a high pressure pycnometer designed for pressures up to 10 MPa and temperatures up t o 473 K. The high-pressure pycnometer consisted of a stainless steel sampling cylinder and an isolation valve, connected via steel capillary tubing to a high pressure hand pump. The volume of the sampling cylinder between 298 and 423 K was determined by calibration with pure mercury. The mass of the fluid under study was obtained by weighing before and after filling the cylinder with the fluid. The density could be readily calculated from a knowledge of the mass and volume. The cylinder was provided with a thermowell into which was inserted a type K thermocouple
* To whom correspondence should be addressed. E-mail:
[email protected].
A, = -0.0113495
+ 0.0212374~- 0 . 0 0 3 6 6 0 7 ~ ~
A, = 8.43584 x
-
1.47636 x 10%
In eq 1, e is the density, T is the temperature, and x is the mole fraction of acetic acid. The average absolute between calculated and experimental deviation (AAD) values was 0.15%,and the maximum absolute deviation (MAD) was 0.54%. The correlation allowed the data to be extrapolated to low temperatures and concentrations for comparison with the density data of Apelblat and Manzurola (1986) and Melzer et al. (1989). Figure 3 shows that our data are in good agreement with the literature data.
0888-5885/95/2634-1327$09.00/00 1995 American Chemical Society
1328 Ind. Eng. Chem. Res., Vol. 34, No. 4, 1995
-0
R-
C'/ \OH I I
I
n
R-C
/-
' O H
I
I n I
Figure 1. Open structure of acetic acid in aqueous solutions suggested by Schrier et al. (1964).
Table 1. Experimental Densities of Acetic Acid-Water Mixtures wt%
acid 25
75
92
p
e
[barl 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 8.0 8.0 11.5 11.5 15.5 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 8.0 8.0 8.0 11.5 15.5
T[Kl [kgm-31 297.80 1028.3 306.05 1023.7 314.30 1018.0 322.55 1012.7 330.85 1007.2 339.15 1000.3 347.35 994.1 355.85 987.1 364.35 980.0 372.90 973.3 388.85 960.1 409.15 942.4 427.55 927.4 445.65 910.8 463.75 894.9 302.75 1059.3 311.65 1051.4 321.40 1042.5 330.65 1031.3 339.55 1022.3 348.95 1013.4 358.55 1003.4 366.70 994.4 378.70 981.7 400.15 960.7 421.95 938.4 444.60 916.7 462.70 898.2
acid 50
1.0 1.0 1.0 1.0 1.0 1.0 8.0 8.0 8.0 11.5 11.5 11.5 11.5 15.5
297.20 513.45 328.50 343.50 358.20 373.45 391.87 402.58 412.44 422.12 433.41 442.02 448.40 461.25
100
1059.1 1042.1 1026.6 1009.0 992.0 975.3 952.8 940.7 928.1 916.2 901.6 890.2 882.2 866.0
84
P [barl 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 8.0 8.0 11.5 11.5 15.5 1.0 1.0 1.0 1.0 1.0 1.0 1.0 8.0 8.0 8.0 8.0 11.5 11.5 11.5 11.5 15.5 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 8.0 8.0 8.0
8.0 11.5 11.5 11.5 15.5
e
T[Kl [kgm-31 301.90 1051.1 311.65 1042.5 321.35 1034.3 330.45 1026.7 339.45 1019.0 348.85 1012.3 358.05 1003.7 366.85 994.6 375.05 987.5 394.80 968.9 411.75 951.2 430.15 933.1 447.75 316.1 461.75 900.4 294.15 308.40 323.25 338.40 356.15 371.15 375.85 383.25 392.35 402.95 413.15 422.95 433.15 443.15 449.15 461.35 296.00 304.00 313.75 324.35 333.35 343.45 353.35 363.15 376.25 388.26 402.58 420.45 432.15 441.51 444.87 455.35
1067.5 1053.2 1037.9 1022.1 1002.8 987.7 982.3 973.3 963.2 950.6 937.3 925.7 913.5 901.1 893.8 880.0 1047.2 1039.3 1028.0 1015.1 1004.2 993.3 981.3 970.1 954.5 940.4 924.0 901.3 886.4 873.9 868.9 856.0
Excess volumes of acetic acid-water mixtures were also calculated as a function of temperature T and concentration of acetic acid XI using the definition
VE = XlMJl/@ - l/@J+ X2M2(1/@- 1/e2)
(2)
where subscripts 1 and 2 refer to acid and water, M is
Temperature (K) Figure 2. Experimental and correlated (eq 2) densities of acetic acid-water mixtures as a function of temperature a t several concentrations.
,
I
Extrapolated irom data of this work
-1.2
I
1
.., 0.00
0.20
0.40
0.60
0.80
1 .oo
Molar fraction acetic acid
Figure 3. Comparison of experimental and calculated excess volumes of acetic acid-water solutions a t 288 K.
the molecular weight, and the densities e, el, and e2 were evaluated from eq 1. Excess volumes were found to be negative in the range of temperatures and concentrations studied (Figure 3). The calculated values ranged from 0 to -2 cm3 mol-', or up to 2% of the actual molar volume. Negative excess volumes in this system have also been reported by Apelblat and Manzurola (19871, who have attributed this behavior to self-association of the acid. Contributions due to ionization or the formation of an acid-water complex due to hydrogen bonding were assumed to be negligible. To explore this hypothesis further, we have examined the data using two association models which are described below.
Association Models The ideal association model was proposed by Kehiaian and Kehiaian (1963) and Kehiaian (1964) and postulates the existence of undissociated acid, self-associated acid, and water in the acetic acid-water system. The mixture thus consists of molecules of the type: A B A2 ... Aj where A denotes the acid, B is water, A2 is a dimer, and 4 is ajmer of the acid. Initially, the number of moles of the acid and water are given by
+ +
+ +
Ind. Eng. Chem. Res., Vol. 34, No. 4, 1995 1329
n = n,
+ n2
(3) xA=-1
Considering the acid associations, the moles nl of acid are then written as (4)
and the moles of water as
n2 = nB The molar fraction of the acid, taking account of association, is defined as
At chemical equilibrium, a system containingjmers may be characterized by j - 1association constants Ki:
Ki = XA,/(xA)'
(6)
Combining the above equations with the relations x1 2 2 = 1 leads to
= nl/n and X I
+
(7)
If XA,,is defined as XA at x1 = 1, the activity coefficients y1 and y 2 of components 1 and 2 can be obtained from the general equation derived by Prigogine and presented by Kehiaian (1964):
(9) Y2
= xB/x2
(10)
&'(2 - xl) +' 1+2K(2 - x') 9
with P
A=
-1
+ d i x E (14) 2K
The graphical solution to the above equations was first presented by Kehiaian and Kehiaian (19631, and the numerical solution was tabulated recently by Apelblat and Manzurola (1987). Equations 13 and 14 show that PIAVO is always negative for any value of K, if AV' is positive. From structural *considerations, the latter is true for the dimerization of acetic acid since AVO (=Vm- 2vA) is about 10 cm3 mol-' for the dimer with an open structure at room temperature. Despite this qualitative agreement, however, the dimerization model suffers from several drawbacks. First, it predicts that the behavior of P is asymmetrical with respect to concentration, which does not agree with the experimental findings of the present work (see Figure 3). Second, values of K determined from excess volume data are not consistent with those obtained from a fit of vapor pressure data. Finally, the model does not yield any regular trend of K values with chain length for carboxylic acids, which has been observed experimentally (Schrier et al. (1964)). It is therefore necessary t o examine alternative descriptions of the structure. When j = = in eqs 11 and 12, the Mecke-Kempter model is obtained. Two additional assumptions of this model are (i) the equilibrium constants K, form a geometric progression:
Ki+JKi= constant = K
(15)
A q = (Z - 1 ) A P
(16)
and (ii)
where A P is the standard volume change on forming one bond. These assumptions lead to:
Combining these with eq 1 yields the following expression for the excess volume as given by Kehiaian and Kehiaian (1963): with PA= -(17)
l+K
A q =
AT
fli- ic
-
(12)
where is the standard volume change upon the formation of (i - 1)bonds, i.e., the volume change for the reaction iA Ai. P in eq 11 can be evaluated at any temperature by substituting XAwith XIand specifylng the coefficients Ki and V. In general, 20' - 1) parameters are required for the formation ofjmers: viz. K2, K3, ...,4, and ..., Whenj = 2 o r j = -, eqs 11 and 12 need only two parameters. The model with j = 2 is the dimerization model and the other is the infinite association Mecke-Kempter model (see Kehiaian (1964)). Equations 11and 12 for the dimerization model (A + B A2) reduce t o
E,fl, q.
+
This equation always yields negative values of P for any value of K . Moreover, P is symmetrical with concentration, in agreement with our experimental results for acetic acid-water mixtures. It should be emphasized that the evaluation of the parameters of the M-K model a t a given temperature requires very precise experimental VE data and that our data are probably not accurate for this purpose. Nevertheless, we have combined our smoothed data with accurate room-temperature data from the literature in order t o draw qualitative conclusions. It should also be emphasized that the two parameters K and A P in the M-K model are not unique if only P data are used in the correlation. As an illustration, two calculated curves at T = 288 K are plotted in Figure 3 with K = 1.19 mol-' and AVO = 10.01 cm3 mol-' and with K = 0.0119 mol-' and AVO = 351.2 cm3 mol-'. The values of K differ by 2 orders of magnitude, but the correlations are similar
1330 Ind. Eng. Chem. Res., Vol. 34, No. 4,1995
in both cases. Therefore, as suggested by Apelblat and Manzurola (19871, a unique value of K at a given temperature can be determined only from vapor pressure data, since the equations for activity coefficients y1 and y2 contain only one adjustable parameter. Activity coefficient data for acetic acid-water mixtures at 298 K reported by Hansen et al. (1955) were used to obtain a value for K = 1.19 mol-'. A fit of VE data then resulted in a value of AVO = 10.58 cm3mol-'. In general, vapor pressure and density data could be correlated satisfactory with the M-K model. However, it should be pointed out that the model predicts IP to be positive and symmetrical with concentration,whereas the experimental data of Christensen et al. (1982) show that HE is asymmetrical and negative at X I < 0.15. The negative excess enthalpy of mixing in the acetic acid-water system is quite unusual and has also been reported for formic acid-water mixtures in the entire concentration range (see also Christensen et al. (1982)). This behavior cannot be explained even qualitatively with either of the association models, although the dimerization model gives good predictions of the negative VE and positive AVvalues in the formic acid-water system (see Apelblat and Manzurola (1987)). Therefore, it is probable that some other process contributes to the mixing enthalpy in these mixtures and becomes dominant at x .e 0.15 in the acetic acid-water system. It is interesting to explore whether acetic acid selfassociates to form micelles in water, as is the case with higher order carboxylic acids. It is known (Tanford (1980))that volume changes in solutions due to possible formation of micelles by small amphiphile molecules are not detectable by experimental methods so that other data must be used to test this hypothesis. A plot of surface tension of acetic acid-water mixtures at 303 K (Weast et al. (1986)) versus the logarithm of the acid concentrations shows a monotonous decrease of surface tension with increasing acid concentration. This indicates no formation of micelles or other amphiphilic aggregates. (The surface tension would attain a maximum above a certain concentration of the acid if micelles are formed.) The association models discussed above provide some insight into the structure of acetic acid-water mixtures but are also incapable of correlating all experimentally observed behavior in this system. Development of a better model would require extensive data and is beyond the scope of this investigation.
GCSP Model The generalized corresponding states principle (GCSP) proposed by Teja (1980)is based on the three parameter corresponding states principle of Pitzer and uses two nonspherical reference fluids. Since the choice of reference fluids is arbitrary, they are generally chosen such that they are similar to the key components of interest. Good predictions of thermodynamic properties can then be expected. The GCSP method relates the quantity (ZCVR) for any substance to the same quantity of two nonspherical reference fluids r l and r2 a t the same reduced temperature TRand reduced pressure PR as follows:
where Z is the compressibility, V is the volume, and w
Table 2. Density Predictions Using the GCSP Method raw data smoothed data raw data smoothed data
412
VlZ
1.0429 1.0429 1.0626 1.0643
1 1 1.0702 1.0760
AAD[%l 0.26 0.25 0.17 0.17
MAD[%] 1.61 1.09 1.02 0.45
is the acentric factor. The subscript C denotes the critical properties, and the superscripts r l and r2 denote the properties of two reference fluids. The above equations can readily be extended to mixtures using the van der Waals one-fluid model:
(20) i
j
(22) together with:
(23)
(24)
TcijVcG= ~G(TciTQVciV,)"2 where q$j and lyij are binary interaction parameters which must be obtained from experimental data. One adjustable parameter is generally sufficient to characterize a binary system. When applying eqs 19-25 to binary mixtures with the reference fluids r l and r2 chosen as the actual components in the mixture, eq 19 simplifies to
(26) The calculation of the density of a binary mixture using eq 26 requires a knowledge only of the densities and critical properties of the pure components. In the present work, r l = acetic acid and r2 = water. The critical properties required in the calculations were obtained from Reid et al. (1987) and are given by Tcl = 592.7 K, Vcl = 171.3cm3mol-', Zcl= 0.201, Tc2 = 647.1 K, VCZ= 56.0 cm3mol-l, and Zc2 = 0.233. The reference fluid densities were obtained from eq 1by letting x = 1 andx = 0. Results of the calculations of the mixture density are listed in Table 2. As can be seen, the overall absolute average deviation (AID) was approximately 0.2%,which is within experimental error. Maximum absolute deviations were of the order of 1-2%, with the largest deviations occurring at low temperatures in the acidrich region. The large value of MAD can be reduced significantly if smoothed experimental data are used to obtain the adjustable parameter (see Table 2), suggesting that the largest source of error is probably experimental error. One binary interaction parameter 4" was used to characterize the system. This parameter did not change with temperature or concentration, despite the fact that the data covered a wide range of temperature and concentration. This appears t o be a great advantage of the GCSP model over models such as those discussed in the previous section. In the M-K model, the parameters K and AVO are sensitive to temperature. (For example, according to Apelblat and Manzurola
Ind. Eng. Chem. Res., Vol. 34, No. 4, 1995 1331 (1987) K = 1.45,AV" = 10.04 cm3 mol-l a t 288 K, but K = 1.19, AV" = 10.58 cm3 mol-l at 298 K, and K = 0.95, AV" = 11.19 cm3mol-l at 308 K). In contrast, the constant value of the binary interaction parameter in the GCSP model is particularly useful for engineering applications, since it allows the extrapolation of data and affords a means of checking the consistency of different sets of data. In our GCSP calculations, the binary interaction parameter was obtained using density data a t room temperature. The model was then extrapolated to the highest ( 4 5 3 K) and the lowest temperature (288 K) at which experimental data were available. No significant deterioration in accuracy could be detected. Figure 3 demonstrates the predictions of excess volumes by both models. It should be emphasized that density predictions at different temperatures using the M-K model cannot be represented here for the purpose of comparison with the GCSP model. As mentioned earlier, the parameter K of the M-K model can be determined only from vapor pressure data, and these data are not available for acetic acid-water mixtures a t high temperatures.
Conclusions Densities of acetic acid-water mixtures were measured at temperatures ranging from 290 to 460 K and concentrations from 25 to 100 wt %. The data were generally consistent with literature data at low temperatures. A correlation for the density of acetic acidwater mixtures was developed and is given in this paper. Three models were evaluated for their ability to correlate and extrapolate the density of these mixtures. The M-K association model offers insight into the structure of acetic acid-water mixtures and is able to simultaneously correlate excess volume and Gibbs energy data. However, the model requires extensive experimental information in order t o evaluate the parameters. Moreover, the model is incapable of predicting all the experimentally observed behavior (especially the negative HE behavior a t z < 0.15) in this system. By contrast, the GCSP method offers no insight into the structure of the solutions but is capable of correlating the density within experimental error with a minimum of experimental information. It can apparently be used to reliably extrapolate data to different temperatures.
physical properties of fluids. The authors would like to thank one of the reviewers for his comments on using surface tension data to explore the formation of micelles.
Literature Cited Apelblat, A.; Manzurola, E. Excess Molar Volumes of Formic Acid Water, Acetic Acid Water and Propionic Acid Water Systems a t 288.15, 298.15 and 308.15K. Fluid Phase Equilib. 1987,32, 163-193. Christensen, J. J.; Hanks, R. W.; Izatt, R. M. Handbook of Heat of Mizing; John Wiley and Sons: New York, 1982; pp 13941397. Hansen, R. S.; Miller, F. A.; Christian, S. D. Activity Coefficients of Components in the Systems Water-Acetic Acid, WaterPropionic Acid and Water-n-Butyric Acid. J . Chem. Phys. 1955, 59,391-397. Kehiaian, H. Thermodynamics of Chemically Reacting Mixtures. XIII. Thermodynamic Excess Functions of Ideal Associated Mixtures of the Mecke-Kempter Type. Bull. Acad. Polon. Sci., Ser. Sci. Chim. 1964,12, 567-573. Kehiaian, H.; Kehiaian, K. K. Thermodynamics of Chemically Reacting Mixtures. VI. Excess Enthalpy and Excess Entropy of Ideal Associated Mixtures of the Type A+B+A2. Bull. Acad. Polon. Sci., Ser. Sei. Chim. 1 9 a , 6, 591-596. Lee, R. J.; DiGuilio, R. M.; Jeter, S. M.; Teja, A. S. Properties of Lithium Bromide-Water Solutions at High Temperatures and Concentrations- 11: Density and Viscosity. ASHRAE Trans. 1990,96, 723-728. Melzer, W. M.; Baldauf, W.; Knapp, H. Measurement of Diffusivity, Viscosity and Refractivity of Eight Binary Liquid Mixtures. Chem. Eng. Process. 1989,26, 71-79. Reid, R. C.; Prausnitz, J. M.; Sherwood, T. K. The Properties of Gases and Liquids, 4th ed., McGraw-Hill: New York, 1987; p 480. Schrier, E. E.; Pottle, M.; Scheraga, H. A. The Influence of Hydrogen and Hydrophobic Bonds on the Stability of the Carboxylic Acid Dimers in Aqueous Solution. J. Am. Chem. Soc. 1964,86, 3444-3449. Tanford, C. The Hydrophobic Effect: Formation of Micelles and Biological Membranes, 2nd ed., John Wiley & Sons: New York, 1980; p 18. Teja, A. S. A Corresponding States Equation for Saturated Liquid Densities I. Applications to Liquified Natural Gas. AIChE J . 1980,26,337-341. Teja, A. S.; Rice, P. A Generalized Corresponding States Method for the Correlation and Prediction of the Viscosities of Binary Liquid Mixtures. Znd. Eng. Chem. Fundam. 1981,20, 77-81. Weast, R. C.; Astle, M. J.; Beyer, W. H. CRC Handbook of Chemistry and Physics, 66th ed.; CRC Press, Inc.: Boca Raton, FL, 1986; p F-31.
+
+
Received for review March 1, 1994 Revised manuscript received September 12, 1994 Accepted December 19, 1994@
Acknowledgment Financial support for this work was provided by Fluid Properties Research Inc., a consortium of companies engaged in the measurement and prediction of thermo-
+
IE940 114H Abstract published in Advance ACS Abstracts, February 15, 1995. @
