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Vapour—liquid equilibria of the acetylene—ammonia system
ChemicalEngineedngScience,1975,Vol. 30, pp. 301-315. PergamonPress. Printed in Great Britain
VAPOUR-LIQUID EQUILIBRIA OF THE ACETYLENE-AMMONIA SYSTEM ALESSANDRO VETERE, ALESSANDRO COJUTTI and MARIA ANTONIETTA
SCARAMUCCI
Laboratori Ricerche Chimica Industriale, SNAM PROGEmI, San Donato Milanese, Italy
(Received 5 September 1973;accepted 25 July 1974)
Abstract-Vapour-liquid equilibrium data of the acetylene-ammonia system for seven isotherms in the range - 60 + 25°Cand 1+ 32 atm are reported. Experimental values are interpreted according to the thermodynamics of the associated systems. It is shown that thermodynamic consistency is observed by assuming a bimolecular complex formation between acetylene and ammonia. Equilibrium constants for this complex in the liquid phase have been derived and related to the corresponding gas phase values known from the literature. Two models based on the association and the equations by Ma&es, Wilson and Van Laar have been employed for correlating and extrapolating the experimental values. INTRODUCTION In recent years an increasing attention has been devoted
to the thermodynamics of associated systems, due to their considerable theoretical and practical interest. In this field it is worth remembering the work by Prigogine and Defay [l] and by many other researchers[2-61 on ideal associated solutions theory, according to which the only interactions among molecules in solutions are of a chemical type. On the other side, non-ideal associated solutions, for which the existence of physical interactions is admitted, have not yet received a fully satisfactory treatment. However extensive studies have appeared on topics of special interest, such as, for instance, by Renon-Prausnitz [7], Wiehe-Bagley [8] and KtreschmerWiebe[9] on solutions of alcohols in inert solvents, and by Harris-Prausnitz[lO] on solutions of CZHZin many polar and non-polar solvents. Other researchers [l l-141 have furthermore shown the possibility of correlating and evaluating the thermodynamic consistency of the experimental vapour-liquid equilibrium data of such systems. Work in this field has generally been restricted to mixtures of liquid compounds at normal conditions of pressure and temperature which may be easily investigated using standard apparatus. Little attention, on the contrary, has been paid to mixtures of highly volatile compounds because of the relevant experimental difficulties involved. To the class of volatile mixtures belongs the C2HrNH3 system which presents a remarkable interest, since ammonia is one of the solvents industrially used for the reaction of ethynilation of aldehydes and ketones to produce acetylenic alcohols, the latter being of interest
either as such or as intermediates, e.g. in the SNAM PROGE’ITI process for the synthesis of isoprene[l5]. The only previous work on the C!zHrN& system is due to S. M. Khodeeva[lblB], who has investigated the behaviour of the mixture both in the gaseous and liquid state. However, while data for the gaseous phase appear reliable according to the thermodynamic analysis of Chueh et al.[19], application of the Redlich-Kister test shows inconsistent results for the vapour-liquid equilibria. It is the purpose of this work to give an accurate analysis of the CzHrN& system on the basis of new and more reliable experimental data.
EXPERIMENTAL
Products and purification methods Acetylene (99.5%) is fed to the equilibrium cell by connecting the gas cylinder to a purification line comprising traps dipped in Dewar vessels cooled at -70°C and to a series of towers for drying and eliminating CO*, containing CaCh, Al203, soda, asbestos and glasswool respectively. Pure NH3 is obtained by distillating the commercial product in two stages on potassium metal under N2 atmosphere in order to lower the concentration of water which is possibly present at level analytically undetectable (100 ppm). All the lines of the purification apparatus are previously flooded in a dry nitrogen stream. Apparatus and technique The equilibrium cell consists of a 1 litre inox steel autoclave provided with a vertical stroke magnetic stirrer 301
302
A. VETERE,A. COJIJITIand M. A. SCARAMUCCI
phase scrubber
Fig. 1.Apparatus for determining the vapowliquid equilibrium.
on which are located Teflon cross-disks, and with a sheath for the thermiresistor connected to the temperature recorder. Devices for sampling the liquid and gaseous phases and for connection to the manometer are inserted in the upper flange (Fig. 1). The equilibrium cell is set in a thermostatic bath cooled by a LAUDA K 70 Kriomat. The bath itself is provided with a 500 W heating resistor and a termoresistor connected with the temperature regulator allowing a *O.l”C temperature control. The measurement of the equilibrium pressure has been carried out with a series of 0.25% class Budenberg manometers. A mercury manometer has been used for pressures below atmospheric. Ammonia is allowed to enter the autoclave after flooding it with both air and nitrogen and after cooling the autoclave itself to -50°C. Acetylene is then brought in under stirring to improve solubilisation. High mole fractions of acetylene in the liquid phase are obtained by imposing a pressure higher than atmospheric in the autoclave by means of a mercury head. Temperature is reduced gradually at -80°C and the &HZ flux continued to saturation. The autoclave is then introduced into the termostatic bath and venting is carried out at least three times for eliminating inert gases from acetylene. The autoclave is then connected to two series of scrubbers and both the liquid and the gaseous phase are drawn till a red colour appears in the first scrubber of the two series of sampling traps which contain O.lN HzS04 and phenolphthalein as indicator. For the liquid phase it is necessary to avoid drawing together both the liquid and the overhead vapour.
Drainage occurs without interruption by colleiting at the beginning of the drawing the C2HrNH3 mixtures in scrubber R through a three-way cock P. In this way it is possible to by-pass the five scrubbers where by commutating P it is then possible to draw the liquid phase without vapour after the phenolphthalein in R has changed colour. For the isotherm at 25°C it has been found necessary to insulate and warm up the vapour lines in order to avoid therein a partial condensation of the vapour phase; for the isotherms at -50°C and -60°C it was necessary to cool the outside line in order to prevent the partial vaporization caused in this zone by the temperature increase. For the equilibrium points at the low mblar fractions of acetylene, whose pressures are lower than one atmosphere, sampling of the phases has been carried out under vacuum. Apart from the precautions required for avoiding suctions of liquid in the scrubbers, drawing of the liquid and vapour is performed according to the same procedure followed for the pressure tests. Analytical method Ammonia has been titrated with N/IO &SO4 and the acid solution resulting from reacting acetylene with an AgNO3 alcoholic solution has been titrated with N/l0 NaOH.
RESULTS The experimental results are reported in Table 1
together with pressure values and vapour-phase compositions calculated by the Harris-Prausnitz, Van Laar, Margules and Wilson equations according to the method of Prausnitz et al.[22]. The pressure-composition relationships for the different isotherms are represented in Figs. 2-5, where the experimental data are interpolated according to the Van Laar’s equation for -60°C to 0°C isotherms and to the Wilson equation for 15°C to 25°C isotherms. The higher differences between experimental and calculated values are observed for the isotherms at -50°C and -60°C. The errors found in some experiments should possibly be ascribed to the presence of inert gases, while at low molar fractions of ammonia in the vapour phase the analytical errors become significant.
THERMODYNAMIC ANALYSIS
Ammonia is a protonophilic compound of average basicity, while acetylene is a proton-donor compound having a weak acid character. The possibility of acid-base interactions between acetylene and ammonia leading to the formation of a complex by hydrogen bonding according to the equilib-
303
Vapour-liquid equilibriaof the acetylene-ammoniasystem Table 1. Experimentaland calculatedequilibriumdata Experimentaldata
T(“C)
25
15
0
-25
-35
x1
Y1
0,028 0,030 0.066 0,109 0.350 0,515 0.675
0.098 0,094 0.173 0.264 0.644 0.777 0.870
0.036 0.039 0.123 0.131 0.135 0.137 0.402 0.559 0.640 0648
0.038 0.038 0,041 0,142 0.161 0.161 0,171 0.382 0.386 0.691
0.089 0.164 0.175 0.410 0.424 0.581 0.597
0.159 0.165 0.172 0.250 0.264 0.268 0.280 0.430 0.435 0.637 0.642
0.103 0.099 0.306 0.322 0.331 0.308 0662 0.812 0.869 0,869
0*106 0,118 0.125 0,358 0.398 0.405 0,404 0.700 0.710 0.886
0.299 0443 0.511 0.792 0.794 0904 0902
0.452 0.460 0.535 0.712 0,724 0.714 0.744 0.826 0.832 0.924 0.928
P,(Ata) 10.30 10.30 11.16 12.21 19.59 26.12 32.07
7.65 7.61 9.31 9.51 9.53 9.41 16.29 21.13 23.75 24.04
4.51 4.63 460 5.98 6.18 6.18 6.18 9.92 10.03 17.03
1.94 2.31 2.59 4.14 4.75 6.81 6.81
146 1.46 1.61 2.22 2.21 2.19 2.28 3.40 3.42 5.09 5.09
(
y’-y” Y
HarrisPrausnitz VanLaar
.loo
(!I$+O
) Wilson
HarrisPrausnitz VanLaar
Margules
Wilson
- 24.49 - 14.89 -3.41 -3.03 -7.14 -0.51 - 1.12
- 26.53 - 18.09 -694 -5.30 -4.91 - 2.70 t 0.46
-32.65 - 24.46 -9.83 -3.03 -3.11 - 1.03 -0.92
- 15.31 -6.38 -4.04 -3.19 -5.59 -5.28 - 1.95
+2.18 t 2.12 t 2.33 t2.13 -6.52 t 3.79 -2.15
+1.84 t 2.23 +0.99 to.01 - 1.79 t 1.30 t 1.43
to.97 t 1.36 0.00 -0.16 +7.% t 4.67 t 4,ll
+3.30 t3.19
7.89
9.28
10.72
6.05
3.11
1.37
2.84
3.21
- 10.68 t3.03 -8.50 -11.18 -9.31 -097 t 1.21 -0.86 -1.50 -0.81
-0.97 t1.11 -1.96 -1.86 -2.11 t6.17 t 2.12 -0.25 - 1.27 -0.69
-6.80 t 5.05 -3.21 -2.80 -3.02 t 5.52 t 4.23 - 0.37 -1.84 - 1.38
-1.17 t4.04 -3.21 -2.80 -3.02 t5.52 t4.53 -0.37 - 1.84 - 1.38
-0.39 - 1.18 -2.10 -3.34 - 2.52 -0.64 -5.96 -4.21 -2.15 - 1.91
t 2.35 t 3.35 to.75 -0.31 to.84 t 2.55 -3.81 - 1.99 t 1.56 t 1.91
t144 t 2.63 toGI -146 -0.21 t 1.38 - 1.90 -0.62 t 0.88 t 0.96
t 1.31 t 2.31 -0.54 - 1.67 -0.42 - 1.28 - 1.47 -0.28 t 1.18 t 1.21
4.81
1.91
3.34
3.34
244
1.76
1.06
1.14
t 4.59 -3.39 -0.80 -0.28 - 1.51 -2.54
t 13.21 t 1.69 t 2.40 t3.35 t2.01 t 0.25
+6&l -4.24 -240 t2.51 t 2.01 t 0.25
t 10.38 -0.85 to.00 t3.35 t 2.26 t 0.49
t 0.88 -0.43 t 0.87 -1.84 -0.81 -0.81 t 1.62 -0.10 -040 t 1.76
t 1.53 0.00 t 1.52 -1.17 -0.16 -0.16 t 3.12 -0.91 - 1.20 t 0.47
Ma&es
t4.03 t 4.42 t 2.25 to.19 -4.93
t2.23
t5.20
t5.20
t5.44
0.00 -0.85 t2.48
to.71 -0.14 t2.11
t 2.43 t 1.55 t 2.93
+ 1.71
0.44 -0.86 t 0.65 -2.17 - 1.46 - 1.46 - 1.13 -0.50
to.85
-0%
t 2.82
t 2.23
t 1.75 to-43 t 1.96 -0.84 to.16 to.16 t 2.21 - 2.12 -3.09 - 2.06
2.98
1.18
1.53
0.97
1.12
0.00
to.52 t2.11 -3.86 -190 t 1.26 -1.47 t 1.62
1.83
3.26
3.13
-0.92 t 6.55 -3.86 to.51 t 1.51 -0.44 t 0.67
-4.01 t1.22 -2.35 t 2.78 t 3.78 t 0.77 t 1.77
-3.01 t1.22 - 2.54 t 2.40 t 3.53 t 0.66 t 1.66
2.07
3.78
3.58
t 9.29 t9.35 -3.74 -899 -760 -5.60 -7.39 t 1.33 t 0.72 t 0.87
t 11.95 t 11.09 - 1.68 -6.46 -5.25 -3.08 -5.38 t3.15 t2.76 t 2.27
t 11.95 t 11.09 - 1.68 -6.46 -5.25 -3.08 -5.38 t3.15 t 2.16 t 2.21
-4.35
i-l.45 t3.80
tl.69
-2.15 t 2.78 t3.90
t 1.77
- 1.93 -2.53 t 0.42 - 1.62 t 1.62
-3.86 - 1.90 t 1.26 - 1.47 t 1.62
t 0.52 t2.11 -3.86 -2.95 to.21 -2.35 t 0.73
3.82
1.92
2,52
2.59
to.77
t 11.95 t11.09 -1.68 - 6.46 -5.11 -3.08 -5.38 t3.15 t 2.88 t 2.27
t 1.55
t7.53 t8.90 t 1.24 -7.21 -3.62 -1.37 -1.32 - 1.76 - 1.46 t 3.93
t 5.48 t 5.73 0.00 t8.11 -3.62 -1.37 O*OO - 1.76 -0.88 t 3.54
t 5.48 t 5.73 0.00 t8.11 -3.62 - 1.37 0.00 - 1.76 - 1.17
2.52 t 5.48 t 5.73 OGII t8.11 -3.62 - 1.37 o*oo - 1.76 - 0.88
to.43
t2.05
t2.05
t2.05
t5.50
t4.52
t3.54 t4.52
t3.54 t4.52
3.46
3.20
3.20
3.20
1.96
2.00
1.96
2.52
0.104 0,486
0.67
-7.61
- 1.65
-2.26
-3.91
t 1.49
t4.48
t4.48
t299
0.106 0,485 0.246 0.756
0.67 1.22
- 5.77 -4.07
-0.41 -2.25
- 1.03 -2.38
- 2.41 - 2.38
t2.99 t3.01
t5.97 -3.28
t5.97 - 3.28
t2.99 -4.10
304
A. VETEFS,A. COJUITIand M. A.
SCAFMUCCI
Table 1(cont.)
x1
Y,
Pr (Ata)
HarrisPrausnitz
0.263 0.312 0.372 0.471 0600
0.764 0.812 0.850 0.899 0.964
1.22 144 1.73 2.16 2.99
t 3.01 -2.22 - 1.41 t 1.56 - 1.70 3.42
T(“C) -50
-60
0.100 0.107 0.230 0.346 0.347 0.537 0.601 0.685
0.532 0.531 0.764 0.865 0.868 0.918 0*%7 0.984
0.41 0.41 0.66 0.99 0.99 1.74 1.98 2.34
(!Ep).lM)
(q+nl
Experimental data
-9.70 -9.79 -6.15 -3.12 -3.11 -2.40 - 1.45 -I*10 4.60
Margules
Wilson
HarrisPrausnitz
VanLaar
Margules
Wilson
-0.79 -0.74 0.00 044 -1.76
-0.79 -0.74 -0.12 t 0.56 - 1.66
-0.79 -0.62 t 0.35 t 0.78 - 1.56
t4,10 t 2.78 t 4.05 t 1.02 0.95
t2.46 o+Il -2.31 0.00 -5.35
t1.64 -0.69 -2.31 o*OO -468
to.82 - 0.69 -2.31 046 -4.01
1.01
1.19
1.61
2.55
2.98
-9.02 -6.03 -2.88 - 1.27 -1.50 t 2.72 -0.83 -1.02
-9.40 -5.27 -2.75 -1.27 - 1.50 +2*61 -0.93 - 1.02
t 2.30
04to
t244 t4.24 t 8.08 t8,08 t 9.50 t 13.13 t 14.40
t 2.38 t 4.24 t 1.01 t1.01 -5.75 -5.05 -5.13
to4M
040 t 2.38
t3.48 t 1.01 t 1.01 -5.75 -4.55 -4.70
t4.24 t 1.01 t 1.01 0.00 -5.05 -5.13
3.16
3.09
7.77
3.09
2.56
3.09
VanLaar
-9.21 -5.27 -2.75 -1.27 -1.50 t2.61 -0.93 -1.02 3.07
x,
2.88 040
2.30
Fig. 2.25”C+ 0°C isotherms. Liquid pressure-composition curves, interpolation lines calculated by applying thermodynamic equations; 0 experimental points; A vapour pressure of pure compounds.
Fig. 3.25”C+ 0°C isotherm. Vapour pressure-composition curves, interpolation lines calculated by applying thermodynamic equations; 0 experimental points; A vapour pressures of pure compounds.
rium reaction
aldehydes and ketones in an ammonia solution. An independent criterion supporting the association hypothesis is given by Chueh[l9] who, applying Lambert’s theory of the associated gaseous mixtures, to the volumetric data for the acetylene-ammonia system
CzHZtNH 3t-‘CH2 Z. ..N&
(a)
has been recognized by Tedeschi[20-211 for the interpretation of the catalytic mechanism of the ethynilation of
Vapour-liquidequilibriaof the acetylene-ammoniasystem
305
developed on the basis of the association among the components. Basic formulae For the vapour-liquid equilibrium isothermal data the equation of Gibbs-D&em may be written as follows: dP Cxidlny,xi-iJ,L-=O. RT I
(1)
If the activity coefficients are calculated at a constant reference pressure (Pr) for all the experimental points Eq. (1) can be written[22] as: 7 xl dln 7jpaxi = 0.
(2)
In order to investigate the thermodynamic consistency of Fig. 4. -25°C+ -60°C isotherms. Liquid pressure-composition the vapour-liquid equilibrium data for the associated curves, interpolation lines calculated by applying ther- systems, it is necessary to distinguish between apparent modynamicequations;0 experimentalpoints; A vapour pressures or stoichiometrical, and actual concentrations. The of purecompounds. former are the ones experimentally detectable and represent in our case the concentrations of CZ& and NH3 without a distinction being made between dissociated and associated molecules. Accordingly for a binary system in which compounds A and B combine to give an AB type complex, Eq. (2) must be rewritten introducing the actual molar fractions X*, XB and Xns instead of the apparent ones XI and X2: xA dhl '~A'~')X.J +XB dln
ys(")Xe+XAB dh $~XAB
=
0.
(3)
According to Trevissoi and Francesconi 1231the following equation can be derived XI dh y~("h txz
dln ,%(“xB = 0.
(4)
Writing -yA”r’ xA and 7B’p”xBexplicitly by means of the equation [22]
Fig. 5. -25°C +-WC isotherms. Vapour pressure-composition curves, interpolation lines calculated by applying thermodyanamic equations; 0 experimental points; A vapour pressures of pure compounds.
reported by Khodeeva [ 181,has been able to calculate the equilibrium constants Kalv for the reaction (a) in the temperature range 50-150°C. The enthalpy and entropy values of the association reaction calculated from the variation of Ka,” with the temperature justify the formation of a very weak hydrogen bond. Since there is both theoretical and experimental evidence supporting the hypothesis of the complex formation, the whole thermodynamic treatment has been
it results that
Tndln
PTY~Q~ (6) fp'.'exp~p%_!!$=o
which may be further simplilied, considering that fp’> is constant for each isotherm and that the changes of the term exp _f2(VidP/RZ’) are negligible. It results XIdln (PTYAQA I+ xz din (PTYBQB I= 0.
(7)
A. VETERE,A. COJUITIand M. A. SCARAMUCCI
306
and This equation, proposed by Francesconi Trevissoi[23] in a somewhat different form, does not include the actual compositions of the liquid phase. Investigation of the thermodynamic consistency of the CtHrNHa system is correspondingly, and remarkably, simplified, since the association constants allowing to derive the actual concentrations from the apparent ones are only known for the vapour phase[l9]. The theory of Lambert[24-261 is the basis of the method for calculating the association constants in the gaseous phase from the analysis of the values of the second virial coefficient. According to this theory, the deviations from the ideal gaseous phase for both pure compounds and binary mixtures may be subdivided in physical interactions of the central type (electrostatic and dispersion forces) and specific interactions leading to the formation of weak chemical bonds. The second virial coefficient may be therefore expressed by a sum of two terms B”=B’+B’
(8)
where BP represents the physical interactions, and B’ the chemical bond forces. The contribution of the physical interactions may be calculated applying the equation of Pitzer and Curl[27]. Provided that the association constant I&, is small, the following equations are valid: K P
_,.w_ RT
2
._
wrm RT
for the association reaction A + BeAB K
P
_WiL. -___ RT
(9)
Since the experimental pressure reach comparatively high values it has been preferred to apply the equation of Redlich-Kwong instead of the virial equation truncated after the second term. The formulae and the mixing rules used for calculating ‘pi are equal to those proposed by Chueh and Prausnitz 1281. The values for the constants of the Redlich-Kwong equation are reported in Table 2 together with some chemical and physical data of acetylene and ammonia occurring in the calculation of the activity coefficients. It should be noticed that it has been preferred to determine the constants a and b appearing in the equation of Redlich-Kwong by interpolating the literature volumetric data of the pure compounds, since the values of the adimensional constants & = O-4278 and & = 0.0867 calculated at the critical point are valid in the whole pressure and temperature field only for compounds strictly following the law of corresponding states. Thermodynamic consistency The integration of Eq. (7) within the experimental limits
of concentration represents the most useful method[23]. In order to calculate YA and YB from Kz values the following procedure was adopted. Assuming the A t B F? AB association and taking as the fugacity reference state for all the compounds the value of 1 atm, it can be written: AG” = -RT In Kz (YM . p.4B - PT.1
= -RT In
and
(YA * QA
= -RT In
W-B$ RT
for the association reaction 2A * At. Accordingly the K, value can be derived provided&@ B” and BP have been calculated from experimental volumetric data and from the equation of Pitzer and Curl, respectively. Furthermore the B” values have been obtained by extrapolating experimental data at P = 0. It follows that Kp coincides with the thermodynamic constant of the equilibrium reaction K,“:
YAS
*
YA * YB
'&)'(yB
'QB
'PT)
Kw
1 (12)
* PT
from which YAB
(13)
YA ’ YB *PT.
The value of Kq, has been obtained assuming that QAB for the complex be equal to the mean value of QA and QB. The KE values have been obtained extrapolating at the temperature of 25°C+-600C the values calculated by Chueh and Coll[19] in the range SO”C-150°C(Table 3). The stoichiometry of the reaction allows to establish the (11) following expressions:
Calculation of fugacity coejicients The deviations from ideality in the vapour phase have
been evaluated on the basis of the volumetric literature[lS] data, the reliability of which has been confirmed by the thermodynamic analysis of Chueh[t9].
YA + y.0 _.
y’= 1 +yAB ’
YB+-YAB yz=
1 +y*B
(14)
which correlate the apparent concentrations to the actual ones. By introducting (14) into (13) and considering that
48.74 38.54 26.37 12.76 9.15 5.25 3.47
9.91 6.95 4.23 1.50 0.93 0.39 0.23
P&J361 29.28 25.43 19.24 1040 7.82 4.78 3.25
f&t 8.78 6.50 3.93 1.45 090 040 0.23
f&t
Fugacity (Ata)
69.2 62.2 56.0 49.7 48.1 46.3 44.8
28.28 27.62 26.55 25.56 25.09 24.27 23.86
V&&351 %,,[361
Molar liquid volumes (cm3/mol)
- 157 -170 -192 -237 -258 -292 -317
&I(C,HJ$ -261 -299 - 345 -466 -540 -670 -730
&z(NH# -282 -300 -332 -390 -415 -454 -484
J&z*
Second virial coefficients (cm3/mol)
*Extrapolated values from 150”+SOY!data[l9]. Walculated from Lyckman-Eckert[22] equation. SCalculated from volumetric data reported by F. Din[36] (NH,), and S. Miller[35] (GHJ. Walculated from volumetric data of S. M. Khodeeva[l8].
298.2 288.2 273.2 248.2 238.2 223.2 213.2
T CK) P&J351
Vapour pressures (AW
094612 x 10’
a,*
50.621
b,S
0.14498x 10’
ait
Constants of Redlich-Kwong equation
Table 2. Thermodynamic properties of pure compounds and mixtures for the ammonia-acetylene system
79.251
b&
0.134453X lr
Cd
A. VETERE, A. COJLIRI and M. A. SCARMJCC~
308
Table 3. Equilibriumconstants for CZH2 t NH, e NH,. . . C2HZ associationsin liquidand in vapour phases with related enthalpy and entronv values T(“C) 25 15 0 -25 -35 -50 -60
K.V,
K:,
AHaV
AHoL
AS””
AS”=
-2200
-2120
-15.2
-8.4
0.0190 0.49 0.0216 0.79 0.0270 0.78 0.0388 099 1.11 oMi6 OG20 1.67 0.0780 2.21
YA+ Ys + YAB= 1 we obtain the final formulae:
consistency of the single experimental points, like the one given by differential methods. In order to carry out the integration, instead of applying the trapezoidal rule[29] it has been preferred to use a stricter method consisting of interpolating xi = f( Yi(piPt)according to a cubic function. The results of the integration, expressed as per cent deviations of the left side of Eq. (7) from zero, with respect to its absolute value, are reported in Fig. 6 together with the values obtained assuming there is no association. The equation of Gibbs-Duhem annears to be better verified if complex formation is admitted, exception made for the points of the isotherm at 25°C. Altogether the deviation from the criterion of ther-
and y,=-(1-2Y2K~P~tK~P~)t~[(f-2Y~K~P~tK~P~)2t4Y~K~P~]
(16)
~Y~KIPT
which are used for calculating the actual mole fractions from the apparent values and the association constant. The values of Y. and Yb calculated in this way have been introduced into (7). Integration of the latter has been carried out at mole fraction intervals of acetylene in the liquid phase of 0.05 so as to get a criterion of local T=25”C
modynamic consistency reduces from a lo-15% value, ir1 case of non association, to 5-7% supposing there is complex formation. It has to be noticed that a remarkable improvement has been obtained in the evaluation of the data although the conversion of acetylene and ammonia in the complex is comparatively small. The molar fraction
T=l5'C 20 ,5
T=O'C
I
l
****.* . 10 . 5 ~~OOoo 0 _____",I__
0.2
0.4
0.6
0.2
0.4 0.6
02
0.4
X
0.6
XI
T--35%
T--25'%
T-
25
-50°C
20
20
15
I5
10
l*
5 0
-‘5tl 0.2
0.4 X
0.6
l****
__~___,__
.
0~~0
o
-5 -10
0
i
-15t-J-uL -‘“iL-u-u0.2
0.4
Xl
0.6
T= - 60°C
25
0.2
0.4
x,
0.6
0.2
0.4
0.6
Xl
Fig. 6. Per cent deviation (A%) from the criterion of thermodynamic consistency according to the method by Francesconi-Trevissoi, 0 hypothesis of association C,H, t NH, P CzH2......NH.; 0 hypothesis of non association.
309
Vapour-liquidequilibriaof the acetylene-ammoniasystem YABchanges in fact from a max value of about 7 per cent at 25°C to a min value of about 0.5 per cent at -60°C and for each isotherm reaches the highest value approximately for xl = 0.5 (data not reported). For a more accurate investigation of the interactions with chemical bond formation which may occur in the gaseous phase, the possibility of autoassociation of pure compounds has been consideredDO]. While for acetylene, a scarcely polar compound, the virial coefficient B,, values (Table 2) exclude the possibility of autoassociation, in the case of ammonia the difference between the values of BS and BP leads to recognize the formation of a bimolecular complex. The constants of ammonia autoassociation have been therefore calculated according to the same procedure previously reported and the values have been graphically extrapolated in the whole experimental temperature field (Fig. 7). Assuming the simultaneous presence of the two association equilibria: K.V, K.V,
2AeA~a A+BsAB
it results that the actual concentrations YAand Yg may be calculated solving the following equation of the third
1.
l
0.01 0.008
-
\.
0.006 -
0.004-
0,002l
I
I
-50
I 5.0
I
-25
0
I
/
I1
I
I
A
25
OC I
/
50
I
4.0
I03/T.
I
1
I 100
i 150
I,
30
OK
7.Relationshipbetweenthe valuesof theassociationconstants in the gaseous phase and the temperaturefor the reactions: 0 MI,+C*Hz~NH,.......C2H2;02NHJ#:NH~.....,.NHs.
Fii.
degree in YA: Y,)[K,Kd’,2(2Y, + Ydl
+ Y.*[I%K@+ YIYz)+ PTKz(
YI +
Y?)]
+YA[&&(Yz-Y:)+Y~+I]+Y,(Yz-2)=0 which gives a single valid solution within 0 and 1. Ys can then be obtained: y J-Y,-KIYA’PT B ltK,Y,PT
’
Integration of ‘Eq. (7) on the basis of the values of the actual concentrations YA and Ys gives no appreciable variation with respect to the calculations performed assuming only the association among different molecules. The two association models seem therefore equivalent, mainly because of the low value of the constant KL. Association constants in the liquid phase for the reaction A+B*AB In order to obtain an indirect confirmation of the validity of the experimental data, the calculation of the association constants has been extended to the liquid phase. Use has been made of the same assumptions of Lambert’s theory for the gaseous phase. In fact, for the liquid phase too, it is possible to make a distinction between weak, or physical, interactions, due to Van der Waal’s dipoles, and specific, or chemical, interactions leading to the formation of more or less stable complexes. Van Laar’s theory is valid for solutions where Van der Waal’s forces prevail, the deviations from the ideal case being due only to differences among intermolecular forces of the species in solution. On the contrary, when there are stable chemical bonds among the molecules (as between Hz0 and NHs), it is possible to neglect the physical forces and assume that the mixture of all chemical species, associated or not, is ideal (Dolezaleck)[31]. In this case, for satisfying Raoult’s law, it is sufficient to replace the apparent concentrations with the actual ones. A synthesis of these theories is the method of Harris-Prausnitz[lO], based on the following hypotheses: (1) Both physical and chemical interactions contribute to the non ideality of the associated solutions. (2) The physical forces can be represented by an equation by Van Laar type (Eqs. (6)-(8) from Table 5 in Appendix). (3) The effect of the chemical interactions is calculated introducing into formulae (2)-(5) of Table 5 the actual concentrations as functions of the apparent ones through the association constant K,,,. The whole calculation arrangement reported in Appendix, is a function of only two unknown quantities, i.e. the constants of association Kf; and of interaction uAB. The Kt, The Kf;, values
A. VETERE,A. Corur’rrand M. A. SCARAMIJCCI
310
obtained for the different isotherm are reported in Table 3 and represented in Fig. 8. It is worth while noticing that the actual activity coefficients values (not reported) are very close to 1 in practically the whole temperature range, excepting the isotherms at -50°C and -60°C for which a higher deviation from the ideal case can be visualized.
2120 cal/mol, in satisfactory agreement with the 2210 cal/mol value calculated by Chueh et a1.[19] for the reaction in the gaseous phase. This value is an index of a very weak hydrogen bond [ 19,30,32]. The similarity of these values is reasonable, since the energy for hydrogen bond formation is a function merely of the electronic configuration of the atoms among which the hydrogen bond takes place and not of the aggregation state[30,32]. It has been further established that the association constants in the liquid and gaseous phases are reciprocally consistent. Since under equilibrium conditions the activity of each component is the same in both phases, the equation Kf;, = KE must be satisfied provided the same standard states are assumed for liquid and vapour phase. As this is not the case, the difference between K,L, and Kz values has to be ascribed only to the different reference fugacity values chosen for the two phases [30,33]. The standard state for the gaseous phase in the calculation of KE is in fact the unitary fugacity of the pure compounds, while for the liquid phase the standard state is the fugacity of the vapour in equilibrium with the pure liquid at the experimental temperature. Taking into account such differences it is possible to transform the value of KE into one of Kf; through a thermodynamic cycle based on Vant’HotTs box, or more simply, by equating j” to j”. Since Kf;=Kx*Ky
0.3 4.6
-60’
-500 I
I 4.6
-35’ I 44
I I 42
-25’ I
I 4.0
I 38
00 I
I 3.6
Ky * Kip, = Kf”.PT
and
150 259 1 I I 3.4
(20)
Fig. 8. Relationship between the values of the associationconstants
in the liquid phase and the temperature for the reaction: CzHz+NHJ*&Hz ....... NH,. Enthalpies and entropies for the association reaction A t B zz AB in the liquid and gaseous phase The values of the association constants at different temperatures previously calculated, allow the obtainment of enthalpies and entropies, both in the liquid and gaseous phase, on the basis of the following relation:
and recalling that according to the definition of standard state for the gaseous phase Kro = 1, it results that
(21) and therefore logK;,-logK;=log$@
Al3
Furthermore, from the equations below: -bG = RT In K., = -AH” t TAS”.
(19)
Since the enthalpy and entropy data relating to the formation of a hydrogen bond are generally known, comparison of the latter with the AH” and AS” values obtained from vapour-liquid equilibrium data can verify the validity of our experimentation. From the values of Kt, reported in Table 3 it is possible to deduce that AH” for the association reaction in the liquid phase is equal to
AHoV AS”’ logK.Y,=-R?;-tR
(23)
(24) and assuming AHoL = AH’“, it is possible to derive the following expression giving the required relationship
Vapour-liquidequilibriaofthe acetylene-amoniasystem between ASoL and AS”“: ASoL = ASo’ - R log fi. A mean f& value has been calculated for each isotherms (see after) and introduced into (25). The mean value of ASoL calculated in this way is equal to -9.9 cal/mol “K and is close to the experimental value of - 8.4 cal/mol “K[19]. The max deviation with respect to the mean value is about 20 per cent and occurs for the -60°C isotherm. Data reduction The most rigorous method for correlating the experimental data is that based on the hypothesis of the bimolecular association between C2H2 and N&, which has in fact justified the thermodynamic consistency of the experimentation. Applying the Harris-Prausnitz equation with the constants K,, and (Ypreviously calculated (Table 4) it is possible to determine the actual values of the compositions in the liquid phase xi and of the activity coefficients “/r.Furthermore, from the following equation.
311
A procedure approximated but less complicated than the previous one, is that of correlating the apparent concentrations of the liquid phase with the equation of Margules, Van Laar and Wilson according to the method proposed by Prausnitz et al. [22]. Application to the &HZ/NH, system of a procedure such as this which does not take into account association phenomena, can be justified due to the limited complex formation in the gaseous phase. Furthermore the association in the liquid phase can be neglected following the Prigogine theorem. Accordingly both treatments can be considered equivalent for most practical purposes. The values of the constants Al2 and AZ, calculated at different temperature are reported in Table 4. While the equations of Margules and Wilson have been used in their usual analytical form, in the case of the Van Laar equation we have applied the following ones[34], more flexible even if more complicated: -I~~z,~:,I
1,,,=A21211[1+222(~-1)]
>I (28)
1
(2%
where: for each experimental point a fugacity value fiB for the complex can be obtained. The actual molar composition yi in the gaseous phase can be determined using the relation: y, -
’
r@ $9,
and hence the apparent molar fractions Yi by applying the Eq. (14). The agreement between calculated and experimental data was good but not wholly satisfactory probably because of the inadequacy of Van Laar’s single parameter equation (see Eqs. (6-8) in Table 5) to take into account the physical interactions.
z1=,A$$2l,X2 and zz= l-Z,. In this way the parameters AI* and AZ, are allowed to assume a different sign without the denominator of (28) and (29) becoming zero, this being the case for the unmodified Van Laar equation if
Xl = IA211 X2
IA12l’
As it appears from Table 4 the constants AI2 and A2, are opposite in sign for the isotherms within the temperature
Table 4. Constants of the thermodynamic relations applied to the ammonia-acetylene svstem Van Laar T(“C)
A,2
25 15 0 -25 -35 -50 -60
-0.26 -0.26 -0.36 -0.69 -0.74 -0.47 -0.62
A2,
0.74 1.62 -0.60 -0.52 -0.67 -0.72 -0.73
Wilson A,>
An
1.10 0.68 1.36 O.% 1.24 1.52 1.57
1.00 1.75 1.09 1.75 1.53 1.13 1.17
Margules An
Am
-0.40 -0.35 -0.45 -0.65 -0.74 -0.48 -0.65
0.37 -0.25 -0.38 -0.56 -0.67 -0.67 -0.72
Harris-Prausnitz K.
0.49 0.80 0.78 1.00 1.11 1.67 2.22
@
2.25 2.30 1.50 1.06 0.78 1.59 2.40
=&
y*=%
(5)
(3)
v, t 0.75v*
II
y*+J 2
(13’)
(11)
x*, Y* . YE
XFJ=e KY_
8,’ v. +(8,t da)‘V, In *
x* =E
v/a) - [ 6*‘v~~~~~.~“vB]1~)*
[
2
(2)
(13)
al-ALI = [ (8, t
A-
•=+4[dkl~~~
x,,
A+BsAB
(12)
@‘)
(4)
Table 5. Harris-Prausnitz method[lO] for calculating the equilibrium constants of association
313
Vapour-liquidequilibriaof theacetylene-ammoniasystem range from 25°C to 15°C in the case of Van Laar’s equations, and of 25°C in the case of the equations of Margules. None of the equations which have been tested shows a well defined trend of the constants with temperature. The activity coefficients calculated with such constants show that the C*HrNHs system presents only slightly negative deviations from Rault’s law, except at concentrations close to inhnite dilution, where the activity coefficient of acetylene is about 0.6. The difference between experimental and calculated values (Table 1) is generally small, thus showing a slightly better correlating ability for Van Laar’s equation as compared with those by Margules and Wilson. The mean difference calculated on all seven’isotherms, varies from 3.5-4.2 per cent for the yi compositions, and from 2.3-2.5 per cent for the total pressures, according to the used equations. Such results appear to confirm that the Van Laar equation is better than the Margules one for components whose molar volume is remarkably different ( vc,.%/v,,, - 2). Furthermore the Wilson equation which can be preferred for highly non-ideal solutions, is slightly less reliable for solutions which do not diverge strongly from the ideal behaviour[W]. Nevertheless for the t25”C and + 15°C isotherms the Margules and Wilson equations gives better results than Van Laar equation. This fact has to be ascribed to the high value of the constant Azl of Van Laar’s equation at these temperatures (Table 4); accordingly, the calculated pressure is too high for the mixtures having a high acetylene content. The results reported in Table 1 show that the values of the pairs Pr - yi, calculated according to HarrisPrausnitz, differ from those obtained by applying the equation of Van Laar or Margules of about l-5 per cent.
CONCLUSIONS
Acetylene-ammonia system shows small negative deviations from Raoult’s law. Such deviations, as foreseen, increase as the temperature decreases and have to be ascribed to interactions both of chemical and physical type. Therefore the simple Dolezalek theory, according to which the different chemical species in solution, either associated or not, constitute an ideal mixture can not be applied. The thermodynamic analysis of the experimental data has shown their consistency on the ground of the hypothesis of the bimolecular association between C2Hz and NH,. This hypothesis, generally accepted, is confirmed also by the congruence of the values of the association constants obtained from equilibrium data with the values of the energy of the hydrogen bond involved in the complex formation. Since conversion to the complex in the gaseous phase is small, the activity coefficients may be correlated and
extrapolated both by the usual empirical equations (Van Lam, Margules, Wilson) which do not imply association and by theoretical methods which take into account the association in the liquid and gaseous phases (Harris-Prausnitz). Acknowledgments-The authors wish to thank Professor Zanderighifor many suggestionsand helpfuldiscussions,Dr. V. Bulla for writingthe computerprogramsand Dr. A. Tiidei for having revised the manuscript.
NOTATION
a, b, c constants of the Redlich-Kwong equation AIZ and AU constants of the Van Laar, Margules and Wilson equations second virial coefficient, cm’lmol fugacity of compound i at its vapour pressure, atm fl ,R, fugacity of compound i in the standard state, atm f7 fugacity of compound i at the reference pressure P, atm AG" free energy for the reaction A t B s AB, cal/mol AH9 enthalpy for the reaction A t B& AB, cal/mol AHi, evaporation enthalpy of compound i, Cal/m01 K.1 equilibrium constant for the reaction A t B8AB KO2 equilibrium constant for the reaction ,O
2A+Az
KP equilibrium constant defined as PZ/ (P2. Pi), atm-’ K, constant defined as K,JKq, Kf constant defined as K,,z/KQ~ KW constant defined as cpnB/QA . QB Kw constant defined as Q,+/Q** KP constant defined as f&/f: *f%,atm-’ KX constant defined as X, /XA*Xg KY constant defined as yAB/Ya'yB P9 vapour pressure of compound i, atm total pressure, atm PT R universal gas constant, atm cm3/g mol “K AS” entropy for the reaction A t Be AB, cal/mol “K T absolute temperature, “K Vi molar volume of compound i, cm’/mol Vi partial molar volume of compound i, cm’/mol molar fraction of compound i in liquid molar fraction of compound i in vapour gas compressibility coefficient
314
A.
VETRRE,
A. CoJu’t-rtand M. A.
Greek symbols lY constant of the one parameter Van Laar equation activity coefficient of compound i Hildebrandt solubility parameter of compound i, (cal/mol cm3)*” normalized extent of complex formation, E o
chemical contribution to second virial coefficient calculated values liquid phase physical contribution to second virial coefficient experimental values vapour phase
REFERENCES [l] PrigogineI. and Defay R., Chemical ThermodynamicsJohn Wiley, New York (1954). 121Kehiaian H. and Treszczanowics A., BUN.Sec. Chins.Fr., 1%9 5 1561. [3] Sarolea-Mathot L., Trans. Faraday Sot. 195349 8. [4] McGlashan M. L. and Rastogi R. P., Trans. Faraday Sot. 195854 4%. [5] Rastogi R. P. and Girdhar H. L., Proc. Nat/. Inst. Sci. 1%2 AX3470. [6] Apelblat A., J. phys. Chem. 197074 2214. [7] Renon H. and Prausnitz J. M., Chem. Engng Sci. 1%722 299. [S] WieheI. A. and BagleyE. B., Znd.EngngChem. Fund. 19676 209. [9] Ktreschmer C. B. and Wiebe R., J. phys. Chem. 195422 1697. [lo] Harris H. G. and Prausnitz J. M., Znd.Engng Chem. Fund. 1%9 8 180. [ll] Marek J. and Standard G., Co/l. Czech. Chem. Comm. 195419 1074.
SCARAMUCCI
1121Marek J. and Standard G. CON.Czech. Chem. Comm. 195520 1490.
1131Sebastiani E. and Lacquaniti L., Chem. Engng Sci. 1%7 22 1155. [I41 Carli A., Di Cave S. and Sebastiani E., C/tern.EngngSci. 1972 27 993. [I51 De Maldd M., Di Cib A. and Massi-Mauri M., Hydroc. Process. 196443 149. Ml Khodeeva S. M., Russian Journal ojphys. Chem. 196135306. WI Lebedeva E. S. and Khodeeva S. M., Russian Journal of phys. Chem. l%l 35 1285. WI Khodeeva, S. M., Russian Journal ojphys. Chem. 196438 1276. 1191Cheuh H. Y., Cannel J. P. 0. and Prausnitz J. M., Can. J. of Chem. 196644 429. PO1 Tedeschi R. J., J. org. Chem. 196530 3045. WI Tedeschi R. J. and Moore G. L. Znd.Engng Chem. Prod. Res. Deuelop. 19709”83. rw Prausnitz J. M., Computer Calculation for Mdticomponent Vapour-LiquidEquilibria, Prentice-Hall, New Jersey (1%7). ~231Francesconi R. and Trevissoi C., Chem. Engng Sci. 197126 1131. m Lambert J. D., Disc. Faraday Sot. 195315 226. v51 Lambert J. D., Clarke J. S., Duke J., Hicks C. L., Lawrence S. D., Morris D. M. and Shone M. G. T., Proc. Roy. Sot. London, Ser. A 1959249 414. WI Lambert J. D., Roberts G. A. H., Rowlinson J. S. and WilkinsonV. J., Proc. Roy. Sot. London, Ser. A 19491% 113. ~271Prausnitz J. M. and Carter W. B.. A.LCh.E. .R 19606 611. WI Chueh P. L. and Prausnitz J. M.,’Znd.Engng Chem. Fund. 1%7 6 492. WI Li J. C. and Lu B. C., Can. J. Chem. Engr. 195937 117. [301Zanderighi L., Private Communication. 1311Prausnitz J. M., Molecular Thermodynamicsof Fluid Phase Equiiibtia, Prentice-Hall, New Jersey (1%9). ~321Pimentel C. C. and McClellan A. L., The Hydrogen Bond, Freeman, San Francisco (l%O). [331 Allen G. and Caldin E. F., Quart. Rev. 19537 255. [341Null H. R., Phase Equiiibn’um in Process Design, Wiley Interscience, N.Y. (1970). [351Miller S. A., Acetylene, E. Benn, London (1965). [361Din F., Thermodynamic Functions of Gases Vol. II, Butterworths, London (1956).
Calculation of the association constants for the acetylene/ ammonia system according to Harris-Prausnitz method In this procedure, whose arrangement is shown in Table 5, there appear three types of activity coefficients defined as follows: Actual, indicated by making use of a letter as a subscript and obtained by applying formulae (6)-(8) of Table 5. Calculated apparent, indicated by making use of a number as a subscript and obtained from Prigogine’s theoremll], through Eqs. (13) and (13’)of Table 5. Experimental apparent, entering as input parameters and calculated by means of the equations:
YB(PBPT = w*f*
ow.,
.
y* and yB being actual molar fractions calculated by means of Eqs. (15) and (16). The solution of the system of Eqs. (D-(13) is based on the
Vapour-liquidequilibriaof theacetylene-ammoniasystem convergency between the values of the experimental and calculated apparent acitivity coefficients. Once arbitrary values are chased for If:, and a and K, is set equal to 1, it is possible to obtain both concentration and actual activity coefficient values following the reported procedure From Eqs. (13) and (13’) it is then’ possible to obtain the
CES Vol. 30. No. 2-D
315
apparent y, for all the experimental points of an isotherm, and from the summation f: (7, - 7,“)’ it is possible to determine, by means of the non linear multiple regression method, the variation to apply to the previous values of K,, and a. The calculation continues until two subsequent iterations give the same values of K., and CI.
VAPOUR-LIQUID EQUILIBRIA OF THE ACETYLENE-AMMONIA SYSTEM ALESSANDRO VETERE, ALESSANDRO COJUTTI and MARIA ANTONIETTA
SCARAMUCCI
Laboratori Ricerche Chimica Industriale, SNAM PROGEmI, San Donato Milanese, Italy
(Received 5 September 1973;accepted 25 July 1974)
Abstract-Vapour-liquid equilibrium data of the acetylene-ammonia system for seven isotherms in the range - 60 + 25°Cand 1+ 32 atm are reported. Experimental values are interpreted according to the thermodynamics of the associated systems. It is shown that thermodynamic consistency is observed by assuming a bimolecular complex formation between acetylene and ammonia. Equilibrium constants for this complex in the liquid phase have been derived and related to the corresponding gas phase values known from the literature. Two models based on the association and the equations by Ma&es, Wilson and Van Laar have been employed for correlating and extrapolating the experimental values. INTRODUCTION In recent years an increasing attention has been devoted
to the thermodynamics of associated systems, due to their considerable theoretical and practical interest. In this field it is worth remembering the work by Prigogine and Defay [l] and by many other researchers[2-61 on ideal associated solutions theory, according to which the only interactions among molecules in solutions are of a chemical type. On the other side, non-ideal associated solutions, for which the existence of physical interactions is admitted, have not yet received a fully satisfactory treatment. However extensive studies have appeared on topics of special interest, such as, for instance, by Renon-Prausnitz [7], Wiehe-Bagley [8] and KtreschmerWiebe[9] on solutions of alcohols in inert solvents, and by Harris-Prausnitz[lO] on solutions of CZHZin many polar and non-polar solvents. Other researchers [l l-141 have furthermore shown the possibility of correlating and evaluating the thermodynamic consistency of the experimental vapour-liquid equilibrium data of such systems. Work in this field has generally been restricted to mixtures of liquid compounds at normal conditions of pressure and temperature which may be easily investigated using standard apparatus. Little attention, on the contrary, has been paid to mixtures of highly volatile compounds because of the relevant experimental difficulties involved. To the class of volatile mixtures belongs the C2HrNH3 system which presents a remarkable interest, since ammonia is one of the solvents industrially used for the reaction of ethynilation of aldehydes and ketones to produce acetylenic alcohols, the latter being of interest
either as such or as intermediates, e.g. in the SNAM PROGE’ITI process for the synthesis of isoprene[l5]. The only previous work on the C!zHrN& system is due to S. M. Khodeeva[lblB], who has investigated the behaviour of the mixture both in the gaseous and liquid state. However, while data for the gaseous phase appear reliable according to the thermodynamic analysis of Chueh et al.[19], application of the Redlich-Kister test shows inconsistent results for the vapour-liquid equilibria. It is the purpose of this work to give an accurate analysis of the CzHrN& system on the basis of new and more reliable experimental data.
EXPERIMENTAL
Products and purification methods Acetylene (99.5%) is fed to the equilibrium cell by connecting the gas cylinder to a purification line comprising traps dipped in Dewar vessels cooled at -70°C and to a series of towers for drying and eliminating CO*, containing CaCh, Al203, soda, asbestos and glasswool respectively. Pure NH3 is obtained by distillating the commercial product in two stages on potassium metal under N2 atmosphere in order to lower the concentration of water which is possibly present at level analytically undetectable (100 ppm). All the lines of the purification apparatus are previously flooded in a dry nitrogen stream. Apparatus and technique The equilibrium cell consists of a 1 litre inox steel autoclave provided with a vertical stroke magnetic stirrer 301
302
A. VETERE,A. COJIJITIand M. A. SCARAMUCCI
phase scrubber
Fig. 1.Apparatus for determining the vapowliquid equilibrium.
on which are located Teflon cross-disks, and with a sheath for the thermiresistor connected to the temperature recorder. Devices for sampling the liquid and gaseous phases and for connection to the manometer are inserted in the upper flange (Fig. 1). The equilibrium cell is set in a thermostatic bath cooled by a LAUDA K 70 Kriomat. The bath itself is provided with a 500 W heating resistor and a termoresistor connected with the temperature regulator allowing a *O.l”C temperature control. The measurement of the equilibrium pressure has been carried out with a series of 0.25% class Budenberg manometers. A mercury manometer has been used for pressures below atmospheric. Ammonia is allowed to enter the autoclave after flooding it with both air and nitrogen and after cooling the autoclave itself to -50°C. Acetylene is then brought in under stirring to improve solubilisation. High mole fractions of acetylene in the liquid phase are obtained by imposing a pressure higher than atmospheric in the autoclave by means of a mercury head. Temperature is reduced gradually at -80°C and the &HZ flux continued to saturation. The autoclave is then introduced into the termostatic bath and venting is carried out at least three times for eliminating inert gases from acetylene. The autoclave is then connected to two series of scrubbers and both the liquid and the gaseous phase are drawn till a red colour appears in the first scrubber of the two series of sampling traps which contain O.lN HzS04 and phenolphthalein as indicator. For the liquid phase it is necessary to avoid drawing together both the liquid and the overhead vapour.
Drainage occurs without interruption by colleiting at the beginning of the drawing the C2HrNH3 mixtures in scrubber R through a three-way cock P. In this way it is possible to by-pass the five scrubbers where by commutating P it is then possible to draw the liquid phase without vapour after the phenolphthalein in R has changed colour. For the isotherm at 25°C it has been found necessary to insulate and warm up the vapour lines in order to avoid therein a partial condensation of the vapour phase; for the isotherms at -50°C and -60°C it was necessary to cool the outside line in order to prevent the partial vaporization caused in this zone by the temperature increase. For the equilibrium points at the low mblar fractions of acetylene, whose pressures are lower than one atmosphere, sampling of the phases has been carried out under vacuum. Apart from the precautions required for avoiding suctions of liquid in the scrubbers, drawing of the liquid and vapour is performed according to the same procedure followed for the pressure tests. Analytical method Ammonia has been titrated with N/IO &SO4 and the acid solution resulting from reacting acetylene with an AgNO3 alcoholic solution has been titrated with N/l0 NaOH.
RESULTS The experimental results are reported in Table 1
together with pressure values and vapour-phase compositions calculated by the Harris-Prausnitz, Van Laar, Margules and Wilson equations according to the method of Prausnitz et al.[22]. The pressure-composition relationships for the different isotherms are represented in Figs. 2-5, where the experimental data are interpolated according to the Van Laar’s equation for -60°C to 0°C isotherms and to the Wilson equation for 15°C to 25°C isotherms. The higher differences between experimental and calculated values are observed for the isotherms at -50°C and -60°C. The errors found in some experiments should possibly be ascribed to the presence of inert gases, while at low molar fractions of ammonia in the vapour phase the analytical errors become significant.
THERMODYNAMIC ANALYSIS
Ammonia is a protonophilic compound of average basicity, while acetylene is a proton-donor compound having a weak acid character. The possibility of acid-base interactions between acetylene and ammonia leading to the formation of a complex by hydrogen bonding according to the equilib-
303
Vapour-liquid equilibriaof the acetylene-ammoniasystem Table 1. Experimentaland calculatedequilibriumdata Experimentaldata
T(“C)
25
15
0
-25
-35
x1
Y1
0,028 0,030 0.066 0,109 0.350 0,515 0.675
0.098 0,094 0.173 0.264 0.644 0.777 0.870
0.036 0.039 0.123 0.131 0.135 0.137 0.402 0.559 0.640 0648
0.038 0.038 0,041 0,142 0.161 0.161 0,171 0.382 0.386 0.691
0.089 0.164 0.175 0.410 0.424 0.581 0.597
0.159 0.165 0.172 0.250 0.264 0.268 0.280 0.430 0.435 0.637 0.642
0.103 0.099 0.306 0.322 0.331 0.308 0662 0.812 0.869 0,869
0*106 0,118 0.125 0,358 0.398 0.405 0,404 0.700 0.710 0.886
0.299 0443 0.511 0.792 0.794 0904 0902
0.452 0.460 0.535 0.712 0,724 0.714 0.744 0.826 0.832 0.924 0.928
P,(Ata) 10.30 10.30 11.16 12.21 19.59 26.12 32.07
7.65 7.61 9.31 9.51 9.53 9.41 16.29 21.13 23.75 24.04
4.51 4.63 460 5.98 6.18 6.18 6.18 9.92 10.03 17.03
1.94 2.31 2.59 4.14 4.75 6.81 6.81
146 1.46 1.61 2.22 2.21 2.19 2.28 3.40 3.42 5.09 5.09
(
y’-y” Y
HarrisPrausnitz VanLaar
.loo
(!I$+O
) Wilson
HarrisPrausnitz VanLaar
Margules
Wilson
- 24.49 - 14.89 -3.41 -3.03 -7.14 -0.51 - 1.12
- 26.53 - 18.09 -694 -5.30 -4.91 - 2.70 t 0.46
-32.65 - 24.46 -9.83 -3.03 -3.11 - 1.03 -0.92
- 15.31 -6.38 -4.04 -3.19 -5.59 -5.28 - 1.95
+2.18 t 2.12 t 2.33 t2.13 -6.52 t 3.79 -2.15
+1.84 t 2.23 +0.99 to.01 - 1.79 t 1.30 t 1.43
to.97 t 1.36 0.00 -0.16 +7.% t 4.67 t 4,ll
+3.30 t3.19
7.89
9.28
10.72
6.05
3.11
1.37
2.84
3.21
- 10.68 t3.03 -8.50 -11.18 -9.31 -097 t 1.21 -0.86 -1.50 -0.81
-0.97 t1.11 -1.96 -1.86 -2.11 t6.17 t 2.12 -0.25 - 1.27 -0.69
-6.80 t 5.05 -3.21 -2.80 -3.02 t 5.52 t 4.23 - 0.37 -1.84 - 1.38
-1.17 t4.04 -3.21 -2.80 -3.02 t5.52 t4.53 -0.37 - 1.84 - 1.38
-0.39 - 1.18 -2.10 -3.34 - 2.52 -0.64 -5.96 -4.21 -2.15 - 1.91
t 2.35 t 3.35 to.75 -0.31 to.84 t 2.55 -3.81 - 1.99 t 1.56 t 1.91
t144 t 2.63 toGI -146 -0.21 t 1.38 - 1.90 -0.62 t 0.88 t 0.96
t 1.31 t 2.31 -0.54 - 1.67 -0.42 - 1.28 - 1.47 -0.28 t 1.18 t 1.21
4.81
1.91
3.34
3.34
244
1.76
1.06
1.14
t 4.59 -3.39 -0.80 -0.28 - 1.51 -2.54
t 13.21 t 1.69 t 2.40 t3.35 t2.01 t 0.25
+6&l -4.24 -240 t2.51 t 2.01 t 0.25
t 10.38 -0.85 to.00 t3.35 t 2.26 t 0.49
t 0.88 -0.43 t 0.87 -1.84 -0.81 -0.81 t 1.62 -0.10 -040 t 1.76
t 1.53 0.00 t 1.52 -1.17 -0.16 -0.16 t 3.12 -0.91 - 1.20 t 0.47
Ma&es
t4.03 t 4.42 t 2.25 to.19 -4.93
t2.23
t5.20
t5.20
t5.44
0.00 -0.85 t2.48
to.71 -0.14 t2.11
t 2.43 t 1.55 t 2.93
+ 1.71
0.44 -0.86 t 0.65 -2.17 - 1.46 - 1.46 - 1.13 -0.50
to.85
-0%
t 2.82
t 2.23
t 1.75 to-43 t 1.96 -0.84 to.16 to.16 t 2.21 - 2.12 -3.09 - 2.06
2.98
1.18
1.53
0.97
1.12
0.00
to.52 t2.11 -3.86 -190 t 1.26 -1.47 t 1.62
1.83
3.26
3.13
-0.92 t 6.55 -3.86 to.51 t 1.51 -0.44 t 0.67
-4.01 t1.22 -2.35 t 2.78 t 3.78 t 0.77 t 1.77
-3.01 t1.22 - 2.54 t 2.40 t 3.53 t 0.66 t 1.66
2.07
3.78
3.58
t 9.29 t9.35 -3.74 -899 -760 -5.60 -7.39 t 1.33 t 0.72 t 0.87
t 11.95 t 11.09 - 1.68 -6.46 -5.25 -3.08 -5.38 t3.15 t2.76 t 2.27
t 11.95 t 11.09 - 1.68 -6.46 -5.25 -3.08 -5.38 t3.15 t 2.16 t 2.21
-4.35
i-l.45 t3.80
tl.69
-2.15 t 2.78 t3.90
t 1.77
- 1.93 -2.53 t 0.42 - 1.62 t 1.62
-3.86 - 1.90 t 1.26 - 1.47 t 1.62
t 0.52 t2.11 -3.86 -2.95 to.21 -2.35 t 0.73
3.82
1.92
2,52
2.59
to.77
t 11.95 t11.09 -1.68 - 6.46 -5.11 -3.08 -5.38 t3.15 t 2.88 t 2.27
t 1.55
t7.53 t8.90 t 1.24 -7.21 -3.62 -1.37 -1.32 - 1.76 - 1.46 t 3.93
t 5.48 t 5.73 0.00 t8.11 -3.62 -1.37 O*OO - 1.76 -0.88 t 3.54
t 5.48 t 5.73 0.00 t8.11 -3.62 - 1.37 0.00 - 1.76 - 1.17
2.52 t 5.48 t 5.73 OGII t8.11 -3.62 - 1.37 o*oo - 1.76 - 0.88
to.43
t2.05
t2.05
t2.05
t5.50
t4.52
t3.54 t4.52
t3.54 t4.52
3.46
3.20
3.20
3.20
1.96
2.00
1.96
2.52
0.104 0,486
0.67
-7.61
- 1.65
-2.26
-3.91
t 1.49
t4.48
t4.48
t299
0.106 0,485 0.246 0.756
0.67 1.22
- 5.77 -4.07
-0.41 -2.25
- 1.03 -2.38
- 2.41 - 2.38
t2.99 t3.01
t5.97 -3.28
t5.97 - 3.28
t2.99 -4.10
304
A. VETEFS,A. COJUITIand M. A.
SCAFMUCCI
Table 1(cont.)
x1
Y,
Pr (Ata)
HarrisPrausnitz
0.263 0.312 0.372 0.471 0600
0.764 0.812 0.850 0.899 0.964
1.22 144 1.73 2.16 2.99
t 3.01 -2.22 - 1.41 t 1.56 - 1.70 3.42
T(“C) -50
-60
0.100 0.107 0.230 0.346 0.347 0.537 0.601 0.685
0.532 0.531 0.764 0.865 0.868 0.918 0*%7 0.984
0.41 0.41 0.66 0.99 0.99 1.74 1.98 2.34
(!Ep).lM)
(q+nl
Experimental data
-9.70 -9.79 -6.15 -3.12 -3.11 -2.40 - 1.45 -I*10 4.60
Margules
Wilson
HarrisPrausnitz
VanLaar
Margules
Wilson
-0.79 -0.74 0.00 044 -1.76
-0.79 -0.74 -0.12 t 0.56 - 1.66
-0.79 -0.62 t 0.35 t 0.78 - 1.56
t4,10 t 2.78 t 4.05 t 1.02 0.95
t2.46 o+Il -2.31 0.00 -5.35
t1.64 -0.69 -2.31 o*OO -468
to.82 - 0.69 -2.31 046 -4.01
1.01
1.19
1.61
2.55
2.98
-9.02 -6.03 -2.88 - 1.27 -1.50 t 2.72 -0.83 -1.02
-9.40 -5.27 -2.75 -1.27 - 1.50 +2*61 -0.93 - 1.02
t 2.30
04to
t244 t4.24 t 8.08 t8,08 t 9.50 t 13.13 t 14.40
t 2.38 t 4.24 t 1.01 t1.01 -5.75 -5.05 -5.13
to4M
040 t 2.38
t3.48 t 1.01 t 1.01 -5.75 -4.55 -4.70
t4.24 t 1.01 t 1.01 0.00 -5.05 -5.13
3.16
3.09
7.77
3.09
2.56
3.09
VanLaar
-9.21 -5.27 -2.75 -1.27 -1.50 t2.61 -0.93 -1.02 3.07
x,
2.88 040
2.30
Fig. 2.25”C+ 0°C isotherms. Liquid pressure-composition curves, interpolation lines calculated by applying thermodynamic equations; 0 experimental points; A vapour pressure of pure compounds.
Fig. 3.25”C+ 0°C isotherm. Vapour pressure-composition curves, interpolation lines calculated by applying thermodynamic equations; 0 experimental points; A vapour pressures of pure compounds.
rium reaction
aldehydes and ketones in an ammonia solution. An independent criterion supporting the association hypothesis is given by Chueh[l9] who, applying Lambert’s theory of the associated gaseous mixtures, to the volumetric data for the acetylene-ammonia system
CzHZtNH 3t-‘CH2 Z. ..N&
(a)
has been recognized by Tedeschi[20-211 for the interpretation of the catalytic mechanism of the ethynilation of
Vapour-liquidequilibriaof the acetylene-ammoniasystem
305
developed on the basis of the association among the components. Basic formulae For the vapour-liquid equilibrium isothermal data the equation of Gibbs-D&em may be written as follows: dP Cxidlny,xi-iJ,L-=O. RT I
(1)
If the activity coefficients are calculated at a constant reference pressure (Pr) for all the experimental points Eq. (1) can be written[22] as: 7 xl dln 7jpaxi = 0.
(2)
In order to investigate the thermodynamic consistency of Fig. 4. -25°C+ -60°C isotherms. Liquid pressure-composition the vapour-liquid equilibrium data for the associated curves, interpolation lines calculated by applying ther- systems, it is necessary to distinguish between apparent modynamicequations;0 experimentalpoints; A vapour pressures or stoichiometrical, and actual concentrations. The of purecompounds. former are the ones experimentally detectable and represent in our case the concentrations of CZ& and NH3 without a distinction being made between dissociated and associated molecules. Accordingly for a binary system in which compounds A and B combine to give an AB type complex, Eq. (2) must be rewritten introducing the actual molar fractions X*, XB and Xns instead of the apparent ones XI and X2: xA dhl '~A'~')X.J +XB dln
ys(")Xe+XAB dh $~XAB
=
0.
(3)
According to Trevissoi and Francesconi 1231the following equation can be derived XI dh y~("h txz
dln ,%(“xB = 0.
(4)
Writing -yA”r’ xA and 7B’p”xBexplicitly by means of the equation [22]
Fig. 5. -25°C +-WC isotherms. Vapour pressure-composition curves, interpolation lines calculated by applying thermodyanamic equations; 0 experimental points; A vapour pressures of pure compounds.
reported by Khodeeva [ 181,has been able to calculate the equilibrium constants Kalv for the reaction (a) in the temperature range 50-150°C. The enthalpy and entropy values of the association reaction calculated from the variation of Ka,” with the temperature justify the formation of a very weak hydrogen bond. Since there is both theoretical and experimental evidence supporting the hypothesis of the complex formation, the whole thermodynamic treatment has been
it results that
Tndln
PTY~Q~ (6) fp'.'exp~p%_!!$=o
which may be further simplilied, considering that fp’> is constant for each isotherm and that the changes of the term exp _f2(VidP/RZ’) are negligible. It results XIdln (PTYAQA I+ xz din (PTYBQB I= 0.
(7)
A. VETERE,A. COJUITIand M. A. SCARAMUCCI
306
and This equation, proposed by Francesconi Trevissoi[23] in a somewhat different form, does not include the actual compositions of the liquid phase. Investigation of the thermodynamic consistency of the CtHrNHa system is correspondingly, and remarkably, simplified, since the association constants allowing to derive the actual concentrations from the apparent ones are only known for the vapour phase[l9]. The theory of Lambert[24-261 is the basis of the method for calculating the association constants in the gaseous phase from the analysis of the values of the second virial coefficient. According to this theory, the deviations from the ideal gaseous phase for both pure compounds and binary mixtures may be subdivided in physical interactions of the central type (electrostatic and dispersion forces) and specific interactions leading to the formation of weak chemical bonds. The second virial coefficient may be therefore expressed by a sum of two terms B”=B’+B’
(8)
where BP represents the physical interactions, and B’ the chemical bond forces. The contribution of the physical interactions may be calculated applying the equation of Pitzer and Curl[27]. Provided that the association constant I&, is small, the following equations are valid: K P
_,.w_ RT
2
._
wrm RT
for the association reaction A + BeAB K
P
_WiL. -___ RT
(9)
Since the experimental pressure reach comparatively high values it has been preferred to apply the equation of Redlich-Kwong instead of the virial equation truncated after the second term. The formulae and the mixing rules used for calculating ‘pi are equal to those proposed by Chueh and Prausnitz 1281. The values for the constants of the Redlich-Kwong equation are reported in Table 2 together with some chemical and physical data of acetylene and ammonia occurring in the calculation of the activity coefficients. It should be noticed that it has been preferred to determine the constants a and b appearing in the equation of Redlich-Kwong by interpolating the literature volumetric data of the pure compounds, since the values of the adimensional constants & = O-4278 and & = 0.0867 calculated at the critical point are valid in the whole pressure and temperature field only for compounds strictly following the law of corresponding states. Thermodynamic consistency The integration of Eq. (7) within the experimental limits
of concentration represents the most useful method[23]. In order to calculate YA and YB from Kz values the following procedure was adopted. Assuming the A t B F? AB association and taking as the fugacity reference state for all the compounds the value of 1 atm, it can be written: AG” = -RT In Kz (YM . p.4B - PT.1
= -RT In
and
(YA * QA
= -RT In
W-B$ RT
for the association reaction 2A * At. Accordingly the K, value can be derived provided&@ B” and BP have been calculated from experimental volumetric data and from the equation of Pitzer and Curl, respectively. Furthermore the B” values have been obtained by extrapolating experimental data at P = 0. It follows that Kp coincides with the thermodynamic constant of the equilibrium reaction K,“:
YAS
*
YA * YB
'&)'(yB
'QB
'PT)
Kw
1 (12)
* PT
from which YAB
(13)
YA ’ YB *PT.
The value of Kq, has been obtained assuming that QAB for the complex be equal to the mean value of QA and QB. The KE values have been obtained extrapolating at the temperature of 25°C+-600C the values calculated by Chueh and Coll[19] in the range SO”C-150°C(Table 3). The stoichiometry of the reaction allows to establish the (11) following expressions:
Calculation of fugacity coejicients The deviations from ideality in the vapour phase have
been evaluated on the basis of the volumetric literature[lS] data, the reliability of which has been confirmed by the thermodynamic analysis of Chueh[t9].
YA + y.0 _.
y’= 1 +yAB ’
YB+-YAB yz=
1 +y*B
(14)
which correlate the apparent concentrations to the actual ones. By introducting (14) into (13) and considering that
48.74 38.54 26.37 12.76 9.15 5.25 3.47
9.91 6.95 4.23 1.50 0.93 0.39 0.23
P&J361 29.28 25.43 19.24 1040 7.82 4.78 3.25
f&t 8.78 6.50 3.93 1.45 090 040 0.23
f&t
Fugacity (Ata)
69.2 62.2 56.0 49.7 48.1 46.3 44.8
28.28 27.62 26.55 25.56 25.09 24.27 23.86
V&&351 %,,[361
Molar liquid volumes (cm3/mol)
- 157 -170 -192 -237 -258 -292 -317
&I(C,HJ$ -261 -299 - 345 -466 -540 -670 -730
&z(NH# -282 -300 -332 -390 -415 -454 -484
J&z*
Second virial coefficients (cm3/mol)
*Extrapolated values from 150”+SOY!data[l9]. Walculated from Lyckman-Eckert[22] equation. SCalculated from volumetric data reported by F. Din[36] (NH,), and S. Miller[35] (GHJ. Walculated from volumetric data of S. M. Khodeeva[l8].
298.2 288.2 273.2 248.2 238.2 223.2 213.2
T CK) P&J351
Vapour pressures (AW
094612 x 10’
a,*
50.621
b,S
0.14498x 10’
ait
Constants of Redlich-Kwong equation
Table 2. Thermodynamic properties of pure compounds and mixtures for the ammonia-acetylene system
79.251
b&
0.134453X lr
Cd
A. VETERE, A. COJLIRI and M. A. SCARMJCC~
308
Table 3. Equilibriumconstants for CZH2 t NH, e NH,. . . C2HZ associationsin liquidand in vapour phases with related enthalpy and entronv values T(“C) 25 15 0 -25 -35 -50 -60
K.V,
K:,
AHaV
AHoL
AS””
AS”=
-2200
-2120
-15.2
-8.4
0.0190 0.49 0.0216 0.79 0.0270 0.78 0.0388 099 1.11 oMi6 OG20 1.67 0.0780 2.21
YA+ Ys + YAB= 1 we obtain the final formulae:
consistency of the single experimental points, like the one given by differential methods. In order to carry out the integration, instead of applying the trapezoidal rule[29] it has been preferred to use a stricter method consisting of interpolating xi = f( Yi(piPt)according to a cubic function. The results of the integration, expressed as per cent deviations of the left side of Eq. (7) from zero, with respect to its absolute value, are reported in Fig. 6 together with the values obtained assuming there is no association. The equation of Gibbs-Duhem annears to be better verified if complex formation is admitted, exception made for the points of the isotherm at 25°C. Altogether the deviation from the criterion of ther-
and y,=-(1-2Y2K~P~tK~P~)t~[(f-2Y~K~P~tK~P~)2t4Y~K~P~]
(16)
~Y~KIPT
which are used for calculating the actual mole fractions from the apparent values and the association constant. The values of Y. and Yb calculated in this way have been introduced into (7). Integration of the latter has been carried out at mole fraction intervals of acetylene in the liquid phase of 0.05 so as to get a criterion of local T=25”C
modynamic consistency reduces from a lo-15% value, ir1 case of non association, to 5-7% supposing there is complex formation. It has to be noticed that a remarkable improvement has been obtained in the evaluation of the data although the conversion of acetylene and ammonia in the complex is comparatively small. The molar fraction
T=l5'C 20 ,5
T=O'C
I
l
****.* . 10 . 5 ~~OOoo 0 _____",I__
0.2
0.4
0.6
0.2
0.4 0.6
02
0.4
X
0.6
XI
T--35%
T--25'%
T-
25
-50°C
20
20
15
I5
10
l*
5 0
-‘5tl 0.2
0.4 X
0.6
l****
__~___,__
.
0~~0
o
-5 -10
0
i
-15t-J-uL -‘“iL-u-u0.2
0.4
Xl
0.6
T= - 60°C
25
0.2
0.4
x,
0.6
0.2
0.4
0.6
Xl
Fig. 6. Per cent deviation (A%) from the criterion of thermodynamic consistency according to the method by Francesconi-Trevissoi, 0 hypothesis of association C,H, t NH, P CzH2......NH.; 0 hypothesis of non association.
309
Vapour-liquidequilibriaof the acetylene-ammoniasystem YABchanges in fact from a max value of about 7 per cent at 25°C to a min value of about 0.5 per cent at -60°C and for each isotherm reaches the highest value approximately for xl = 0.5 (data not reported). For a more accurate investigation of the interactions with chemical bond formation which may occur in the gaseous phase, the possibility of autoassociation of pure compounds has been consideredDO]. While for acetylene, a scarcely polar compound, the virial coefficient B,, values (Table 2) exclude the possibility of autoassociation, in the case of ammonia the difference between the values of BS and BP leads to recognize the formation of a bimolecular complex. The constants of ammonia autoassociation have been therefore calculated according to the same procedure previously reported and the values have been graphically extrapolated in the whole experimental temperature field (Fig. 7). Assuming the simultaneous presence of the two association equilibria: K.V, K.V,
2AeA~a A+BsAB
it results that the actual concentrations YAand Yg may be calculated solving the following equation of the third
1.
l
0.01 0.008
-
\.
0.006 -
0.004-
0,002l
I
I
-50
I 5.0
I
-25
0
I
/
I1
I
I
A
25
OC I
/
50
I
4.0
I03/T.
I
1
I 100
i 150
I,
30
OK
7.Relationshipbetweenthe valuesof theassociationconstants in the gaseous phase and the temperaturefor the reactions: 0 MI,+C*Hz~NH,.......C2H2;02NHJ#:NH~.....,.NHs.
Fii.
degree in YA: Y,)[K,Kd’,2(2Y, + Ydl
+ Y.*[I%K@+ YIYz)+ PTKz(
YI +
Y?)]
+YA[&&(Yz-Y:)+Y~+I]+Y,(Yz-2)=0 which gives a single valid solution within 0 and 1. Ys can then be obtained: y J-Y,-KIYA’PT B ltK,Y,PT
’
Integration of ‘Eq. (7) on the basis of the values of the actual concentrations YA and Ys gives no appreciable variation with respect to the calculations performed assuming only the association among different molecules. The two association models seem therefore equivalent, mainly because of the low value of the constant KL. Association constants in the liquid phase for the reaction A+B*AB In order to obtain an indirect confirmation of the validity of the experimental data, the calculation of the association constants has been extended to the liquid phase. Use has been made of the same assumptions of Lambert’s theory for the gaseous phase. In fact, for the liquid phase too, it is possible to make a distinction between weak, or physical, interactions, due to Van der Waal’s dipoles, and specific, or chemical, interactions leading to the formation of more or less stable complexes. Van Laar’s theory is valid for solutions where Van der Waal’s forces prevail, the deviations from the ideal case being due only to differences among intermolecular forces of the species in solution. On the contrary, when there are stable chemical bonds among the molecules (as between Hz0 and NHs), it is possible to neglect the physical forces and assume that the mixture of all chemical species, associated or not, is ideal (Dolezaleck)[31]. In this case, for satisfying Raoult’s law, it is sufficient to replace the apparent concentrations with the actual ones. A synthesis of these theories is the method of Harris-Prausnitz[lO], based on the following hypotheses: (1) Both physical and chemical interactions contribute to the non ideality of the associated solutions. (2) The physical forces can be represented by an equation by Van Laar type (Eqs. (6)-(8) from Table 5 in Appendix). (3) The effect of the chemical interactions is calculated introducing into formulae (2)-(5) of Table 5 the actual concentrations as functions of the apparent ones through the association constant K,,,. The whole calculation arrangement reported in Appendix, is a function of only two unknown quantities, i.e. the constants of association Kf; and of interaction uAB. The Kt, The Kf;, values
A. VETERE,A. Corur’rrand M. A. SCARAMIJCCI
310
obtained for the different isotherm are reported in Table 3 and represented in Fig. 8. It is worth while noticing that the actual activity coefficients values (not reported) are very close to 1 in practically the whole temperature range, excepting the isotherms at -50°C and -60°C for which a higher deviation from the ideal case can be visualized.
2120 cal/mol, in satisfactory agreement with the 2210 cal/mol value calculated by Chueh et a1.[19] for the reaction in the gaseous phase. This value is an index of a very weak hydrogen bond [ 19,30,32]. The similarity of these values is reasonable, since the energy for hydrogen bond formation is a function merely of the electronic configuration of the atoms among which the hydrogen bond takes place and not of the aggregation state[30,32]. It has been further established that the association constants in the liquid and gaseous phases are reciprocally consistent. Since under equilibrium conditions the activity of each component is the same in both phases, the equation Kf;, = KE must be satisfied provided the same standard states are assumed for liquid and vapour phase. As this is not the case, the difference between K,L, and Kz values has to be ascribed only to the different reference fugacity values chosen for the two phases [30,33]. The standard state for the gaseous phase in the calculation of KE is in fact the unitary fugacity of the pure compounds, while for the liquid phase the standard state is the fugacity of the vapour in equilibrium with the pure liquid at the experimental temperature. Taking into account such differences it is possible to transform the value of KE into one of Kf; through a thermodynamic cycle based on Vant’HotTs box, or more simply, by equating j” to j”. Since Kf;=Kx*Ky
0.3 4.6
-60’
-500 I
I 4.6
-35’ I 44
I I 42
-25’ I
I 4.0
I 38
00 I
I 3.6
Ky * Kip, = Kf”.PT
and
150 259 1 I I 3.4
(20)
Fig. 8. Relationship between the values of the associationconstants
in the liquid phase and the temperature for the reaction: CzHz+NHJ*&Hz ....... NH,. Enthalpies and entropies for the association reaction A t B zz AB in the liquid and gaseous phase The values of the association constants at different temperatures previously calculated, allow the obtainment of enthalpies and entropies, both in the liquid and gaseous phase, on the basis of the following relation:
and recalling that according to the definition of standard state for the gaseous phase Kro = 1, it results that
(21) and therefore logK;,-logK;=log$@
Al3
Furthermore, from the equations below: -bG = RT In K., = -AH” t TAS”.
(19)
Since the enthalpy and entropy data relating to the formation of a hydrogen bond are generally known, comparison of the latter with the AH” and AS” values obtained from vapour-liquid equilibrium data can verify the validity of our experimentation. From the values of Kt, reported in Table 3 it is possible to deduce that AH” for the association reaction in the liquid phase is equal to
AHoV AS”’ logK.Y,=-R?;-tR
(23)
(24) and assuming AHoL = AH’“, it is possible to derive the following expression giving the required relationship
Vapour-liquidequilibriaofthe acetylene-amoniasystem between ASoL and AS”“: ASoL = ASo’ - R log fi. A mean f& value has been calculated for each isotherms (see after) and introduced into (25). The mean value of ASoL calculated in this way is equal to -9.9 cal/mol “K and is close to the experimental value of - 8.4 cal/mol “K[19]. The max deviation with respect to the mean value is about 20 per cent and occurs for the -60°C isotherm. Data reduction The most rigorous method for correlating the experimental data is that based on the hypothesis of the bimolecular association between C2H2 and N&, which has in fact justified the thermodynamic consistency of the experimentation. Applying the Harris-Prausnitz equation with the constants K,, and (Ypreviously calculated (Table 4) it is possible to determine the actual values of the compositions in the liquid phase xi and of the activity coefficients “/r.Furthermore, from the following equation.
311
A procedure approximated but less complicated than the previous one, is that of correlating the apparent concentrations of the liquid phase with the equation of Margules, Van Laar and Wilson according to the method proposed by Prausnitz et al. [22]. Application to the &HZ/NH, system of a procedure such as this which does not take into account association phenomena, can be justified due to the limited complex formation in the gaseous phase. Furthermore the association in the liquid phase can be neglected following the Prigogine theorem. Accordingly both treatments can be considered equivalent for most practical purposes. The values of the constants Al2 and AZ, calculated at different temperature are reported in Table 4. While the equations of Margules and Wilson have been used in their usual analytical form, in the case of the Van Laar equation we have applied the following ones[34], more flexible even if more complicated: -I~~z,~:,I
1,,,=A21211[1+222(~-1)]
>I (28)
1
(2%
where: for each experimental point a fugacity value fiB for the complex can be obtained. The actual molar composition yi in the gaseous phase can be determined using the relation: y, -
’
r@ $9,
and hence the apparent molar fractions Yi by applying the Eq. (14). The agreement between calculated and experimental data was good but not wholly satisfactory probably because of the inadequacy of Van Laar’s single parameter equation (see Eqs. (6-8) in Table 5) to take into account the physical interactions.
z1=,A$$2l,X2 and zz= l-Z,. In this way the parameters AI* and AZ, are allowed to assume a different sign without the denominator of (28) and (29) becoming zero, this being the case for the unmodified Van Laar equation if
Xl = IA211 X2
IA12l’
As it appears from Table 4 the constants AI2 and A2, are opposite in sign for the isotherms within the temperature
Table 4. Constants of the thermodynamic relations applied to the ammonia-acetylene svstem Van Laar T(“C)
A,2
25 15 0 -25 -35 -50 -60
-0.26 -0.26 -0.36 -0.69 -0.74 -0.47 -0.62
A2,
0.74 1.62 -0.60 -0.52 -0.67 -0.72 -0.73
Wilson A,>
An
1.10 0.68 1.36 O.% 1.24 1.52 1.57
1.00 1.75 1.09 1.75 1.53 1.13 1.17
Margules An
Am
-0.40 -0.35 -0.45 -0.65 -0.74 -0.48 -0.65
0.37 -0.25 -0.38 -0.56 -0.67 -0.67 -0.72
Harris-Prausnitz K.
0.49 0.80 0.78 1.00 1.11 1.67 2.22
@
2.25 2.30 1.50 1.06 0.78 1.59 2.40
=&
y*=%
(5)
(3)
v, t 0.75v*
II
y*+J 2
(13’)
(11)
x*, Y* . YE
XFJ=e KY_
8,’ v. +(8,t da)‘V, In *
x* =E
v/a) - [ 6*‘v~~~~~.~“vB]1~)*
[
2
(2)
(13)
al-ALI = [ (8, t
A-
•=+4[dkl~~~
x,,
A+BsAB
(12)
@‘)
(4)
Table 5. Harris-Prausnitz method[lO] for calculating the equilibrium constants of association
313
Vapour-liquidequilibriaof theacetylene-ammoniasystem range from 25°C to 15°C in the case of Van Laar’s equations, and of 25°C in the case of the equations of Margules. None of the equations which have been tested shows a well defined trend of the constants with temperature. The activity coefficients calculated with such constants show that the C*HrNHs system presents only slightly negative deviations from Rault’s law, except at concentrations close to inhnite dilution, where the activity coefficient of acetylene is about 0.6. The difference between experimental and calculated values (Table 1) is generally small, thus showing a slightly better correlating ability for Van Laar’s equation as compared with those by Margules and Wilson. The mean difference calculated on all seven’isotherms, varies from 3.5-4.2 per cent for the yi compositions, and from 2.3-2.5 per cent for the total pressures, according to the used equations. Such results appear to confirm that the Van Laar equation is better than the Margules one for components whose molar volume is remarkably different ( vc,.%/v,,, - 2). Furthermore the Wilson equation which can be preferred for highly non-ideal solutions, is slightly less reliable for solutions which do not diverge strongly from the ideal behaviour[W]. Nevertheless for the t25”C and + 15°C isotherms the Margules and Wilson equations gives better results than Van Laar equation. This fact has to be ascribed to the high value of the constant Azl of Van Laar’s equation at these temperatures (Table 4); accordingly, the calculated pressure is too high for the mixtures having a high acetylene content. The results reported in Table 1 show that the values of the pairs Pr - yi, calculated according to HarrisPrausnitz, differ from those obtained by applying the equation of Van Laar or Margules of about l-5 per cent.
CONCLUSIONS
Acetylene-ammonia system shows small negative deviations from Raoult’s law. Such deviations, as foreseen, increase as the temperature decreases and have to be ascribed to interactions both of chemical and physical type. Therefore the simple Dolezalek theory, according to which the different chemical species in solution, either associated or not, constitute an ideal mixture can not be applied. The thermodynamic analysis of the experimental data has shown their consistency on the ground of the hypothesis of the bimolecular association between C2Hz and NH,. This hypothesis, generally accepted, is confirmed also by the congruence of the values of the association constants obtained from equilibrium data with the values of the energy of the hydrogen bond involved in the complex formation. Since conversion to the complex in the gaseous phase is small, the activity coefficients may be correlated and
extrapolated both by the usual empirical equations (Van Lam, Margules, Wilson) which do not imply association and by theoretical methods which take into account the association in the liquid and gaseous phases (Harris-Prausnitz). Acknowledgments-The authors wish to thank Professor Zanderighifor many suggestionsand helpfuldiscussions,Dr. V. Bulla for writingthe computerprogramsand Dr. A. Tiidei for having revised the manuscript.
NOTATION
a, b, c constants of the Redlich-Kwong equation AIZ and AU constants of the Van Laar, Margules and Wilson equations second virial coefficient, cm’lmol fugacity of compound i at its vapour pressure, atm fl ,R, fugacity of compound i in the standard state, atm f7 fugacity of compound i at the reference pressure P, atm AG" free energy for the reaction A t B s AB, cal/mol AH9 enthalpy for the reaction A t B& AB, cal/mol AHi, evaporation enthalpy of compound i, Cal/m01 K.1 equilibrium constant for the reaction A t B8AB KO2 equilibrium constant for the reaction ,O
2A+Az
KP equilibrium constant defined as PZ/ (P2. Pi), atm-’ K, constant defined as K,JKq, Kf constant defined as K,,z/KQ~ KW constant defined as cpnB/QA . QB Kw constant defined as Q,+/Q** KP constant defined as f&/f: *f%,atm-’ KX constant defined as X, /XA*Xg KY constant defined as yAB/Ya'yB P9 vapour pressure of compound i, atm total pressure, atm PT R universal gas constant, atm cm3/g mol “K AS” entropy for the reaction A t Be AB, cal/mol “K T absolute temperature, “K Vi molar volume of compound i, cm’/mol Vi partial molar volume of compound i, cm’/mol molar fraction of compound i in liquid molar fraction of compound i in vapour gas compressibility coefficient
314
A.
VETRRE,
A. CoJu’t-rtand M. A.
Greek symbols lY constant of the one parameter Van Laar equation activity coefficient of compound i Hildebrandt solubility parameter of compound i, (cal/mol cm3)*” normalized extent of complex formation, E o
chemical contribution to second virial coefficient calculated values liquid phase physical contribution to second virial coefficient experimental values vapour phase
REFERENCES [l] PrigogineI. and Defay R., Chemical ThermodynamicsJohn Wiley, New York (1954). 121Kehiaian H. and Treszczanowics A., BUN.Sec. Chins.Fr., 1%9 5 1561. [3] Sarolea-Mathot L., Trans. Faraday Sot. 195349 8. [4] McGlashan M. L. and Rastogi R. P., Trans. Faraday Sot. 195854 4%. [5] Rastogi R. P. and Girdhar H. L., Proc. Nat/. Inst. Sci. 1%2 AX3470. [6] Apelblat A., J. phys. Chem. 197074 2214. [7] Renon H. and Prausnitz J. M., Chem. Engng Sci. 1%722 299. [S] WieheI. A. and BagleyE. B., Znd.EngngChem. Fund. 19676 209. [9] Ktreschmer C. B. and Wiebe R., J. phys. Chem. 195422 1697. [lo] Harris H. G. and Prausnitz J. M., Znd.Engng Chem. Fund. 1%9 8 180. [ll] Marek J. and Standard G., Co/l. Czech. Chem. Comm. 195419 1074.
SCARAMUCCI
1121Marek J. and Standard G. CON.Czech. Chem. Comm. 195520 1490.
1131Sebastiani E. and Lacquaniti L., Chem. Engng Sci. 1%7 22 1155. [I41 Carli A., Di Cave S. and Sebastiani E., C/tern.EngngSci. 1972 27 993. [I51 De Maldd M., Di Cib A. and Massi-Mauri M., Hydroc. Process. 196443 149. Ml Khodeeva S. M., Russian Journal ojphys. Chem. 196135306. WI Lebedeva E. S. and Khodeeva S. M., Russian Journal of phys. Chem. l%l 35 1285. WI Khodeeva, S. M., Russian Journal ojphys. Chem. 196438 1276. 1191Cheuh H. Y., Cannel J. P. 0. and Prausnitz J. M., Can. J. of Chem. 196644 429. PO1 Tedeschi R. J., J. org. Chem. 196530 3045. WI Tedeschi R. J. and Moore G. L. Znd.Engng Chem. Prod. Res. Deuelop. 19709”83. rw Prausnitz J. M., Computer Calculation for Mdticomponent Vapour-LiquidEquilibria, Prentice-Hall, New Jersey (1%7). ~231Francesconi R. and Trevissoi C., Chem. Engng Sci. 197126 1131. m Lambert J. D., Disc. Faraday Sot. 195315 226. v51 Lambert J. D., Clarke J. S., Duke J., Hicks C. L., Lawrence S. D., Morris D. M. and Shone M. G. T., Proc. Roy. Sot. London, Ser. A 1959249 414. WI Lambert J. D., Roberts G. A. H., Rowlinson J. S. and WilkinsonV. J., Proc. Roy. Sot. London, Ser. A 19491% 113. ~271Prausnitz J. M. and Carter W. B.. A.LCh.E. .R 19606 611. WI Chueh P. L. and Prausnitz J. M.,’Znd.Engng Chem. Fund. 1%7 6 492. WI Li J. C. and Lu B. C., Can. J. Chem. Engr. 195937 117. [301Zanderighi L., Private Communication. 1311Prausnitz J. M., Molecular Thermodynamicsof Fluid Phase Equiiibtia, Prentice-Hall, New Jersey (1%9). ~321Pimentel C. C. and McClellan A. L., The Hydrogen Bond, Freeman, San Francisco (l%O). [331 Allen G. and Caldin E. F., Quart. Rev. 19537 255. [341Null H. R., Phase Equiiibn’um in Process Design, Wiley Interscience, N.Y. (1970). [351Miller S. A., Acetylene, E. Benn, London (1965). [361Din F., Thermodynamic Functions of Gases Vol. II, Butterworths, London (1956).
Calculation of the association constants for the acetylene/ ammonia system according to Harris-Prausnitz method In this procedure, whose arrangement is shown in Table 5, there appear three types of activity coefficients defined as follows: Actual, indicated by making use of a letter as a subscript and obtained by applying formulae (6)-(8) of Table 5. Calculated apparent, indicated by making use of a number as a subscript and obtained from Prigogine’s theoremll], through Eqs. (13) and (13’)of Table 5. Experimental apparent, entering as input parameters and calculated by means of the equations:
YB(PBPT = w*f*
ow.,
.
y* and yB being actual molar fractions calculated by means of Eqs. (15) and (16). The solution of the system of Eqs. (D-(13) is based on the
Vapour-liquidequilibriaof theacetylene-ammoniasystem convergency between the values of the experimental and calculated apparent acitivity coefficients. Once arbitrary values are chased for If:, and a and K, is set equal to 1, it is possible to obtain both concentration and actual activity coefficient values following the reported procedure From Eqs. (13) and (13’) it is then’ possible to obtain the
CES Vol. 30. No. 2-D
315
apparent y, for all the experimental points of an isotherm, and from the summation f: (7, - 7,“)’ it is possible to determine, by means of the non linear multiple regression method, the variation to apply to the previous values of K,, and a. The calculation continues until two subsequent iterations give the same values of K., and CI.