Thermodynamic study of liquid phase synthesis of ethyl tert-butyl ether using tert-butyl alcohol and ethanol

Article abstract of DOI:10.1021/je900208n

In this study, a detailed thermodynamic analysis of the ethyl tert-butyl ether (ETBE) synthesis reaction between tert-butyl alcohol (TBA) and ethanol is performed to determine a liquid phase equilibrium constant expression. The result is of practical sign

Full text of DOI:10.1021/je900208n

3208
J. Chem. Eng. Data 2009, 54, 3208–3214
Thermodynamic Study of Liquid Phase Synthesis of Ethyl tert-Butyl Ether Using
tert-Butyl Alcohol and Ethanol
Nalan Ozbay and Nuray Oktar*
Department of Chemical Engineering, Faculty of Engineering & Architecture, Gazi University, 06570 Maltepe, Ankara, Turkey
In this study, a detailed thermodynamic analysis of the ethyl tert-butyl ether (ETBE) synthesis reaction
between tert-butyl alcohol (TBA) and ethanol is performed to determine a liquid phase equilibrium constant
expression. The result is of practical significance in view of the imminent prominence of ETBE to be produced
from TBA and ethanol, as a gasoline blending oxygenate. In this study, enthalpy of formation, Gibbs, enthalpy
of vaporization, and heat capacities (as a function of temperature) of the reactants and products were estimated.
At 298 K, the standard molar enthalpy of reaction for ETBE from TBA and ethanol was found as -1.23
kJ ·mol-1. The liquid phase nonideality of the system was tested, and it was found that the system approaches
ideal conditions. The thermodynamic analysis approach given here is expected to be useful for other liquid-
phase systems.
tion technology can be extended easily to ETBE synthesis with
similar benefits.6
Commercially, ETBE is synthesized by etherification reaction
of isobutene with ethanol7 at moderate temperatures and
pressures in the liquid phase over sulfonated acidic ion-exchange
resin catalysts, such as Amberlyst-158-11 and Lewatit K2631.12-14
Introduction
New approaches in reformulation of gasoline were adopted
following the regulations proposed by the U.S. Clean Air Act.
Due to removal of alkyl-lead compounds from gasoline for
environmental and public health reasons, oxygenated compounds
have gained importance as octane enhancing fuel blending
compounds.1 Alcohols and ethers are among these oxygenated
compounds, proposed as octane enhancers. Addition of oxygen-
ates into gasoline also reduces exhaust emissions of CO and
unburned hydrocarbons and helps to reduce the formation of
atmospheric ozone.2 Tertiary ethers are generally preferred to
alcohols as gasoline blending components, due to their lower
blending vapor pressures and their missibility advantages over
gasoline. Alcohols have disadvantages arising from their proper-
ties such as phase separation in the presence of a small amount
of water. Among the ethers suggested as fuel blending com-
ponents, methyl tert-butyl ether (MTBE), ethyl tert-butyl ether
(ETBE), tert-amyl methyl ether (TAME), and tert-amyl ethyl
ether (TAEE) are the best known oxygenates to be used to
increase the octane level and to promote cleaner burning of
gasoline and thus decrease harmful emissions from vehicles.3
MTBE has become the major gasoline additive used in the last
decade, due to the availability of methanol, produced starting
from natural gas. There are many studies on MTBE.4,5 However,
MTBE has high water solubility, and it causes water pollution
problems. Isobutene used in the production of MTBE is a
petrochemical feedstock. In the synthesis of tert-ethers, the use
of another compound (such as tert-butyl alcohol) instead of
isobutene has attracted the attention of researchers. As a result,
alternative oxygenates were being investigated.
(CH3)2CdCH2 + CH3CH2OH T (CH3)3COCH2CH3
(I)
However, the supply of isobutene, which is mostly derived
from nonrenewable crude oil, is mainly limited from petroleum
refining and also used in other chemical industries. Hence,
reactants other than isobutene are being investigated in ETBE
production. tert-Butyl alcohol (TBA), as a coproduct of pro-
pylene oxide production from isobutane and propylene in the
ARCO process, is proposed as an alternative reactant, instead
of isobutene, in ETBE synthesis.15-23 There are two ways to
produce ETBE from TBA, namely, an indirect and a direct
method. In the indirect method, TBA is dehydrated to isobutene
in the first reactor according to reaction II, and then isobutene
is reacted with ethanol to form ETBE.
(CH3)3COH T (CH3)2CdCH2 + H2O
(II)
However, in the direct method, ETBE can be produced by
reacting TBA directly with ethanol in a reactor in the presence
of an acid catalyst, during which water is also formed as a
byproduct
(CH3)3COH + CH3CH2OH T (CH3)3COCH2CH3 + H2O
(III)
Synthesis of ETBE by using TBA and ethanol and utilizing
concentrated sulfuric acid as the homogeneous catalyst was
investigated by Habenicht et al.20 Yin et al.21 studied synthesis
of ETBE from TBA and ethanol catalyzed by Amberlyst-15
and heteropoly acids (HPA) in a batch reactor. Heteropoly acids
were found to yield superior selectivity; however, they were
less attractive because of dissolution of these catalysts in polar
solvents. Production of ETBE using TBA and ethanol was also
ETBE has superior qualities as an octane enhancer compared
to MTBE and could be produced from bioethanol, which is a
renewable source. Its average octane value is 110. Thus, the
production of ETBE reduces the dependence on methanol and
also contributes to reduce the greenhouse effect. MTBE produc-
* To whom all correspondence should be addressed. Tel.: +90-312-5823556.
Fax: +90-312-2308434. E-mail: nurayoktar@gazi.edu.tr.
10.1021/je900208n CCC: $40.75  2009 American Chemical Society
Published on Web 07/09/2009

Journal of Chemical & Engineering Data, Vol. 54, No. 12, 2009 3209
Table 1. Correlations of Equilibrium Constants, K, for ETBE Synthesis in the Literature
source
Vila et al.28
reactants
K
isobutene and ethanol
K ) exp(1140 - 14580(T/K)-1 - 232.9 ln(T/K) + 1.087(T/K) -
1.114·10-3(T/K)2 + 5.538·10-7(T/K)3)
Jensen et al.10
isobutene and ethanol
(1) K ) exp(10.387 + 4060.59(T/K)-1 - 2.89055 ln(T/K) -
1.91544·10-2(T/K) + 5.28586·10-5(T/K)2 - 5.32977·10-8(T/K)3
(2) K ) exp(10.6162 + 4060.49(T/K)-1 - 2.89055 ln(T/K) +
1.91544·10-2(T/K) + 5.28586·10-5(T/K)2 - 5.32977·10-8(T/K)3)
(3) K ) exp(0.558036 + 5345.01(T/K)-1 - 3.56724 ln(T/K) +
3.65829·10-2(T/K) - 6.02157·10-5(T/K)2 + 5.32295·10-8(T/K)3)
K ) exp(1140 - 14580(T/K)-1 + 232.9 ln(T/K) + 1.087(T/K) -
1.114·10-3(T/K)2 + 5.538·10-7(T/K)3)
Assabumrungat et al.17
Assabumrungat et al.23
Kiatkittipong et al.22
TBA and ethanol
TBA and ethanol
TBA and ethanol
K ) exp(1140 - 14580(T/K)-1 + 232.9 ln(T/K) + 1.087(T/K) -
1.114·10-3(T/K)2 + 5.538·10-7(T/K)3)
K ) exp(1140 - 14580(T/K)-1 + 232.9 ln(T/K) + 1.087(T/K) -
1.114·10-3(T/K)2 + 5.538·10-7(T/K)3)
Table 2. Physical Properties of Amberlyst-1529 a
accomplished by reactive distillation in the study performed by
Yang and Goto,16 in which the combined process of pervapo-
ration with reactive distillation had been investigated using
Amberlyst-15. ETBE synthesis was further investigated by using
Amberlyst 15, ꢀ-zeolite, and supported polyvinyl alcohol
membrane by various researchers.17,22,23 Yang et al.19 also
studied liquid phase etherification between ethanol and TBA
under atmospheric pressure for the production of ETBE. Matouq
et al.24 employed KHSO4, NaHSO4, H2SO4, and Amberlyst-15
as catalysts for the production of ETBE from TBA and ethanol
in a reactive distillation column. Umar et al.18 studied this
reaction in the liquid phase by using ion exchange resins, such
as Purolite CT-124, CT-145H, CT-151, CT-175, CT-275,
Amberlyst-15, and Amberlyst-35 wet.
s/m2 ·g-1
ε
TIEC/meq of H+ ·g of dry material-1
davg/m
8.2 ·10-8
59.2
0.32
5.2
a s is the surface area; ε is the macroporosity; davg is the average
micrograin diameter; and TIEC is total ion exchange capacity. s and ε
(ratio of macropore volume to total catalyst volume) values correspond
to pores having diameters greater than 6.7 ·10-9 m.
acidic ion-exchange resin Amberlyst-15 (Merck) used as the
catalyst is a macroporous sulfonated copolymer of styrene-
divinylbenzene (DVB), containing a cross-linked matrix. Before
the experiments, Amberlyst-15 was dried for 12 h at 383 K.
Physical properties29 of the catalyst used in this work are
summarized in Table 2.
A number of correlations have been proposed in the literature
for the prediction of equilibrium constant, K, for the liquid phase
MTBE synthesis reaction.7,25-27 Unlike the case of MTBE, few
studies have been published regarding to the thermodynamics
of synthesis of ETBE from isobutene and ethanol. Vila et al.28
reported a study of the equilibrium constant for liquid phase
ETBE synthesis from isobutene and ethanol. Experimental
equilibrium constant values were determined by direct measure-
ment of the mixture composition at equilibrium at several
temperatures. An equilibrium constant relationship for liquid
phase ETBE synthesis reaction using isobutene and ethanol as
the reactants was developed by Jensen and Datta,10 using the
thermodynamic pathways to obtain enthalpy and Gibbs free
energy values.
Continuous Flow Reactor Experiments. Liquid phase etheri-
fication of TBA with ethanol was investigated in a continuous
In spite of the increasing interest in ETBE production from
TBA and ethanol and its anticipated industrial importance, to
our knowledge there is no published report on the thermody-
namics of the liquid phase synthesis of ETBE from TBA and
ethanol. Some researchers assumed the equilibrium constant
relation of ETBE synthesis from isobutene and ethanol to be
the same as the equilibrium constant relation of ETBE synthesis
from TBA and ethanol. Assabumrungat et al.17,23 and Kiatkit-
tipong et al.22 used the correlation of equilibrium constant for
isobutene and ethanol reaction28 also for TBA and ethanol
reaction. The correlations for the equilibrium constant of ETBE
synthesized from isobutene and ethanol are given in Table 1.
The objective of this paper is to provide a detailed thermody-
namic analysis of the liquid phase ETBE synthesis from TBA
and ethanol and propose a relation for the equilibrium constant
of this reaction. Also, a set of experimental results are obtained
at different temperatures to check the equilibrium conversion
value predicted from the derived expression.
Experimental Work
Materials. Analytic grade ethanol (Merck) and TBA (Merck)
were used as reactants in the etherification reaction. The strongly
Figure 1. Flow scheme of the thermodynamic analysis.

3210 Journal of Chemical & Engineering Data, Vol. 54, No. 12, 2009
Table 3. Gas Phase Thermochemical Data of TBA, Ethanol, ETBE,
H2O, and Constants for the Gas Phase Heat Capacity Equation
(Cp(g)/J·mol-1 ·K-1) Term in Equations 7 and 8
Table 9. Comparison of Some Thermochemical Properties of H2O
in the Liquid Phase
∆
vapH°/(kJ·mol-1
reference value reference value
this work 45.9 this work -238.2 this work -287.9
Murphy, 200544 45.0 IAPWS45 -237.2 IAPWS45 -285.8
)
∆fG°/(kJ·mol-1
)
∆fH°/(kJ·mol-1
)
TBA34
∆fG°/kJ·mol-1 -177.8
∆fH°/kJ·mol-1 -312.8
ethanol34
ETBE10
H2O34
reference value
-168.4
-121.15
-316.50
7.50
-228.8
-235
-242
a
b
c
d
-48.61
9.01
32.2
7.172·10-1 2.141·10-1 6.293·10-1 1.924·10-3
-7.084·10-4 -8.390·10-5 -3.690·10-4 1.055·10-5
2.920·10-7 1.373·10-9 7.072·10-9 -3.596·10-9
-
-
-
-
Cox et al., -285.8 ( 0.04
198435
Thermodynamic Analysis. Calculation of the Equilibrium
Constant from Thermochemical Data. Thermodynamic equi-
librium constant, K, for liquid phase (l) reaction, Σnj)1νjNj ) 0,
among the n species Nj is given by
Table 4. Comparison of Enthalpy of Vaporization of TBA
reference
∆
vapH°/kJ·mol-1
this work
46.21
46.74
46.94 ( 0.02
46.02
Majer & Svoboda, 198535
Polak & Benson, 197135
Skinner & Snelson, 196035
n
n
n
n
K(l) ≡
aVj )
(γ )Vj(x )Vj ) (
γVj)(
xVj) ≡ K K
γ
∏
∏
∏ ∏
je
j e j e
je
je
x
j)1
j)1
j)1
j)1
(1)
Table 5. Comparison of Heat Capacity Values of TBA
reference
T/K
Cp/J·mol-1 ·K-1
The activity of species j in the liquid phase, aj′γjxj, is calculated
from its mole fraction, xj, and the activity coefficient, γj, which
can be determined through a UNIFAC method. Vj is the
stoichiometric coefficient of species j in reaction. Here, Kγ and
Kx are equilibrium constants in terms of activity coefficients
and mole fractions, respectively. The calculation method is
indicated in a flow scheme in Figure 1. The detailed calculation
process is given in the Appendix.
this work
298
298
299
298
298
298
300
298
211.7
215.4
221.9
210.0
224.9
218.6
224.7
224.8
Caceres-Alonso & Costas, 198835
Okano & Ogawa, 197835
De Visser & Peron, 197736
Murthy & Subrahmanyam, 197735
Skold & Suurkuusk, 197635
Parks & Anderson, 192637
ChemCad v.5.2
Prediction of Liquid Phase Thermochemical Data. Heat and
free energy of formation values (at the standard state) of ethanol,
isobutene, and ETBE are the thermochemical data to be
evaluated to obtain an equilibrium constant. Molar heat capaci-
ties of the reactants and products are also obtained in the form
of power functions. The enthalpy of formation of species j in
the liquid phase is related to that in the gas phase by the
following relation.10
Table 6. Comparison of Enthalpy of Formation of TBA in the
Liquid Phase
Reference
∆fH°/kJ·mol-1
this work
-359
Wiberg & Hao, 199138
Skinner & Snelson, 196035
Taft & Riesz, 195539
-359.2 ( 0.84
-359.3 ( 0.79
-356
∆fHoj (T, l) ) ∆fHjo(T, g) - ∆vHoj
Here, ∆vHoj is the standard enthalpy of vaporization of species
j at the temperature T and is obtained by the New Group
Contribution Method30 at T ) 298.15 K.
(2)
flow reactor, which was made of a stainless steel tube in which
2.85 g of catalyst was packed. The reactor was immersed into
a temperature-controlled furnace. TBA and ethanol (with a molar
ratio of TBA/ethanol ) 0.1; 0.3; 0.5) were mixed and sent to
the system with pressurized nitrogen. Reaction was carried out
at 1 atm pressure. A bypass line allowed the flow of reactants
through the system without entering the reactor, when desired.
The flow rate of the mixture was changed between (0.5 and 1)
cm3 ·min-1. Etherification reaction experiments were performed
in the temperature range of (373 to 383) K. Reaction products
were analyzed by gas chromatography (Agilent 6890N) equipped
with an FID and Poropak Q column. The column temperature
was 473 K.
n0
m0
∆ Ho(298.15 K) ) h +
N C + w
M D
+
∑
∑
j)1
o0
v
0
h0,i h0,i
h0,j h0,j
i)1
z
O
Eh
(3)
∑
h0,k
0,k
i)1
Here, h0 is an adjustable additional parameter, and Ch , Dh
Eh are the first, second, and third level group contributions
,
0,j
0,i
0,k
Table 7. Comparison of Some Thermochemical Properties of Ethanol in the Liquid Phase
vapH°/kJ·mol-1 ∆fG°/kJ·mol-1
reference reference
∆
∆fH°/kJ·mol-1
value
value
reference
value
this work
41.6
42.6
-
-
-
-
this work
-174.7
this work
-276.6
Jensen & Datta, 199510
Jensen & Datta, 199510
-174.8
Jensen & Datta, 199510
Chao & Rossini, 196540
Green, 196035
-277.5
-
-
-
-
-
-
-
-
-
-
-
-
-277.0 ( 0.3
-277.6 ( 0.42
-277.6
Kelley, 192941
Parks, 192542
-274.7
Table 8. Comparison of Some Thermochemical Properties of ETBE in the Liquid Phase
vapH°/kJ·mol-1 ∆fG°/kJ·mol-1
reference reference
∆
∆fH°/kJ·mol-1
reference
value
value
value
this work
32.4
33.0
41.0
This work
-125.6
-126.8
-
This work
-348.9
Majer & Svoboda, 198535
Jensen & Datta, 199510
Jensen & Datta, 199510
-
Jensen & Datta, 199510
Sharonov et al. 199543
-357.5
-350.8 ( 2.6

Journal of Chemical & Engineering Data, Vol. 54, No. 12, 2009 3211
0.436
(1 - Tr)
CoP(T, l) ) R 2.56 +
+
[
0.296
ω 2.91 + 4.28(1 - Tr)1/3/Tr +
(6)
[
(1 - T )]]
r
An alternative procedure is the Sternling and Brown correla-
tion10
CoP(T, l) - CoP(T, g)
11.64
) (0.51 + 2.2ω) 3.67 +
+
(1 - Tr)4
R
[
0.634(1 - Tr)-1
(7)
]
Equations 6 and 7 are for nonpolar liquids. They are accurate
to within 8 % except for Tr > 0.95 for polar compounds, such
as ethanol and TBA. There is an alternative correlation given
by Yuan and Stiel for polar compounds.33
Figure 2. Comparison of liquid phase heat capacities for ethanol. (, this
work; 0, ref 10; 2, ref 26; O, ref 28; ×, ChemCad v5.2.
(0)
(1)
(2)
CoPj(l) - CPoj(g) ) ∆CP + w∆CP + x∆CP
+
(3)
(4)
(5)
x2∆CP + w2∆CP + xw∆CP
(8)
Here (0), (1), and (2) are fluid function and correction terms,
and (3), (4), and (5) are coefficients for higher-order terms.
Here, x is the fourth parameter and Pr is reduced vapor
pressure, given by the following expression.
x ) log Pr|T )0.6 + 1.70ω + 1.552
(9)
r
Results and Discussion
Gas phase thermodynamic data are available for a large
number of species.31 However, there are not sufficient data for
liquid phase applications. There are insufficient thermodynamic
data for ETBE synthesis from TBA and ethanol in the literature.
In this study, liquid phase data were estimated from gas phase
thermodynamic data.
Table 3 shows the values for the gas phase thermochemical
data and the coefficients of the equation for molar heat capacity
of the components (TBA, ethanol, ETBE, and water) in the
vapor phase.10,34 The liquid phase data for the Gibbs free energy
and the heat capacity of TBA as a function of temperature are
not available in the literature. So, enthalpy of vaporization was
estimated by the group contribution method31 at T ) 298 K
according to eq 3 and compared with the literature35 (Table 4).
The estimated value of enthalpy of vaporization was used for
the calculation of Gibbs free energy of TBA (-185.254
Figure 3. Comparison of liquid phase heat capacities for ETBE. ], This
work; 9, ref 33; +, ref 26; ×, ref 10; 2, ref 13; O, ChemCad v5.2.
Table 10. Liquid Phase Thermochemical Data of TBA, Ethanol,
ETBE, H2O, and Constants for the Liquid Phase Heat Capacity
Equation (Cp(g)/J·mol-1 ·K-1) Term in Equations 7 and 8
TBA
ethanol
ETBE
H2O
∆fG°/kJ·mol-1 -185.25
-174.70
-276.60
-386.058
3.4299
-125.57
-348.93
18.79
-238.15
-287.91
44.56
∆fH°/kJ·mol-1 -359.01
a
b
c
d
-2971.14
24.74
1.251
0.450
-0.0637
-0.0081
-3.015·10-3 -1.64·10-3
5.543·10-5 7.379·10-6 3.637·10-6
1.786·10-6
of types i, j, and k in eq 3. Nh , Mh , and Oh are the number
0,i
0,k
of occurrences of the first, second0,,jand third level groups in
eq 3.
Another expression for ∆vHoj is Pitzer’s approximation31
∆vHoj
) 7.08(1 - Tr)0.354 + 10.95ω(1 - Tr)0.456
RTc
(4)
Here, Tc, Tr, and ω are critical temperature, reduced temperature
(T/Tc), and acentric factor, respectively.
The liquid phase Gibbs free energy of formation of species
j can be obtained from the gas phase by10
∆fGoj (T, l)
∆fGoj (T, g)
∆vHoj (T, l)
T
1
R
)
+
dT (5)
∫
T2
Tbj
RT
RT
Figure 4. Equilibrium conversions of TBA versus temperature. s, This
work (TBA + Ethanol reaction); - - - -, ref 10 (Isobutene + Ethanol
reaction).
The liquid phase heat capacity may be related to that in the gas
phase by the Bondi and Rowlinson correlation32

3212 Journal of Chemical & Engineering Data, Vol. 54, No. 12, 2009
the experimental data tend to scatter. Table 10 shows all these
liquid phase thermochemical data. Employing the calculation
method of the equilibrium constant from thermochemical data
in Table 10, the following expression results
38672.73
T
K
ln K(l) ) -2101.93 +
+ 411.41 ln
-
(
)
T/K
2
3
T
T
T
1.592
+ 1.345·10-3
- 5.7517·10-7
(10)
(
)
(
)
(
)
K
K
K
Equilibrium conversion of TBA to ETBE was estimated by
using the equilibrium constant relation (eq 10) derived above
in a temperature range of (300 to 800) K, and the data plotted
are given in Figure 4. A typical curve obtained with a TBA/
ethanol feed ratio of 0.1 is given in Figure 4. In this analysis,
activity coefficients are estimated from the UNIFAC program.
In the same figure, equilibrium conversion values estimated by
using the equilibrium constant relation proposed by Jensen and
Datta10 for the isobutene-ethanol reaction is also given. As seen
in this figure, in the temperature range lower than about 380 K,
the predictions of both correlations are quite close. However,
at higher temperatures the equilibrium conversion estimated by
the correlation proposed in this work for the TBA-ethanol
reaction is much higher than the equilibrium conversion plotted
according to Jensen and Datta’s correlation10 for the isobutene-
ethanol reaction. This deviation is reasonable since those two
curves are for different reaction systems.
Figure 5. Equilibrium conversions of TBA as a function of temperature
for different TBA/Ethanol ratios. s, TBA/Ethanol ) 0.1; - - -, TBA/Ethanol
) 0.2; ∆, TBA/Ethanol ) 0.3; ×, TBA/Ethanol ) 0.4; O, TBA/Ethanol )
0.5.
Table 11. Comparison of Experimental Equilibrium Conversions at
Different Space Times with Equilibrium Conversion (T ) 373 K)
a
space time (g ·min·cm-3
TBA conversion (%)
)
0.05
30
0.3
78
0.5
91
1
92
5.7
96
97
a Theoretically evaluated using eq 10.
kJ·mol-1) in the liquid phase by the method of Jensen and
Datta,10 according to eq 5. The molar heat capacities of TBA
in the liquid phase at different temperatures were estimated by
the Yuan and Stiel method33 for polar liquids using eq 8. By
substituting the CurveExpert 1.3 program, the molar heat
capacities were expressed as a function of temperature in cubic
polynomial form. They were also estimated at 298 K by using
ChemCad v.5.2. The heat capacity value at 298 K was compared
in Table 5 with the literature35-37 to justify the temperature
dependence form. The liquid phase enthalpy of formation of
TBA was available in the literature.35,38,39 It was also determined
from eq 2 and compared with the literature values in Table 6.
The estimation methods were also used for the calculations of
enthalpy of vaporization, liquid phase Gibbs free energy, and
enthalpy of formation of ethanol, ETBE, and H2O and compared
with literature values in Tables 7, 8, and 9, respectively. The
coefficients for the liquid phase heat capacity of ethanol and
H2O were estimated by eq 8, and the coefficients for ETBE
were estimated by the Sternling and Brown correlation according
to eq 7. They were also compared with the literature in Figures
2 and 3. Liquid phase heat capacities of ETBE are different for
separate studies. Small variations as stated in Figure 3 were
shown except for the curve obtained in Yuan and Stiel’s work.33
ETBE is a polar compound. As far as polar compounds are
considered, some factors such as short-range intermolecular
forces and quantum effects for low molecular weight substances
may cause deviations.33 Especially at low reduced temperatures,
Equilibrium conversion of TBA at different TBA/ethanol
ratios (0.1 to 0.5) estimated by the correlation proposed in this
work is given in Figure 5. In this figure, it is clearly seen that
equilibrium conversion of TBA has reached the highest value
for a molar ratio of TBA/ethanol ) 0.1 which corresponds to
the mostly used feed range in industry.
Experimental equilibrium TBA conversion results obtained
at 373 K at different space times, in the range of (0.05 to 5.7)
min·g·cm-3, are reported in Table 11. At long space times,
equilibrium is closely approached. The comparison between
experimental equilibrium conversions and theoretically calcu-
lated equilibrium conversions in the presence of various TBA/
ethanol molar ratios (0.1, 0.3, and 0.5) is given in Table 12.
For TBA/ethanol ) 0.1, the experimental equilibrium conversion
value (0.96) obtained at a space time of 5.7 min ·g·cm-3 was
very close to the corresponding predicted equilibrium conversion
value (0.97). All these values quite agree with each other.
Experimental and predicted equilibrium conversion values at
different temperatures in the range of (373 to 383) K are reported
in Table 12. Due to deactivation of Amberlyst-15 at around
393 K, maximum reaction temperature was selected as 383 K.
Conclusions
A new equilibrium constant relation was derived for the
synthesis of ETBE from TBA and ethanol. The present study
was thought to be a new and necessary approach for liquid phase
applications considering the scarcity of liquid phase thermo-
Table 12. Comparison of Experimental Equilibrium Conversions with Equilibrium Conversions From Predicted Correlation (Equation 10)
(Space Time ) 5.7 g ·min·cm-3
)
0.1
0.3
0.5
equilibrium
conversion
of TBA
(experimental)
(%)
equilibrium
conversion
of TBA
equilibrium
conversion
of TBA
(experimental)
(%)
equilibrium
conversion
of TBA
equilibrium
conversion
of TBA
(experimental)
(%)
equilibrium
conversion
of TBA
TBA/ethanol
molar ratio
T/K
(from correlation)
(%)
(from correlation)
(%)
(from correlation)
(%)
373
378
383
96
95
94
97
97
97
92
91
91
92
91
91
84
83
83
84
84
84

Journal of Chemical & Engineering Data, Vol. 54, No. 12, 2009 3213
CoP(T, l)/J · mol-1 · K-1 ) a + b(T/K) + c(T/K)2 +
d(T/K)3 (A8)
Here CoP(T,l) is the liquid phase molar heat capacity of the
species, and a, b, c, and d are the coefficients of molar heat
capacity expression. Integrating eq A6 and taking into account
eq A7 and eq A8 provides the following expressions10
dynamic data for this reaction. Thermodynamic data for the
formation enthalpy, Gibbs free energy, vaporization enthalphy,
and specific heat capacity were calculated for reactants and
products with the aid of an approach obtained by the combina-
tion of various methods. It was shown that the equilibrium
conversion values of the TBA-ethanol reaction are much higher
than the isobutene-ethanol reaction at temperatures over 380
K. Predicted conversion values agreed well with the experi-
mental results in the temperature range of (373 to 383) K.
2
3
4
T
K
∆b T
2 K
∆c T
3 K
∆d T
4 K
∆Ho(T, l) ) IH + ∆a
+
+
+
(
)
(
)
(
)
(
)
Acknowledgment
(A9)
The authors gratefully acknowledge Prof. Dr. Gulsen Dogu (Gazi
University, Department of Chemical Engineering) and Prof. Dr.
Timur Dogu (Middle East Technical University, Department of
Chemical Engineers) for their advice.
Here, IH is the constant of integration
To
K
∆b To
∆c To
2
3
I ≡ ∆Ho(To, L) - ∆a
-
-
-
( )
( )
( )
H
2
K
3
K
4
∆d To
Appendix
(A10)
( )
4
K
The equilibrium constant can be related to the thermodynamic
properties of the system for a reaction occurring at the reaction
temperature T, using eq A1
and
n
n
n
n
∆Go(T, l)
∆a ≡
V a ∆b ≡
V b ∆c ≡
V c ∆d ≡
V d
j j
∑
∑
∑
∑
j
j
j
j
j
j
K(l) ) exp -
(A1)
(
)
j)1
j)1
j)1
j)1
RT
(A11)
The standard Gibbs energy change for the liquid phase
reaction is computed from eq A2
Using eq A9 in eq A5 yields
n
∆Go(T, l)
∆a
R
T
K
∆b T
2R K
IH
∆Go(T, l) )
V ∆ Go(T, l)
(A2)
) -IK +
-
ln
-
-
∑
j
f
j
(
)
(
)
RT
R(T/K)
j)1
2
3
∆c T
∆d T
12R K
Here, ∆fGoj (T,l) is the Gibbs energy of formation of species j in
the liquid phase at the reaction temperature T. R is the gas
constant, 8.3143 J ·mol-1 ·K-1
-
(A12)
(
)
(
)
6R K
where IK is the constant of integration
The enthalpy of reaction at the temperature T is given by
eq 4.
IH
R(To/K)
∆a
R
To
K
∆b To
2R K
IK ≡ ln KTo
+
-
ln
-
-
( )
( )
n
∆c To
6R K
∆d To
2
3
∆Ho(T, l) ≡
V ∆ Ho(T, l)
(A3)
∑
j
f
j
-
(A13)
(A14)
( )
( )
j)1
12R K
The standard Gibbs free energy change for the liquid phase
reaction can also be obtained from the standard enthalpy and
entropy changes (So(T,l))
The use of eq A12 in eq A1 results in
IH
∆a
R
T
∆b T
2R K
ln K ) IK -
+
ln
+
+
(
)
(
)
R(T/K)
K
∆Go(T, l) ) ∆Ho(T, l) - T∆So(T, l)
(A4)
2
3
∆c T
∆d T
12R K
+
(
)
(
)
Temperature dependence of standard Gibbs free energy
change of reaction at constant pressure is obtained from
6R K
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o
∆Go(T, l)
∆Go(To, l)
1
R
∆H (T, l)
T
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Received for review February 23, 2009. Accepted June 26, 2009. The
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TUBITAK-BIDEB-2228 is also gratefully acknowledged.
JE900208N