Chemical equilibria study of the reacting system of the alkyl cumyl ether synthesis from n-alkanols and α-methylstyrene

Article abstract of DOI:10.1021/je000162a

Tremendous growth was observed in the 1990s in the use of oxygenates based on ethers such as MTBE and TAME. However, there has been a growing concern over the last years due to the contamination of groundwater by MTBE, because of the leaking storage tanks and pipelines. Thus, seeking for an alternative additives remains a significant problem. Further candidates for additives are alkyl cumyl ethers synthesized in the liquid phase over acid-functionalized ion-exchanged resin catalysts from n-alkanols and α-methylstyrene. The chemical equilibrium of the reactive systems n-alkanol + α-methylstyrene ? alkyl cumyl ether (alkyl is ethyl, propyl, and butyl) was investigated in the liquid phase at 300-383 K using a cation exchanger as heterogeneous catalyst. Enthalpies of reactions of alkyl cumyl ether synthesis in the liquid phase were obtained from the temperature dependence of thermodynamic equilibrium constant and agreed well with those reaction enthalpies derived from the values of standard molar enthalpies of formation in the liquid phase of ethyl cumyl ether by combustion calorimetry. The standard molar enthalpies of vaporization of alkyl cumyl ethers were obtained from the temperature dependence of the vapor pressure measured by using the transpiration method.

Full text of DOI:10.1021/je000162a

J . Chem. Eng. Data 2001, 46, 41-46
41
Ch em ica l Equ ilibr ia Stu d y of th e Rea ctin g System of th e Alk yl
Cu m yl Eth er Syn th esis fr om n -Alk a n ols a n d r-Meth ylstyr en e
Ser gey P . Ver evk in * a n d An d r ea s Hein tz
Department of Physical Chemistry, University of Rostock, Hermannstrasse 14, 18051 Rostock, Germany
The chemical equilibrium of the reactive systems n-alkanol + R-methylstyrene S alkyl cumyl ether (alkyl
is ethyl, propyl, and butyl) was studied in the liquid phase in the temperature range (300 to 383) K using
a cation exchanger as heterogeneous catalyst. Equilibrium ratios Kx obtained from concentrations of the
reaction participants in the mixtures with an excess amount of alkanol are practically independent of
the reactive mixture composition and can be identified with the thermodynamic equilibrium constant
Ka. Enthalpies of reactions ∆rH° of alkyl cumyl ether synthesis in the liquid phase were obtained from
m
the temperature dependence of Ka and showed a good agreement with those reaction enthalpies derived
from the values ∆fH° (l) of the reactions participants measured for alkyl cumyl ethers by combustion
m
calorimetry. The standard molar enthalpies of vaporization of alkyl cumyl ethers were obtained from the
temperature dependence of the vapor pressure measured by using the transpiration method. Resulting
values of ∆fH° (g) were used to prove the consistency of the experimental data and to derive strain
m
enthalpies of alkyl cumyl ethers. The strain effects were discussed in terms of deviations of ∆fH° (g) from
m
the group additivity rules.
1. In tr od u ction
γether
Ka )
Kx
(2)
γalkanolγR-MS
The use of oxygenates based on ethers such as methyl
tert-butyl ether (MTBE) and tert-amyl methyl ether (TAME)
has seen tremendous growth in the 1990s. These ethers
have been the oxygenates of choice, mainly due to the
economics and availability of feedstocks. However, over the
last years there has been a growing concern about con-
tamination of a groundwater by MTBE, due to leaking
storage tanks and pipelines. The major factor affecting the
impact of MTBE on potable water stems from its high
water solubility. Therefore, seeking alternative additives
remains an important problem. Beside the widely used
MTBE and TAME, further candidates are alkyl cumyl
ethers synthesized in the liquid phase over acid-function-
alized ion-exchanged resin catalysts from n-alkanols and
R-methylstyrene (see Figure 1).
where γi is the activity coefficient of component i depending
on the mixture composition. In our previous work3 we
investigated the chemical equilibrium in the liquid and
gaseous phases of the methyl cumyl ether synthesis reac-
tion. We performed a set of experiments to determine the
thermodynamic equilibrium constants and reaction enthal-
pies in the liquid as well as in the vapor phase and the
activity coefficients in the liquid phase. For that purpose
a static vapor-liquid equilibrium apparatus was used
which allowed simultaneous measurement of the liquid and
vapor compositions as well as the vapor saturation pressure
of the reactive mixture being in chemical equilibrium. From
the results obtained in this work3 we have drawn the
important conclusion that values of Kx in excess methanol
are indistinguishable from the thermodynamic constants
Ka for the methyl cumyl ether synthesis reaction within
the experimental error limits. Therefore, the assumption
is allowed that the reaction enthalpy obtained from the
temperature dependence of Kx measured above xMeOH > 0.5
It has been well documented in the literature that the
reacting systems of the alkyl ether syntheses such as those
of MTBE1 and TAME2 behave strongly nonideally. We have
established recently3 that the methyl cumyl ether synthesis
mixture also deviates distinctly from ideal behavior. It has
been observed that the equilibrium ratio Kx, defined as
xether
Kx )
(1)
xalkanolxR-MS
strongly depends on the composition of the equilibrium
mixture; xi in eq 1 are the mole fractions of reaction
participants in the liquid phase. The thermodynamic
equilibrium constant Ka in the liquid phase is related to
Kx by the following equation:
F igu r e 1. Reaction of the alkyl cumyl ether synthesis (R )
methyl, ethyl, propyl, and butyl) and ethers studied in this work:
ethyl cumyl ether (EtCE); propyl cumyl ether (PrCE); butyl cumyl
ether (BuCE).
* To whom correspondence should be addressed. E-mail:
sergey.verevkin@chemie.uni-rostock.de.
10.1021/je000162a CCC: $20.00 © 2001 American Chemical Society
Published on Web 11/03/2000

42 J ournal of Chemical and Engineering Data, Vol. 46, No. 1, 2001
provides the standard enthalpy of reaction ∆rH° (l) as if it
from the results of the equilibrium study of the reaction of
its synthesis.
m
would have been obtained from Ka values. It is of interest
to know whether such an assumption could be generalized
for all ether synthesis reactions. Thus, as an extension of
our previous work we have performed further systematic
investigation of the chemical equilibrium in the reacting
systems of the alkyl cumyl ether synthesis such as ethyl
cumyl ether (EtCE), propyl cumyl ether (PrCE), and butyl
cumyl ether (BuCE) (see Figure 1). We report new experi-
mental data of the reaction enthalpies derived from the
temperature dependence of equilibrium constants mea-
sured in the reactive mixtures with an excess of alkanol.
To prove the validity of the procedure used, these data on
2.2. Ch em ica l Equ ilibr iu m Stu d y. Glass vials with
screwed caps were filled two-thirds full with the initial
liquid mixture of alkanol and R-methylstyrene. The cation-
exchange resin Amberlist 15 (Aldrich) in H+ form was
added as a solid catalyst. The quantity of catalyst was
approximately 10% from the weight of the mixture. The
vial was thermostated at Ti ( 0.1 K and periodically
shaken. After definite time intervals, the vial was cooled
rapidly in ice and opened. A sample for the GC analysis
was taken from the liquid phase using a syringe. The
thermostating of vial was then continued at the same
temperature. The samples were taken successively until
no further change of the compositions was observed,
indicating that the chemical equilibrium was established.
∆rH° (l) are compared with those calculated from differ-
m
ences of the enthalpies of formation of the reaction par-
ticipants. For the latter purpose, standard molar enthalpies
of formation in the liquid phase ∆fH° (l) of ethyl cumyl
m
The compositions of the reaction mixtures were analyzed
with a Hewlett-Packard gas chromatograph 5890 Series
II equipped with a flame ionization detector and Hewlett-
Packard 3390A integrator. The carrier gas (nitrogen) flow
was 12.1 cm3‚s-1. A capillary column HP-5 (stationary
phase cross-linked 5% PH ME silicone) was used with a
column length of 30 m, an inside diameter of 0.32 mm, and
a film thickness of 0.25 µm. The standard temperature
program of the GC was T ) 353 K for 180 s followed by a
heating rate of 0.167 K‚s-1 to T ) 523 K. Response factors
of all reagents were determined using calibration mixtures
of the corresponding components prepared gravimetrically.
ether and butyl cumyl ether were additionally obtained
from calorimetrically measured enthalpies of combustion.
Further support of the reliability of the procedures applied
in this work is expected from quantitative analysis of
standard molar enthalpies of formation in the gaseous
phase ∆fH° (g). Values of ∆fH° (g) of alkyl cumyl ethers
m
m
were obtained from calorimetrically measured ∆fH° (l)
m
and their enthalpies of vaporization measured by a tran-
spiration method. Thus, the systematic investigation of the
alkyl cumyl ethers synthesis reactions would be of value
for three reasons. First, if good agreement with the
standard reaction enthalpies, ∆rH° (l), obtained from the
m
2.3. Com bu stion Ca lor im etr y. For measurements of
the energies of combustion of the alkyl cumyl ethers, an
isoperibolic calorimeter5 equipped with a static bomb and
an isothermal water jacket was used. The temperature in
the water jacket was maintained within (0.0015 K with
the help of a high-precision mercury contact thermometer.
To exclude traces of water in the liquid samples used for
the combustion experiments, the purified samples were
dried over molecular sieves and distilled once more prior
to combustion. Each sample was sealed in a container to
avoid oxidation and contamination with moisture. In the
present study, we used commercially available polyethene
ampules (Fa. NeoLab, Heidelberg) of 1 cm3 volume as the
sample container for liquids in order to reduce the capillary
effect and make the encapsulation easier. The liquid
sample was transferred to a polyethene ampule with a
syringe. The narrow neck of the container was compressed
with special tweezers and sealed by heating with hot air.
Then, the loaded container was placed in the platinum
crucible within the bomb, knotted to the wire, and burned
in oxygen at a pressure of 3.04 MPa with 1.00 g of water
added to the bomb. The ignition was performed by a
capacitor discharged through a platinum wire. The ignition
of the sample and the recording of the temperature rise
were performed automatically using an interface connec-
tion to a computer. Thermometric measurements were
carried out using 100 Ω Pt-resistance thermometers by
recording the amplified signal with a digital voltmeter. The
initial temperature of the combustion experiments was
298.15 K for each experiment. The corrected temperature
rise was calculated using recommendations from the
literature.6 The energy equivalent of the calorimeters ꢀcalor
was determined with a standard reference sample of
benzoic acid (sample SRM 39i, N.I.S.T.). From seven
temperature dependence of Kx is found, it would confirm
that the reliability and accuracy of our procedures are
satisfactory. Second, it would allow us to establish the
guideline of the thermodynamic treatment of the equilib-
rium constants in the strongly nonideal reactive systems.
Third, experimental values of ∆fH° (g) would provide use-
m
ful information on the strain effects and the relation
between structure and properties of alkyl cumyl ethers. The
results of the study also could be aimed at an improvement
of the Benson4 group-contribution methodology.
2. Exp er im en ta l Section
2.1. Ma ter ia ls. R-Methylstyrene (R-MS), ethanol (EtOH),
propan-1-ol (PrOH), and butan-1-ol (BuOH) (water content
less than 0.01%) were purchased from Merck. GC analyses
of the as-purchased samples gave a purity > 99.9% in
agreement with specifications. Alkyl cumyl ethers (Figure
1) were synthesized via alkylation of an appropriate
n-alkanol with R-methylstyrene in the presence of a
catalytic amount of cation-exchange resin in H+ form
(Amberlist 15, Aldrich) at room temperature. Prior to the
experiments the cation-exchange resin Amberlist 15 in H+
form was dried for 8 h at 383 K in a vacuum oven at
reduced pressure.
The pure samples of alkyl cumyl ethers were obtained
by repeated distillations using a spinning-band column at
reduced pressure under N2, after being dried with molec-
ular sieves (0.4 nm). No impurities could be detected in
ethyl and butyl cumyl ethers by GC. In the sample of propyl
cumyl ether about 0.8% of nonidentified components has
been found by GC. Repeated distillations did not improve
the quality of the specimen. Thus, the sample of propyl
cumyl ether with the purity 99.2% satisfies only the
requirements for the determination of vaporization enthal-
pies but not the requirements needed in the combustion
experiments. As a consequence no combustion experiments
were performed with propyl cumyl ether, and the enthalpy
experiments, ꢀcalor was measured to be 15 296.0 ( 2.3 J ‚K-1
.
The internal volume of the bomb was 328.9 cm3. Nitrogen
oxides were not formed in the calibration experiments due
to the high purity of the oxygen used and preliminary bomb
flushing. For converting the energy of the actual bomb
of formation ∆fH° (l) for this compound was obtained only
m

J ournal of Chemical and Engineering Data, Vol. 46, No. 1, 2001 43
Ta ble 1. Exp er im en ta lly Deter m in ed Com p osition of
Ta ble 2. Exp er im en ta lly Deter m in ed Com p osition of
Equ ilibr iu m Mixtu r es a n d Kx Va lu es in th e Liqu id P h a se,
Ca lcu la ted fr om Eq 1, for th e System Eth a n ol +
r-Meth ylstyr en e S Eth yl Cu m yl Eth er a
Equ ilibr iu m Mixtu r es a n d Kx Va lu es in th e Liqu id P h a se,
Ca lcu la ted fr om Eq 1, for th e System P r op a n ol +
r-Meth ylstyr en e S P r op yl Cu m yl Eth er a
b
b
T/ K
n
xEtOH
xR-MS
xEtCE
Kx
T/ K
n
xPrOH
xR-MS
xPrCE
Kx
300.1
10
11
10
9
12
14
16
11
12
8
9
10
9
10
11
9
0.2984
0.6243
0.7710
0.8192
0.8478
0.2692
0.5376
0.7658
0.8146
0.2280
0.3783
0.5948
0.7641
0.8409
0.4485
0.6417
0.7572
0.8550
0.4775
0.5884
0.7100
0.7716
0.8633
0.5961
0.7354
0.8446
0.2432
0.1274
0.0722
0.0541
0.0440
0.3142
0.1883
0.0801
0.0591
0.5307
0.3935
0.2596
0.1346
0.0853
0.3728
0.2309
0.1671
0.0963
0.4398
0.3306
0.2211
0.1730
0.1012
0.3469
0.2208
0.1252
0.4563
0.2483
0.1568
0.1267
0.1082
0.4167
0.2741
0.1541
0.1262
0.2413
0.2282
0.1456
0.1013
0.0738
0.1787
0.1273
0.0757
0.0487
0.0827
0.0810
0.0689
0.0554
0.0355
0.0570
0.0438
0.0302
6.24 ( 0.33
3.12 ( 0.12
2.82 ( 0.15
2.86 ( 0.13
2.90 ( 0.17
4.93 ( 0.28
2.71 ( 0.09
2.51 ( 0.11
2.62 ( 0.12
1.99 ( 0.16
1.53 ( 0.09
0.94 ( 0.07
0.98 ( 0.06
1.03 ( 0.05
1.07 ( 0.08
0.86 ( 0.07
0.60 ( 0.04
0.59 ( 0.05
0.39 ( 0.02
0.42 ( 0.03
0.44 ( 0.02
0.41 ( 0.03
0.41 ( 0.03
0.27 ( 0.02
0.27 ( 0.03
0.29 ( 0.03
300.1
10
11
13
10
11
8
12
9
11
16
10
9
15
14
12
11
7
13
12
10
10
11
0.0935
0.1898
0.2870
0.6054
0.7466
0.8446
0.9040
0.3244
0.5848
0.6022
0.4269
0.5211
0.6315
0.6654
0.4801
0.5694
0.6883
0.7198
0.5417
0.6382
0.6945
0.7795
0.3711
0.3210
0.2584
0.1351
0.0724
0.0399
0.0234
0.3739
0.2027
0.1935
0.3524
0.3247
0.2392
0.1994
0.4068
0.3272
0.2210
0.1955
0.3734
0.2860
0.2371
0.1647
0.5354
0.4892
0.4546
0.2595
0.1809
0.1155
0.0726
0.3017
0.2124
0.2043
0.2207
0.1542
0.1293
0.1352
0.1131
0.1034
0.0906
0.0846
0.0849
0.0758
0.0684
0.0558
15.43 ( 0.36
8.03 ( 0.25
6.13 ( 0.11
3.17 ( 0.18
3.35 ( 0.18
3.43 ( 0.11
3.43 ( 0.12
2.49 ( 0.08
1.79 ( 0.06
1.75 ( 0.04
1.47 ( 0.05
0.91 ( 0.03
0.86 ( 0.05
1.02 ( 0.02
0.58 ( 0.04
0.55 ( 0.05
0.60 ( 0.02
0.60 ( 0.05
0.42 ( 0.04
0.41 ( 0.04
0.42 ( 0.05
0.43 ( 0.02
303.1
333.1
323.1
343.1
353.1
373.1
363.1
383.1
12
11
8
9
11
10
13
11
10
11
a
393.1
T is the temperature of the investigation; n is the number of
determinations of the composition within the time of the equilib-
rium study; xi is the mole fraction measured chromatographically.
b
Uncertainty is the standard deviation.
a
T is the temperature of the investigation; n is the number of
determinations of composition within the time of the equilibrium
study; xi is the mole fraction measured chromatographically.
Ta ble 3. Exp er im en ta lly Deter m in ed Com p osition of
Equ ilibr iu m Mixtu r es a n d Kx Va lu es in th e Liqu id P h a se,
Ca lcu la ted fr om th e Eq 1, for th e System Bu ta n ol +
r-Meth ylstyr en e S Bu tyl Cu m yl Eth er a
b
Uncertainty is the standard deviation.
process to that of the isothermal process and reducing to
standard states, the conventional procedure7 was applied.
The sample masses of alkyl cumyl ethers were reduced in
vacuum, taking into consideration the density value F(293)
) 0.921 g‚cm-3 for ethyl cumyl ether and F(293) ) 0.912
g‚cm-3 for butyl cumyl ether, which were determined in a
calibrated 10 cm3 pycnometer. The energies of combustion
of cotton thread, ∆cu°(CH1.774O0.887) ) -(16945.2 ( 4.2)
b
T/ K
n
xBuOH
xR-MS
xBuCE
Kx
300.1
15
12
13
12
12
11
10
11
10
16
11
12
11
12
13
14
12
11
13
12
11
15
16
11
10
9
0.1102
0.2804
0.4025
0.5121
0.6029
0.6281
0.7411
0.8266
0.8886
0.5872
0.7678
0.8554
0.4727
0.6322
0.7201
0.8160
0.8514
0.8908
0.9246
0.5131
0.6062
0.6870
0.7610
0.8748
0.6417
0.7343
0.8069
0.8922
0.4412
0.3457
0.2709
0.1847
0.1400
0.1297
0.0813
0.0483
0.0297
0.2271
0.1122
0.0661
0.3780
0.2345
0.1650
0.1073
0.0843
0.0612
0.0431
0.3735
0.2864
0.2172
0.1640
0.0822
0.2918
0.2144
0.1485
0.0846
0.4486
0.3739
0.3266
0.3021
0.2571
0.2422
0.1746
0.1241
0.0817
0.1857
0.1200
0.0785
0.1493
0.1333
0.1149
0.0767
0.0643
0.0480
0.0323
0.1134
0.1075
0.0959
0.0750
0.0430
0.0665
0.0514
0.0446
0.0232
9.23 ( 0.33
3.86 ( 0.11
3.00 ( 0.09
3.19 ( 0.15
3.05 ( 0.08
2.97 ( 0.15
2.94 ( 0.07
3.10 ( 0.05
3.10 ( 0.06
1.39 ( 0.08
1.39 ( 0.07
1.39 ( 0.06
0.84 ( 0.05
0.90 ( 0.06
0.97 ( 0.04
0.88 ( 0.09
0.90 ( 0.07
0.88 ( 0.03
0.81 ( 0.04
0.59 ( 0.03
0.62 ( 0.02
0.64 ( 0.01
0.60 ( 0.03
0.60 ( 0.01
0.36 ( 0.05
0.33 ( 0.03
0.37 ( 0.06
0.31 ( 0.03
J ‚g-1, and polyethene, ∆cu°(CH1.930) ) -46361.0 ( 3.1 J ‚g-1
,
323.1
343.1
were measured earlier. The molar masses of alkyl cumyl
ethers were evaluated from the relative atomic masses of
the elements.8
2.4. Tr a n spir a tion Meth od . The enthalpies of vapor-
ization of alkyl cumyl ethers were determined using the
method of transpiration in a saturated N2 stream and
applying the Clausius-Clapeyron equation. The method
has been described before9 and has proven to give results
in excellent agreement with those of other established
techniques for determining vapor pressures of pure sub-
stances in the range 0.005 to ∼10 000 Pa and enthalpies
of vaporization from the temperature dependence of the
vapor pressure.
363.1
383.1
a
11
12
3. Resu lts
3.1. Equ ilibr iu m Con sta n ts a n d Rea ction En th a l-
pies. The experimental results of the chemical equilibrium
study of the alkyl cumyl ethers’ synthesis are listed in
Tables 1-3. Inspection of these Tables and Figure 2 shows
that Kx values are almost independent of the mole fraction
of alkanol if xAlkOH > 0.5. The same behavior has already
been observed for the methyl cumyl ether synthesis reac-
tion3 also presented in Figure 2. For this system it has been
shown that Kx ≈ Ka for xMeOH > 0.5. Therefore, the
assumption is justified that the enthalpy of reaction
obtained from the temperature dependence of Kx measured
above xAlkOH > 0.5 provides the standard enthalpy of
T is the temperature of the investigation; n is the number of
determinations of composition within the time of the equilibrium
study; xi is the mole fraction measured chromatographically.
b
Uncertainty is the standard deviation.
reaction ∆rH° (l). For all three systems studied, a plot of lg
m
Kx as a function of 1/T with Kx values obtained from the
glass vials technique at values of xAlkOH between 0.6 and
0.8 gives straight lines which are almost parallel to those
of the methyl cumyl ether synthesis (see Figure 3). Ex-
perimental values of Kx were approximated as a function
of temperature by the linear equation lg Kx ) a + b(T/K)-1

44 J ournal of Chemical and Engineering Data, Vol. 46, No. 1, 2001
Ta ble 4. Com p a r ison of th e Th er m od yn a m ic F u n ction s ∆rH° a n d ∆rS° of th e Alk yl Cu m yl Eth er Syn th esis Rea ction s in
m
m
th e Liqu id P h a se a t T ) 298.15 K; lg Kx ) a + b(1000T/K)-1
a
b
c
∆rH°
∆rH°
Τ
∆rS° a
m(equilibrium)
m(calorimetry)
m
alkyl group
kJ ‚mol-1
kJ ‚mol-1
a
b
K
J ‚K-1‚mol-1
methyl
ethyl
propyl
butyl
-22.2 ( 0.5d
-24.9 ( 1.2
-24.5 ( 1.6
-24.1 ( 2.3
-24.0 ( 2.6d
-24.0 ( 2.7
-2.961 ( 0.003d
-3.88 ( 0.01
-3.72 ( 0.01
-3.74 ( 0.01
1.16 ( 0.01d
1.30 ( 0.03
1.28 ( 0.04
1.26 ( 0.06
357.1d
346.6
341.6
341.6
-56.7 ( 0.3d
-74.3 ( 1.4
-71.2 ( 2.0
-71.6 ( 3.0
-25.1 ( 2.8
a
Derived from the temperature dependence of Kx (it was assumed21 that the enthalpy of reaction changes on passing from the average
temperature of the experimental range to T ) 298.15 K are negligible within the boundaries of the uncertainties); uncertainty is the
b
standard deviation. Calculated from the enthalpies of formation of the reaction participants, measured by combustion calorimetry. c The
d
average temperature of the equilibrium study. Taken from our previous work.3
Ta ble 5. Resu lts for a Typ ica l Com bu stion Exp er im en t
a t T ) 298.15 K (p° ) 0.1 MP a )a
ethyl cumyl ether butyl cumyl ether
m (substance)b/g
m′ (cotton)b/g
0.303 49
0.000 96
0.231 12
1.472 85
-22 528.71
10.40
16.27
10 714.95
-38 820.5
0.311 28
0.001 11
0.229 64
1.511 09
-23 113.6
10.61
18.81
10 646.33
-39 939.6
m′′ (polythen)b/g
c
∆Tc /K
(ꢀcalor)(-∆Tc)/J
∆Ucorrd/J
-m′∆cu′/J
-m′′∆cu′′/J
∆cu° (substance)/(J ‚g-1
)
a
For the definition of the symbols see ref 7: Vbomb ) 0.3289
dm3; pi ) 3.04 MPa; mi
) 1.00 g; Eignition ) 5.4 J ; mplatin )
gas
b
water
9.64 g. Masses obtained from apparent masses. c ∆Tc ) Tf - Ti
d
+ ∆Tcorr
.
∆Ucorr, the correction to standard state, is the sum of
items 81 to 85, 87 to 90, 93, and 94 in Hubbard et al.7
F igu r e 3. Concentration equilibrium constants Kx at a mole
fraction xalcohol between 0.6 and 0.8 as a function of temperature.
lated according to the established procedure7 using the
molar enthalpies of formation for H2O(l) and CO2(g) as
recommended by the IUPAC.10 The assigned standard
deviations of the mean values of ∆fH° include the uncer-
m
tainties from calibration, from the combustion energies of
the auxiliary materials, and from the enthalpies of forma-
tion of the reaction products H2O and CO2.
3.3. En th a lpies of Va por iza tion . Results obtained
from measurements of the vapor pressure p of alkyl cumyl
ethers by the transpiration method are presented in Table
7. To ensure that vapor saturation is reached in the carrier
gas at each specified temperature, the experiments were
carried out at two nitrogen flow rates, 0.22 and 0.42
cm3‚s-1. No difference of the results was observed. The
results were treated together and are presented in Table
7. Because of the slight deviations of the average temper-
atures of measurement from the reference temperature
298.15 K, the observed values of the enthalpy of vaporiza-
tion had to be corrected to this reference temperature. The
corrections were estimated with the help of the correction
formula:
F igu r e 2. Concentration equilibrium constants Kx for the alkyl
cumyl ether synthesis reaction as a function of alkanol mole
fraction x in the equilibrium mixture at T ) 300.1 K.
using the method of least squares. The slopes of these lines
when multiplied by the gas constant afford the standard
enthalpy of reaction ∆rH° of the alkyl cumyl ether syn-
m
thesis reaction in the liquid or gaseous phase, and the
intercept gives the standard entropy of reaction ∆rS° .
m
Numerical results are presented in Table 4. The errors in
the thermodynamic functions from the equilibrium study
are given by the standard deviations for the meaningful
level 0.05.
{∆gl H° ( T ) - ∆gl H° (298.15 K)}/(kJ ‚mol-1) )
m
m
-5.44 × 10-2{( T /K) - 298.15} (3)
3.2. En er gies of Com bu stion a n d En th a lpies of
For m a tion . The results for a typical combustion experi-
ment of alkyl cumyl ethers are given in Table 5. The
individual values of the standard specific energies of
combustion, ∆cu°, are given as follows (in J ‚g-1): ethyl
cumyl ether 38 823.7, 38 820.5, 38 820.1, 38 824.3, 38 817.6,
and 38 822.6; butyl cumyl ether: 39 941.0, 39 940.1,
39 939.6, 39 938.1, 39 937.5, and 39 939.8. The mean values
of ∆cu° and their standard deviations are presented in
following the recommendation of Chickos et al.,11 where
is the temperature averaged over the temperature
T
range covered by the experiments. Using eq 3, the observed
value of ∆gl H° ( T ), the standard molar enthalpy of vapor-
m
ization at T ) 298.15 K, was calculated (see Tables 6 and
7).
4. Discu ssion
Table 6. Standard enthalpies of combustion ∆cH° and
4.1. Com pa r ison of th e Rea ction En th a lpies Ob-
ta in ed fr om Equ ilibr iu m Stu d ies a n d fr om Com bu s-
m
enthalpies of formation ∆fH° (see Table 6) were calcu-
m

J ournal of Chemical and Engineering Data, Vol. 46, No. 1, 2001 45
Ta ble 6. Th er m och em ica l Resu lts a t T ) 298.15 K (p° ) 0.1MP a )
∆cu°(liq)
J ‚g-1
∆cH° (liq)
kJ ‚mol-1
∆fH° (liq)
kJ ‚mol-1
∆gl H°
kJ ‚mol-1
∆fH° (g)
kJ ‚mol-1
m
m
m
m
methyl cumyl ether
ethyl cumyl ether
propyl cumyl etherb
butyl cumyl ether
-38 168.9 ( 2.7a
-38 821.5 ( 2.5
-5742.5 ( 2.1a
-6385.1 ( 2.3
-193.4 ( 2.5a
-230.2 ( 2.7
-257.4 ( 2.4c
-282.3 ( 3.1
52.85 ( 0.16a
54.70 ( 0.52
59.31 ( 0.20
63.84 ( 0.50
-140.5 ( 2.5a
-175.5 ( 2.7
-198.1 ( 2.4
-218.5 ( 3.1
-39 939.3 ( 0.5
-7691.6 ( 2.6
a
b
Data from our previous work.3 Compound was not pure enough for the combustion experiments (see experimental part). c Calculated
from the results of the chemical equilibrium study (see text).
Ta ble 7. Resu lts fr om Mea su r em en ts of th e Va p or P r essu r e p of Alk yl Cu m yl Eth er s Usin g th e Tr a n sp ir a tion Meth od
Ta/K
mb/mg
V(N2)c/dm3
pd/Pa
Ta/K
mb/mg
V(N2)c/dm3
pd/Pa
Ethyl Cumyl Ether ln(p/Pa) ) (26.03 ( 0.21) - (6594 ( 62)(T/K)-1
278.3
283.3
288.2
288.4
293.2
293.5
298.2
1.85
2.11
2.27
2.18
2.80
2.22
2.78
2.77e
2.07e
1.56f
1.42e
1.30f
0.959e
0.869
10.43
15.72
22.68
23.52
33.30
35.23
48.99
298.4
303.2
303.3
308.1
308.4
313.2
1.53
2.99
1.56
3.50
1.60
1.69
0.446e
0.646f
0.311e
0.534f
0.225e
0.180e
52.31
70.59
76.06
99.71
107.5
142.4
∆gl H° ( T )295.7 K) ) (54.83 ( 0.52) kJ ‚mol-1; ∆lgH° (298.15 K) ) (54.70 ( 0.52) kJ ‚mol-1
m
m
Propyl Cumyl Ether ln(p/Pa) ) (26.92 ( 0.08) - (7110 ( 24)(T/K)-1
278.3
293.2
298.2
301.3
304.3
307.3
8.11
5.54
5.37
5.79
6.97
5.37
30.05
5.33
3.43
2.88
2.82
1.72
3.847
14.55
21.83
28.05
34.46
43.45
310.2
313.2
316.2
319.2
322.2
325.2
5.82
6.30
6.19
6.00
6.01
6.22
1.48
1.28
1.02
0.804
0.660
0.559
54.75
68.52
84.39
103.8
126.7
154.7
∆gl H° ( T )301.7 K) ) (59.12 ( 0.20) kJ ‚mol-1; ∆lgH° (298.15 K) ) (59.31 ( 0.20) kJ ‚mol-1
m
m
Butyl Cumyl Ether ln(p/Pa) ) (27.85 ( 0.21) - (7678 ( 60)(T/K)-1
278.3
283.1
283.1
288.2
290.2
293.2
293.5
298.2
0.562
2.93
1.32
0.823
1.16
0.601
1.20
6.09f
19.11e
8.71f
3.13f
3.57e
1.44f
2.81e
1.42f
1.240
2.002
2.005
3.441
4.211
5.429
5.538
8.235
298.3
303.2
303.4
308.2
308.3
313.2
318.3
1.37
0.850
1.76
1.19
1.23
1.27
1.09
2.16e
8.205
13.01
12.43
18.52
18.59
27.90
40.59
0.845f
1.83e
0.830f
0.855e
0.585e
0.345e
0.902
∆gl H° ( T )298.1 K) ) (63.84 ( 0.50) kJ ‚mol-1; ∆lgH° (298.15 K) ) (63.84 ( 0.50) kJ ‚mol-1
m
m
Temperature of saturation, N2 gas flow 0.22-0.42 cm3‚s-1
.
Mass of transferred sample condensed at T ) 243 K. c Volume of nitrogen
a
b
used to transfer mass m of sample. Vapor pressure at temperature T, calculated from m and the residual vapor pressure at 243 K.e N2
d
gas flow 0.42 cm3‚s-1
. .
f N2 gas flow 0.22 cm3‚s-1
Ta ble 8. Str a in En th a lp ies of Cu m yl Der iva tives a t T ) 298.15 K
∆fH° (g)(calc)a
HS
b
∆fH° (g)(exp)
m
m
kJ ‚mol-1
kJ ‚mol-1
kJ ‚mol-1
cumyl alcohol (R,R-dimethylbenzyl alcohol)
methyl cumyl ether
ethyl cumyl ether
propyl cumyl ether
butyl cumyl ether
-168.1 ( 2.4c
-140.5 ( 2.5d
-175.5 ( 2.7
-198.1 ( 2.4
-218.5 ( 3.1
-176.8
-151.4
-184.5
-205.9
-227.4
8.7
10.9
9.0
7.8
8.9
a
b
Calculated as the sum of strain-free increments (see text). Strain enthalpy of cumyl derivatives HS ) ∆fH° (g)(exp) - ∆fH° (g)
m
m
(calc). c The result was taken from Verevkin.19 The result was taken from Heintz and Verevkin.3
d
tion Exper im en ts. We investigated the chemical equilib-
rium of reactions of the synthesis of alkyl cumyl ethers from
n-alkanols and R-methylstyrene in the temperature range
(300 to 393) K and derived the standard enthalpies of these
reactions in the liquid phase. The validity of the results
obtained from the chemical equilibrium study can be
verified by comparison with the values of the reaction
enthalpies calculated from the formation enthalpies of the
reaction participants. For this purpose the standard molar
kJ ‚mol-1. Data for propanol, ∆fH° (l) ) (-302.5 ( 0.2)
m
kJ ‚mol-1, and for butanol, ∆fH° (l) ) (-327.0 ( 0.2)
m
kJ ‚mol-1, were taken from Mosselman and Dekker.14 These
data were used to calculate independently ∆rH°
m(calorimetry)
of the alkyl cumyl ether synthesis reaction in the liquid
phase (e.g. for ethyl cumyl ether):
∆rH° (l)(calorimetry) ) ∆fH° (l)(EtCE)
-
m
m
∆fH° (l)(EtOH) - ∆fH° (l)(R-MS) ) -(24.0 ( 2.6) kJ ‚mol-1
m
m
enthalpies of formation ∆fH° (l) of ethyl and butyl cumyl
m
ethers at 298.15 K were measured by means of combustion
calorimetry in this work (Table 6). Further experimental
data necessary for comparison are available in the litera-
The comparison with experimental values obtained from
the chemical equilibrium study is given in Table 4. The
ture: for R-methylstyrene12 ∆fH° (l) ) (70.07 ( 0.82)
calculated values of ∆rH° (l)(calorimetry) for the reactions of
m
m
kJ ‚mol-1 and for ethanol13 ∆fH° (l) ) (-277.0 ( 0.3)
methyl, ethyl, and butyl cumyl ethers are in very close
m

46 J ournal of Chemical and Engineering Data, Vol. 46, No. 1, 2001
agreement (within the boundaries of experimental uncer-
devoid of sterical interaction and apparently does not
tainties) with those ∆rH° (l)(equilibrium) derived from the
contribute to strain. Because of this, one can ensure that
no additional group-additivity parameters or correction
terms are necessary (besides the correction for strain HS
) 10.9 kJ ‚mol-1 like in tert-butylbenzene) for the group-
m
chemical equilibria studies. Hence, the important assump-
tion that values of Kx in excess alkanol are indistinguish-
able from the thermodynamic constants Ka could be
generalized for ether synthesis reactions.
contribution correlation for ∆fH° (g) of alkyl cumyl ethers.
m
The thermodynamic consistency observed allows us to
calculate the enthalpy of formation of propyl cumyl ether
Liter a tu r e Cited
∆fH° (l) ) -(257.4 ( 2.4) kJ ‚mol-1 from the known en-
m
(1) Izquierdo, J . F.; Cunill, F.; Vila, M.; Iborra, M.; Tejero, J .
Equilibrium Constants for Methyl tert-Butyl Ether and Ethyl tert-
Butyl Ether Liquid-Phase Synthesis Using C4 Olefinic Cut. Ind.
Eng. Chem. Res. 1994, 33, 2830-2835.
(2) Rihko, L.; Linnekoski, J . A.; Krause, A. Reaction Equilibria in
the Synthesis of 2- Methoxy-2-Methylbutane in the Liquid Phase.
J . Chem. Eng. Data 1994, 39, 700-704.
(3) Heintz, A.; Verevkin, S. P. Simultaneous study of chemical and
vapor-liquid equilibria in the reacting system of the methyl cumyl
ether synthesis from methanol and R-methyl- styrene. Fluid
Phase Equilib., in press.
thalpies of formation of propanol and R-methylstyrene and
the standard enthalpy of reaction obtained from the
temperature dependence of Kx (see Table 6).
4.2. Str a in En th a lpies HS of Alkyl Cu m yl Eth er s. An
important test to establish the validity of the experimental
and calculation procedures presented in this paper provides
the comparison of strain enthalpies of alkyl cumyl ethers,
which could be derived from their gaseous standard molar
enthalpies of formation ∆fH° (g) at 298.15 K (Table 6).
m
(4) Benson, S. W. Thermochemical Kinetics; Wiley: New York, 1976,
Indeed, the methyl, ethyl, propyl, and butyl cumyl ethers
listed in Table 6 present a typical example of the homologi-
cal. It is well established that for homologic rows such as
p 274.
(5) Simirsky, V. V.; Kabo, G. J .; Frenkel, M. L. Additivity of the
enthalpies of formation of urea derivatives in the crystalline state.
J . Chem. Thermodyn. 1987, 19, 1121-1927.
alkanes or alkanols14 the enthalpic contribution to ∆fH°
m
(6) Skuratov, S. M.; Kolesov, V. P.; Vorobe´v, V. F. Thermochemistry;
(g) from the CH2 group should remain constant. In other
words, no additional strain interactions in a molecule are
expected by passing from methyl to butyl cumyl ether. The
Moscow: Moscow State University, 1966.
(7) Hubbard, W. N.; Scott, D. W.; Waddington, G. In Experimental
Thermochemistry; Rossini, F. D., Ed.; Interscience: New York,
1956, pp 75-127.
(8) Atomic weights of the elements. Pure Appl. Chem. 1994, 66,
2423-2444.
resulting values of ∆fH° (g) of alkyl cumyl ether calculated
m
as the sum of ∆fH° (l) and ∆gl H° are shown in Tables 6
m
m
and 8.
(9) Verevkin, S. P. Measurement and Prediction of the Monocarbox-
ylic Acids Thermochemical Properties. J . Chem. Eng. Data 2000,
45, 953-960.
We define the strain enthalpy HS of a molecule as the
difference between the experimental standard enthalpy of
formation ∆fH° (g) and the calculated sum of the strain-
m
(10) CODATA Key Values for Thermodynamics; Cox, J . D., Wagman,
free Benson type increments4 for this molecule. The strain-
free increments for the calculation of enthalpies of forma-
tion of alkanes,15 alkylbenzenes,16 and ethers17,18 are
already well established. By using these group-additivity
D. D., Medvedev, V. A., Eds.; Hemisphere: New York, 1989.
(11) Chickos, J . S.; Hosseini, S.; Hesse, D. G.; Liebman, J . F. Heat
Capacity Corrections to a Standard State: A Comparison of New
and Some Literature Methods for Organic Liquids and Solids.
Struct. Chem. 1993, 4, 271-278.
(12) Verevkin, S. P. Thermochemical investigation on R-methyl-styrene
and parent phenyl substituted alkenes. Thermochim. Acta 1999,
326, 17-25.
parameters and the values of ∆fH° (g) of cumyl deriva-
m
tives (Table 8), their values of strain enthalpies HS
)
{∆fH° (g) - ∑ increments} have been estimated (Table 8).
m
All alkyl cumyl ethers studied here are very similarly
(13) Chao, J .; Rossini, F. D. Heats of combustion, formation, and
isomerization of nineteen alkanols. J . Chem. Eng. Data 1965, 10,
374-379.
(14) Mosselman, C.; Dekker, H. Enthalpies of formation of n-alkan-
1-ols. J . Chem. Soc., Faraday Trans. 1 1975, 417-424.
(15) Schleyer, P. v. R.; Williams, J . E.; Blanchard, K. B. The evaluation
of strain in hydrocarbons. The strain in adamantane and its
origin. J . Am. Chem. Soc. 1970, 92, 2377-2386.
(16) Beckhaus, H.-D. Force Field for the Calculation of Structure and
Enthalpy of Formation of Alkylbenzenes. Chem. Ber. 1983, 116,
86-96.
(17) Rakus, K.; Verevkin, S. P.; Peng, W.-H.; Beckhaus, H.-D.;
Ru¨chardt, C. Geminal Substituent Effects. 11 The Anomeric Effect
in Orthoesters. The Concept of Geminal Pairwise Interactions for
the Interpretation of Enthalpies of Formation. Liebigs Ann. 1995,
2059-2067.
(18) Verevkin, S. P.; Beckhaus, H.-D.; Belen’kaja, R. S.; Rakus, K.;
Ru¨chardt, C. Geminal Substituent Effects. 9. Enthalpies of
Formation and Strain Free Increments of Branched Esters and
Ethers. Thermochim. Acta 1996, 279, 47-64.
(19) Verevkin, S. P. Strain effects in phenyl substituted methanes.
Geminal interaction between phenyl and electron releasing
substituent in benzylamines and benzyl alcohols. J . Chem. Eng.
Data 1999, 44, 1245-1251.
strained by about 10 kJ ‚mol-1 (Table 8). This fact is a
further indication that the data for ∆fH° (g) of alkyl cumyl
m
ethers, obtained by combining the different experimental
techniques (calorimetry, transpiration, equilibrium study),
are generally consistent, supporting the confidence in the
experimental procedures used. To ascertain the strain
effect, we also involved in the interpretation our recent
result (see Table 8) for cumyl alcohol.19 Cumyl alcohol also
exhibits an amount of strain similar to that for alkyl cumyl
ethers (see Table 8). What reasons cause strain in these
molecules? Elucidation of the nature of strain in alkyl
cumyl ethers is aided by comparison with the strain of the
similar shaped tert-butylbenzene,20 ∆fH° (g) ) -(24.42 (
m
0.80) kJ‚mol-1, and the strain enthalpy, HS ) 10.9 kJ‚mol-1
.
tert-Butylbenzene is a relevant structural pattern of strain
in the cumyl derivatives studied. Its strain enthalpy is a
reflection of the intrinsic strain of the molecule due to steric
repulsions of methyl groups and the benzene ring attached
to the central quaternary carbon atom. It is expected from
the analogy with the strain of tert-butylbenzene that the
observed amount of destabilization in cumyl derivatives
could no doubt be attributed to the steric repulsions of
methyl groups and the benzene ring attached to the central
quaternary carbon atom. Because cumyl ethers and cumyl
alcohol are strained similarly by about 8 to 10 kJ ‚mol-1
(Table 8), it is evident that strain in cumyl derivatives is
governed only by steric interactions of methyl groups and
the benzene ring while the OH or alkoxy group is rather
(20) Verevkin, S. P. Thermochemical Properties of Branched Alkyl
substituted Benzenes. J . Chem. Thermodyn. 1998, 30, 1029-1040.
(21) Verevkin, S. P. Thermochemistry of Phenols. Quantification of
the Ortho-, Para-, and Meta- interactions in Tert-alkyl Substi-
tuted Phenols. J . Chem. Thermodyn. 1999, 31, 559-585.
Received for review May 29, 2000. Accepted September 4, 2000.
J E000162A