ACTA CHROMATOGRAPHICA, NO. 17, 2006
CALORIMETRY COMPARED
WITH GAS CHROMATOGRAPHY:
ARE COMPARABLE MOLAR HEAT CAPACITIES
OBTAINED BY USE OF THESE TWO APPROACHES?
K. Ciążyńska-Halarewicz, P. Korzenecki, M. Helbin, and T. Kowalska
Institute of Chemistry, Silesian University, 9 Szkolna Street, 40-006 Katowice, Poland
SUMMARY
In this study molar heat capacities (Cp) were determined for aliphatic alcohols by using simple gas chromatographic data and mathematical
models correctly derived from the laws and rules of physical chemistry
and chromatography. The results obtained were compared with those derived by direct calorimetric measurement and with data calculated by use of
the Kopp and Neumann rule.
In this way an attempt was made to answer the question posed in
the title of this paper–is the accuracy of the non-standard approach (even,
if computationally rather complicated) comparable with that of the traditional measurement technique? From the results obtained it is clearly apparent that the results obtained by use of our novel approach are comparable with those originating from the other measurement and computational
approaches.
This paper is the latest in a series devoted to alternative methods
for derivation of thermodynamic data from gas chromatographic results.
INTRODUCTION
In a previous publication [1] we dealt with estimation of the molar
heat capacity (Cp) for three classes of compound, alkylbenzenes, aldehydes,
and ketones. Instead of tedious and traditional calorimetric measurement
of these values we proposed a novel approach which made use of several
mathematical equations. These equations couple gas chromatographic data
with physicochemical magnitudes and connect the theory of gas chromatography with the laws and rules of physical chemistry. They enable
estimation of Cp values by indirect and relatively complex computation,
yet from experiments much simpler than calorimetric determination. The
- 72 -
only data needed for these calculations are the retention times of the analytes, acquired under strictly defined chromatographic conditions.
The starting point for derivation of the ultimate relationships enabling determination of molar heat capacity are given in Table I, where r is
the relative retention, rG the non-reduced relative retention, k the retention
factor, Vm the molar volume of the analyte, TB the boiling point of the
analyte, ∆H° the enthalpy of vaporization of the analyte, recalculated per
volume unit of a given congener, Tc the temperature of the column, and R
the gas constant. A, B, and C are physicochemically meaningful fitting
terms (in Table I we give the values of B and C only, because they alone
are thermodynamically important; these terms are identical for all the relationships considered).
Table I
Basic equations used for derivation of relationships enabling calculation of molar heat
capacity, Cp
Equation
Derivation

V 
r = A exp BVm + C m 
TB 


Vm 
 + const.
b rG = A exp BVm + C
TB 

a
c
V 
ln k = A + BVm + C  m 
 TB 
Fitting terms
[2]
[3]
B=
∆H o
RTc
C=−
∆H o
R
[4]
In all three equations the chromatographic property (r, rG, or ln k)
depends on two physical magnitudes, the molar volume, Vm, and boiling
point, TB, of the analyte. Thus the same procedure can be applied to each of
these three equations, resulting in the dependences enabling estimation of
Cp.
Three simple relationships are needed:
Vm =
M
d
(1)
where M and d are, respectively, the molar weight and density of the compound.
- 73 -
The molar weight can, however, be expressed as the ratio of the
molar heat capacity (or the molar heat), Cp, to the specific heat capacity, c:
M=
Cp
(2)
c
Combining eqs (1) and (2), we obtain:
Vm =
Cp
(3)
dc
Now let us make use of the Kopp and Neumann rule. According to
this rule the molar heat capacity of a compound in the condensed state is
equal to the sum of the atomic heats of the individual atoms that constitute
the compound. If we divide the molar heat capacity approximated in this
way for a given compound by its molar weight, we obtain the specific heat
capacity, which can be inserted in the denominator of eq. (3). The molar
heat capacity in the numerator of the same expression is the physical magnitude we are trying to obtain.
We should, perhaps, add that the Kopp and Neumann rule cannot
be applied to the specific heat capacities of the elements in the sense that
we cannot sum them to obtain the specific heat capacities of our analytes,
the magnitude of which must be introduced in eq. (3).
Table II
Final relationships enabling estimation of the molar heat capacities of the chromatographed analytes
Equation
Fitting terms
 1
1 
r = A exp  B + C

dcTB 
 dc
 1
1 
 + const.
II rG = A exp B + C
dcTB 
 dc
I
III ln k = A + B
B=
∆H oCp
RTc
C=−
∆H oCp
R
1
1
+C
dc
dcTB
Further transformations consist in inserting the complete physical
description of the fitting terms B and C and of eq. (3) into the relationships
- 74 -
given in Table I. The necessary rearrangements lead to the relationships
presented in Table II.
Here again the fitting terms B and C of each equation have the same physical description, thus the practical procedure for calculating the molar heat capacity will be the same in each case. These physical descriptions
are:
BRTc
∆H o
from term B:
Cp =
from term C:
Cp = −
CR
∆H o
The relationships listed in Table II are derived elsewhere [1] so the
derivations will not be repeated here. It might, however, prove useful to
recollect the main assumptions that connect all these models, because some
of these assumptions will be referred to below. They focus mainly on the
following issues:
• The retention process. This consists in partitioning of the analyte between the stationary and mobile phases (in partition chromatography);
the non-chromatographic physical analogy of the retention process can
be alternate vaporization and condensation;
• Transfer of the analyte from the low-polarity stationary phase to the
gas phase; in non-chromatographic physical terms this can be described
as vaporization of the pure liquid analyte;
• Vaporization of a liquid. For the vast majority of liquids the entropy of
their vaporization is approximately 85 ± 3 J mol–1 K–1 (Trouton’s Rule);
• The processes of vaporization and condensation. These are the mutually
opposite processes and according to the Lavoisier–Laplace law their
thermodynamic characteristics should be the same absolute values but
with opposite signs;
• Intermolecular interactions. The assumed models do not take into consideration any intermolecular interactions and, therefore, systems with
the weak, and therefore negligible, interactions should fit these models
better than those in which the interactions are strong.
It is apparent from previous results [1] that agreement between molar heat capacities available in the literature for alkylbenzenes, aldehydes,
and ketones and those determined by our approach is fully satisfactory.
The situation for the analytes investigated in this work, aliphatic alcohols,
- 75 -
depends on the results of the chromatographic experiment. Scrutiny of this
agreement is the main objective of this study.
EXPERIMENTAL
As has already been mentioned, the analytes investigated in this
study were aliphatic alcohols. n-Alkanes were used as reference analytes
enabling determination of Kováts retention indices (PolyScience Corporation, Niles, IL, USA and J.T. Baker, Deventer, The Netherlands; purity grade: standards for GC). The analytes and the respective physical data needed
for calculations are listed in Table III.
The measurement conditions were the same as in our previous investigations. Experiments were performed with a Fisons Instruments (Rodano/Milan, Italy) GC 8000 series capillary gas chromatograph with oncolumn injection and flame-ionization detection. Isothermal chromatography was performed in the temperature range 323 to 423 K at 25-K
intervals (five measurement temperatures in total).
Analysis was performed on three different capillary columns (Agilent Technologies, Palo Alto, CA, USA, formerly J&W Scientific, Folsom,
CA, USA) each of length 30 m, internal diameter 0.32 mm, and stationary
phase film thickness 1 µm. Two low-polarity stationary phases, DB-1 (100%
polydimethylsiloxane, polarity on the McReynolds scale 217) and DB-5
(95% polydimethylsiloxane + 5% phenyl, polarity 323) and one mediumpolarity stationary phase, DB-Wax (100% poly(ethylene glycol), polarity
2188) were used.
Acquisition and immediate processing of the chromatographic data
were achieved by use of the computer software Chromax (Artur Dzieniszewski, Pol-Lab, Warsaw, Poland). The software Statistica 5.1. PL (StatSoft, Tulsa, OK, USA) and Matlab 6.5.0. (The MathWorks, Natick, MA,
USA) was used for statistical analysis of the data. Excel (Microsoft Corporation, Redmond, WA, USA) was used for other computations.
EXPERIMENTAL AND COMPUTATIONAL PROCEDURE.
RESULTS AND DISCUSSION
Models I–III presented in this study were tested in the first instance to assess their ability to predict the chromatographic behaviour of the
alcohols under the working condition used (an indispensable precondition)
but also their usefulness for estimation of molar heat capacities for these
- 76 -
Table III
Physicochemical properties of the aliphatic alcohols used in the gas chromatographic investigations
Alcohol
Methanol
Ethanol
1-Propanol
1-Butanol
1-Pentanol
1-Hexanol
1-Heptanol
1-Octanol
1-Nonanol
1-Decanol
1-Undecanol
1-Dodecanol
2-Propanol
2-Butanol
2-Hexanol
2-Heptanol
2-Octanol
3-Hexanol
2-Methyl-1-propanol
2-Methyl-1-butanol
3-Methyl-1-butanol
2-Methyl-2-butanol
2-Methyl-1-pentanol
4-Methyl-2-pentanol
2-Methyl-3-pentanol
3-Methyl-3-pentanol
2,4-Dimethyl-3-pentanol
Empirical
formula
CH3OH
C2H5OH
C3H7OH
C4H9OH
C5H11OH
C6H13OH
C7H15OH
C8H17OH
C9H19OH
C10H21OH
C11H23OH
C12H25OH
C3H7OH
C4H9OH
C6H13OH
C7H15OH
C8H17OH
C6H13OH
C4H9OH
C5H11OH
C5H11OH
C5H11OH
C6H13OH
C6H13OH
C6H13OH
C6H13OH
C7H15OH
d20
Vm
TB
c
0.790
0.790
0.800
0.810
0.810
0.820
0.820
0.830
0.830
0.830
0.830
0.830
0.786
0.810
0.810
0.820
0.820
0.819
0.802
0.820
0.810
0.818
0.824
0.802
0.819
0.824
0.829
40.56
58.32
75.12
91.51
108.83
124.61
141.71
156.90
173.81
190.71
207.60
224.51
76.46
91.51
126.15
141.71
158.82
124.76
92.42
107.50
108.83
107.76
124.00
127.41
124.76
124.00
140.17
337.65
351.45
370.40
391.15
411.15
430.15
449.15
466.15
488.15
504.65
521.50
534.65
355.55
372.65
410.15
433.15
452.15
408.15
381.15
401.15
404.65
384.65
421.15
405.15
401.15
396.00
412.65
2.524
2.566
2.589
2.603
2.613
2.620
2.625
2.629
2.632
2.635
2.638
2.639
2.589
2.603
2.620
2.625
2.629
2.620
2.603
2.613
2.613
2.613
2.620
2.620
2.620
2.620
2.625
d20 is the density at 20°C (g cm–3), Vm is the molar volume (cm3 mol–1), TB is the boiling
point (K), and c is the specific heat capacity (J g–1 K–1)
compounds. The statistical correctness of the models, when used to predict
retention data for the alcohols, enabled further acquisition of the thermodynamic data.
As is clearly apparent from models I–III, to determine the molar heat
capacity, Cp, knowledge of another thermodynamic magnitude is necessary,
i.e. the enthalpy of vaporization of the compounds (more precisely, in each
of these models we encounter the magnitude ∆H°, which must be multi- 77 -
plied by the molar volume of the analyte to give its enthalpy of vaporization, ∆Hvap).
Achieving the ultimate objective, the molar heat capacity, Cp, is
rather complicated; let us present and comment on the entire data-acquisition procedure in detail.
1. Acquisition of the experimental data
This stage is purely experimental and devoted to collecting the
chromatographic data (i.e. the retention times of the analytes) under the
working conditions given in the Experimental section. Here it must be
stated that the group of 27 normal and branched aliphatic alcohols selected was in a sense a ‘risk’ group, because the models assumed are supposed to perform best for low-polarity analytes and some of the alcohols employed in this study (those the lowest molecular weight) are quite polar.
Chromatography was performed at five different temperatures under isothermal conditions, using three stationary phases of different polarity in
columns with identical dimensions, to avoid any effect of these on the results. The film thickness of the stationary phases (1 µm) on all the columns
was relatively high, to prevent intermolecular interactions between the
analytes and the capillary walls. To minimize intermolecular interactions
between the analytes and the stationary phase, we selected two different
low-polarity stationary phases and one medium-polarity stationary phase,
deliberately avoiding stationary phases of high polarity.
The retention times of the n-alkanes, needed to calculate the Kováts
retention indices used in some equations, were determined analogously.
2. Experimental basis
The retention data needed, i.e. the relative retention (r), the nonreduced relative retention (rG), the retention factor (k) (and the Kováts retention index, I, needed for determination of enthalpy of vaporization only)
were derived from the chromatographic data collected. In that way a large
database emerged. Determination of the numerical values of all these quantities was required by the retention models tested in this study.
3. Computational basis – search for statistically valid datasets
Statistically valid datasets were built separately for each group of
results collected under the given measurement conditions. This was done
with aid of the LMS (least median of squares) procedure. The LMS method – very useful for elimination of results burdened with substantial ex- 78 -
perimental error (i.e. outliers) and for preliminary determination of fitting
and statistical data – can only be applied to linear equations, so non-linear
equations must first be linearized. This applies to equations from which
both molar heat capacity and the enthalpy of vaporization were derived.
4. Appropriate computational procedures
Appropriate computational procedures performed with both sets of
the equations enabled the fitting terms (A, B, and C) and statistical data
characterizing the tested datasets to be obtained. For the linear equations
the linear regression procedure was used; for the exponential equations the
procedure of non-linear estimation (i.e. the quasi-Newton method) was
used.
5. Statistical evaluation of the models
After having constructed the computational basis (point 3) and performed the computational procedure appropriate for the type of the equation
(point 4), the errors describing the quality of fits of the models to the
experimental data (RMS, root-mean-square error) were determined and the
predictive power of the models was assessed (by means of RMSCV, the root
mean square of cross-validation). Last, but not least, the correlation coefficients, r, were also determined. This evaluation was performed for each
equation (both those used to obtain the molar heat capacities and those used
to determine the enthalpy of vaporization) according to the procedures described for each of the five working temperatures and for each of the three
stationary phases.
The retention data obtained differed by as much as three orders of
magnitude, which might to some extent affect RMS and RMSCV values.
Thus to compare the magnitudes of the errors the respective percentage
values (%RMS, %RMSCV) had to be calculated. Lower values of the percentage errors indicated that the given model performs better for one dataset than for another (i.e. that for which error values were higher). The errors very seldom exceeded a few percent, and slightly higher values were
obtained only very sporadically. Comparison of all the data revealed the
best results (i.e. those with the lowest percentage errors) originated from
the most polar (DB-Wax) column.
The correlation coefficients (r) obtained were also very satisfactory,
usually in excess of 0.99 (the lowest value was 0.94).
Examples of results from statistical analysis are shown in Table IV.
- 79 -
Table IV
Statistical evaluation of mathematical models I–III and of the values of the fitting terms
B and C, with the respective errors (n is the number of valid cases)
Eq.
I
II
III
Stationary
phase
DB-1
DB-5
DB-Wax
DB-1
DB-5
DB-Wax
DB-1
DB-5
DB-Wax
Fitting terms
B ± sB
78.13 ± 0.53
16.27 ± 0.35
80.04 ± 0.95
72.28 ± 1.39
11.69 ± 0.28
74.34 ± 5.61
37 ± 1.7
68 ± 0.6
14 ± 0.8
C ± sC
−18263 ± 18
−15917 ± 24
−15285 ± 14
−16139 ± 21
−14049 ± 29
−13533 ± 28
−13551 ± 18
−16645 ± 52
−95236 ± 85
n
36
45
48
42
57
42
45
48
33
RMS
%
RMS
2.67
7.54
1.14
0.08
0.17
0.19
0.22
0.08
0.11
6.0
7.6
3.3
4.1
6.5
3.4
8.4
5.4
4.0
%
RMSCV RMSCV
2.77
7.82
1.64
0.10
0.18
0.41
0.23
0.08
0.12
6.2
7.9
3.8
4.6
6.8
4.1
8.6
5.7
4.2
r
0.9987
0.9988
0.9998
0.9978
0.9982
0.9898
0.9812
0.9986
0.9938
In eqs. (I), (II), and (III) Tc = 348, 373, and 323 K, respectively
To better illustrate the statistical data, predicted values were plotted
against experimental results (Fig. 1) for one – although somewhat extended
– example taken from Table IV. These plots show that agreement between
experimental data and those predicted by regression analysis was excellent.
The high quality statistical data confirmed that the indispensable
precondition was fulfilled by the equations considered, which meant they
could now be used for prediction of the retention of the test analytes in the
chromatographic systems selected. Let us therefore proceed to the next stage of the computations, determination of the thermodynamic data.
6. Determination of thermodynamic data and their evaluation
by comparison with those taken from the literature
As already mentioned, the molar heat capacities (Cp) must be derived in two steps. First, numerical values of the enthalpy of vaporization,
∆Hvap, must be known for the compounds. These can be acquired by transformation of the fitting terms A, B, or C of eqs (a)–(i) given in Table V
(the physical significance of these terms can be found elsewhere [2,5,6]).
In models I–III there is a term related to the enthalpy of vaporization (∆H°); we therefore need to know the molar volumes of all the analytes investigated. When ∆H° was first introduced [4] it was defined as the
enthalpy of vaporization calculated per the unit volume of a compound belonging to a given group of congeners (eq. 4), because of the method used
for acquisition of the thermodynamic data:
- 80 -
∆H vap = ∆H °×Vm
(4)
The magnitude of ∆H° and such physical constants as the analytes’
boiling points (TB), densities (d), and specific heat capacities (c) (all from
reference sources) plus the gas constant (R) and the temperature of analysis (Tc) were used to determine the respective molar heat capacities from
the regressionally fitted terms B or C of eqs (I)–(III).
Observed
30
26
22
18
14
10
6
(a)
2
-2
0
4
8
12
16
20
Predicted
Observed
30
26
22
18
14
10
6
(b)
2
-2
-2
2
6
10
14
18
22
26
30
Predicted
140
Observed
120
100
80
60
40
20
(c)
0
-20
-20
0
20
40
60
80
100
120
140
Predicted
Fig. 1
Graphical evaluation of the predictive power of the models used. Plots of observed (experimental) values against predicted values (eq. (I), stationary phase: DB-Wax, dependent
variable r) (a) Tc = 323 K, (b) Tc = 373 K, (c) Tc = 423 K
- 81 -
Table V
Mathematical models used to determine enthalpies of vaporization (the fitting terms are described in detail elsewhere [2,5,6])
Model
a

V 
r = A exp  BVm + C m 
TB 

b

 V 
rG = A exp  BVm + C  m  + const.
 TB 

c
V 
ln k = A + BVm + C  m 
 TB 
d

R 
r = A exp  BRm + C m 
TB 

e
f

 R 
rG = A exp  BRm + C  m  + const.
 TB 

R 
ln k = A + BRm + C  m 
 TB 
g
rG = A exp(BTB ) + const.
h
I = A + BTB
i
I = A+
B
TB
The two-step determination of the thermodynamic magnitude has
already been practised (eqs (h) and (i) [5,6]) for determination of the enthalpy of vaporization of the analytes (step 2) with the aid of the chemical
potential of partitioning of one methylene group between the stationary and
mobile phases (∆µp(-CH2-); step 1). It has been our previous experience that
in the course of the two-step procedure overall determination error tends to
increase and so we might now expect a similar effect of a marked error of
determination with molar heat capacities also.
Let us return to our current subject, however. The experimental enthalpy of vaporization values, i.e. those obtained for the test analytes by use
- 82 -
of eqs (a)–(i), are in very good agreement with data taken from the literature. The best results were obtained for DB-Wax, the most polar of the
three stationary phases used. Most of the results from this stationary phase
agree with the reference data within 10%. The results obtained from the
low-polarity stationary phases were also very satisfactory and were easily
within 25% of the reference data. (This issue will be discussed in more depth
elsewhere [7].)
To summarise, we obtained a vast number of enthalpy of vaporization data, ∆Hvap, from the nine different equations, eight of which had two
thermodynamically relevant fitting terms (eqs (a)–(f), (h), and (i)) and eq.
(g) had one such fitting term. All of these numerical values could be inserted in eqs (I)–(III) to derive the Cp values from either B or C. We tested all
possible combinations and our assumptions about the quality of the results
obtained in the two-step procedure proved true. In the other words, despite
the abundance of the ∆Hvap data obtained, those furnishing acceptable values of molar heat capacity (Cp) proved much less numerous.
These circumstances give rise the question: Would it not be more
practical to use reference values of the enthalpy of vaporization rather than
those calculated from our experiment? The answer is, however, no. First,
reference data originating from direct (i.e. calorimetric) measurements are
few and those originating from the other computational approaches are also
burdened with approximation errors. Second, no criteria are available enabling assessment of the quality of thermodynamic results originating from
the literature that might help us distinguish between ‘good’ and ‘wrong’
results. One argument in favour of our approach is that values for both enthalpy of vaporization and molar heat capacity were obtained from relationships that underwent an analogous statistical–computational procedure and
were derived from the same database. Last, but not least, it is not only the
two-step determination procedure which must be blamed, but also the many simplifications and approximations contained in the models given by
eqs (a)–(i) and (I)–(III).
There is yet one more reason for the moderate success of our comparisons – the availability of reference data. Molar heat capacity values for
primary alcohols are relatively readily available in the literature whereas
for the secondary and the ternary alcohols most of the reference data were
calculated by use of the highly approximate Kopp and Neumann rule (Table VI). This procedure consists in adding the atomic heats for all the atoms
of the elements present in the structure of a given compound. In our experiment we were making use of the atomic heats for three elements only, car- 83 -
bon (graphite; 8.53 J mol–1 K–1), hydrogen (14.415 J mol–1 K–1), and oxygen
(14.68 J mol–1 K–1) [12].
Table VI
Literature values of the molar heat capacities (Cp, kJ mol−1) of the alcohols
Numerical values of Cp taken from literature [kJ mol–1]
Alcohol
a)
b)
c)
d)
e)
f)
g)
h)
i)
Methanol
Ethanol
1-Propanol
1-Butanol
1-Pentanol
1-Hexanol
1-Heptanol
1-Octanol
1-Nonanol
1-Decanol
1-Undecanol
1-Dodecanol
2-Propanol
2-Butanol
2-Hexanol
2-Heptanol
2-Octanol
3-Hexanol
2-Methyl-1-propanol
2-Methyl-1-butanol
3-Methyl-1-butanol
2-Methyl-2-butanol
2-Methyl-1-pentanol
4-Methyl-1-pentanol
2-Methyl-3-pentanol
3-Methyl-3-pentanol
2,4-Dimethyl-3-pentanol
81.06
112.41
143.64
177.15
208.03
240.49
272.49
304.74
336.48
368.47
400.47
432.46
156.26
81.92
115.90
146.88
177.70
207.40
241.32
270.80
305.55
335.56
367.14
398.72
430.31
85.73
121.79
157.38
194.13
227.21
262.90
295.40
329.50
363.70
398.50
441.00
467.90
93.71
137.66
179.50
219.46
255.45
295.20
332.40
368.20
404.70
436.50
481.00
507.00
100.22
149.95
195.40
235.40
272.87
313.00
353.00
390.00
427.70
458.90
502.00
529.60
112.00
179.20
218.00
255.40
293.00
333.00
373.00
410.00
448.20
483.10
526.00
554.30
121.80
191.71
230.40
265.70
303.00
342.00
381.00
417.00
454.20
491.80
536.00
562.80
73.15
106.37
139.59
172.81
206.03
240.10
272.10
305.20
334.40
370.60
407.20
438.30
80.87
118.23
155.59
192.95
230.31
267.67
305.03
342.39
379.75
417.11
454.47
491.83
155.59
192.95
267.67
305.03
342.39
267.67
192.95
230.31
230.31
230.31
267.67
267.67
267.67
267.67
305.03
198.03
181.59
181.05
247.30
247.63
293.38
a) measurement at the boiling point, p = 1 atm [8]; b) [9]; c) 320 K [10]; d) 350 K [10]; e)
370 K [10]; f) 400 K [10]; g) 420 K [10]; h) 298.15 K, HP-5 [11]; i) Kopp and Neumann
rule
Comparison of the results obtained in this study with those from
the literature and with other reference data (calculated by use of the Kopp
and Neumann rule) enables evaluation of the models tested and, consequently, evaluation of the sensitivity and correctness of our approach.
Let us discuss our final results. Here we present a small fraction of
the data only, because of their gargantuan abundance (all the results obtained are available elsewhere [13]). The data shown in Tables VII–IX alone,
however, enable assessment of the quality of the thermodynamic results. It
- 84 -
is readily apparent that a substantial number of these results can be described as very good or good, i.e. deviating by ±10 or ±25%, respectively, from
the reference values (i.e. from those taken from literature or calculated by
use of the Kopp and Neumann rule). These data are indicated in bold characters. Another batch of the results can be described as satisfactory, because their deviation from the reference data is within the range ±50% (these data are written in italics). From eqs (a)–(c) one can obtain average values of the enthalpy of vaporization only, hence single molar heat capacity
values also, for the whole set of the congeners chromatographed under the
given working conditions.
Another insight into the data is provided in Fig. 2. From this figure
it is apparent that use of fitting term B from eq. (I) in combination with
enthalpy of vaporization values derived from eq. (i) (term A) results in
unexpectedly good prediction of the molar heat capacity values, despite the
complexity of this two-step approach. The vast majority of the results obtained deviate from the reference data by ±50% and at the lowest measurement temperature the deviation is even less (±25% or ±10% only).
The dependence of the quality of predicted molar heat capacity values on stationary phase polarity is readily apparent from Fig. 3. This comparison was made for analyses run at the same temperature and for computations with the same equations. From the data in Fig. 3a it can be concluded that the performance of the mathematical models tested does not
depend on the type of stationary phase used. For each stationary phase the
number of results falling outside the range of ±50% is very low and most
of the results fall well within ±25% or ±10%.
To summarise, it can be stated that the best results (i.e. the molar
heat capacity values closest to the reference data) were obtained from use
of the medium-polarity DB-Wax stationary phase. This may seem somewhat striking, because one of the basic assumptions made when deriving
the equations of the model was that the models – taking no account of any
intermolecular interactions within the chromatographic system – should
perform best for systems lacking specific intermolecular interactions. How
can we explain this seeming contradiction? Among the model assumptions
we find another that refers to transfer of the analyte from the liquid stationary phase to the gaseous mobile phase – it was assumed that this transfer resembles vaporization of a liquid from its bulk phase. Because our
test analytes are alcohols and the most polar stationary phase applied is
100% poly(ethylene glycol) (and thus the analytes and stationary phase
have hydroxyl groups in common), the assumption that the physical natu- 85 -
Table VII
Molar heat capacity values (Cp) calculated from the fitting terms B or C of eq. (III) by use of experimental gas chromatographic data
(DB-Wax, Tc = 323K) and implementation of the enthalpy of vaporization values derived from eqs (a)–(i) (terms A, B, or C)
Analyte
Term, eq. (III)
Tc = 323K
Methanol
Ethanol
1-Propanol
1-Butanol
1-Pentanol
1-Hexanol
1-Heptanol
1-Octanol
1-Nonanol
1-Decanol
1-Undecanol
1-Dodecanol
2-Propanol
2-Butanol
2-Hexanol
2-Heptanol
2-Octanol
3-Hexanol
2-Methyl-1-propanol
2-Methyl-1-butanol
3-Methyl-1-butanol
2-Methyl-2-butanol
2-Methyl-1-pentanol
4-Methyl-1-pentanol
2-Methyl-3-pentanol
3-Methyl-3-pentanol
2,4-Dimethyl-3-pentanol
a/B
B
a/C
C
87.82 189.01
B
C
72.84 156.76
Cp values (kJ mol–1) calculated by use of the fitting terms of eq:
b/B
b/C
c/B
c/C
B
C
B
C
B
C
B
C
79.19 170.43
66.02 142.10
- 86 -
86.16 185.44
73.79 158.81
d/B
B
96.45
87.49
83.00
80.17
78.32
77.02
76.02
75.26
74.60
74.04
73.63
73.63
84.37
80.58
77.74
76.52
76.14
77.49
80.85
78.20
79.12
79.17
77.00
78.15
77.16
77.00
75.89
d/C
C
207.57
188.29
178.62
172.54
168.56
165.76
163.60
161.97
160.56
159.35
158.46
158.46
181.58
173.42
167.31
164.69
163.87
166.77
174.01
168.31
170.28
170.39
165.72
168.20
166.07
165.72
163.33
B
80.16
72.71
68.98
66.63
65.09
64.01
63.18
62.54
62.00
61.53
61.19
61.19
70.12
66.97
64.61
63.60
63.28
64.40
67.19
64.99
65.76
65.80
64.00
64.95
64.13
64.00
63.07
C
172.51
156.49
148.45
143.39
140.09
137.76
135.96
134.61
133.44
132.43
131.70
131.70
150.90
144.13
139.04
136.87
136.19
138.60
144.61
139.88
141.52
141.61
137.73
139.79
138.02
137.73
135.74
Analyte
Term, eq. (III)
Tc = 323K
Methanol
Ethanol
1-Propanol
1-Butanol
1-Pentanol
1-Hexanol
1-Heptanol
1-Octanol
1-Nonanol
1-Decanol
1-Undecanol
1-Dodecanol
2-Propanol
2-Butanol
2-Hexanol
2-Heptanol
2-Octanol
3-Hexanol
2-Methyl-1-propanol
2-Methyl-1-butanol
3-Methyl-1-butanol
2-Methyl-2-butanol
2-Methyl-1-pentanol
4-Methyl-1-pentanol
2-Methyl-3-pentanol
3-Methyl-3-pentanol
2,4-Dimethyl-3-pentanol
e/B
e/C
B
C
B
C
96.31
87.37
82.88
80.06
78.21
76.91
75.91
75.15
74.50
73.93
73.53
73.53
84.25
80.47
77.63
76.41
76.03
77.38
80.74
78.09
79.01
79.06
76.89
78.04
77.06
76.89
75.78
207.28
188.03
178.37
172.30
168.32
165.52
163.37
161.74
160.34
159.12
158.24
158.24
181.32
173.18
167.07
164.45
163.64
166.54
173.76
168.07
170.04
170.15
165.49
167.96
165.84
165.49
163.10
80.08
72.65
68.91
66.57
65.03
63.95
63.12
62.49
61.95
61.48
61.14
61.14
70.05
66.91
64.55
63.54
63.22
64.34
67.13
64.94
65.70
65.74
63.94
64.89
64.07
63.94
63.01
172.35
156.35
148.32
143.27
139.96
137.63
135.84
134.48
133.32
132.31
131.58
131.58
150.77
144.00
138.92
136.75
136.07
138.48
144.48
139.75
141.39
141.48
137.61
139.66
137.89
137.61
135.62
Cp values (kJ mol–1) calculated by use of the fitting terms of eq:
f/B
f/C
g/B
h/A
h/B
B
C
B
C
B
C
B
C
B
C
105.90
96.06
91.13
88.02
86.00
84.57
83.46
82.63
81.91
81.29
80.84
80.84
92.63
88.48
85.35
84.02
83.60
85.08
88.77
85.87
86.87
86.93
84.55
85.81
84.73
84.55
83.33
227.91
206.74
196.12
189.45
185.08
182.00
179.63
177.83
176.29
174.96
173.99
173.99
199.37
190.42
183.70
180.82
179.93
183.11
191.05
184.80
186.97
187.09
181.96
184.68
182.34
181.96
179.33
91.23
82.76
78.51
75.83
74.09
72.85
71.90
71.19
70.57
70.03
69.65
69.65
79.81
76.22
73.53
72.38
72.02
73.30
76.48
73.97
74.84
74.89
72.84
73.93
72.99
72.84
71.79
196.35
178.11
168.96
163.21
159.44
156.79
154.75
153.20
151.88
150.73
149.89
149.89
171.75
164.04
158.26
155.78
155.01
157.75
164.59
159.21
161.07
161.18
156.76
159.10
157.09
156.76
154.50
34.29
47.36
57.88
66.77
75.55
82.68
90.05
96.07
101.63
107.86
113.62
119.85
61.38
70.09
87.79
93.38
100.25
87.24
69.21
76.49
76.76
79.96
84.04
89.76
88.77
89.37
96.95
73.79
101.93
124.58
143.71
162.59
177.95
193.81
206.75
218.72
232.13
244.53
257.94
132.10
150.84
188.93
200.96
215.76
187.76
148.95
164.61
165.21
172.09
180.86
193.17
191.04
192.35
208.66
23.52
31.80
38.22
44.27
50.61
68.45
82.25
95.29
34.52
47.69
58.66
69.07
74.29
102.64
126.25
148.65
41.76 89.87 62.58 134.68
47.35 101.90 72.27 155.55
58.96 126.89 92.96 200.07
62.16
47.39
51.80
52.41
58.81
58.82
62.38
60.12
60.90
68.18
133.79
101.99
111.48
112.79
126.57
126.60
134.25
129.40
131.06
146.73
96.06
72.56
80.91
81.87
88.16
92.32
96.94
93.91
94.54
106.17
206.73
156.15
174.12
176.21
189.73
198.69
208.64
202.12
203.47
228.49
i/A
i/B
B
C
B
C
30.27
43.52
56.05
68.28
81.21
92.98
105.74
117.08
129.70
142.31
154.91
167.53
57.05
68.28
94.13
105.74
118.51
93.10
68.96
80.22
81.21
80.41
92.53
95.07
93.10
92.53
104.59
65.14
93.66
120.64
146.96
174.78
200.12
227.58
251.97
279.13
306.27
333.39
360.55
122.79
146.96
202.59
227.58
255.06
200.36
148.42
172.64
174.78
173.06
199.14
204.61
200.36
199.14
225.11
42.80
61.54
79.26
96.56
114.83
131.48
149.53
165.56
183.40
201.23
219.05
236.90
80.68
96.56
133.11
149.53
167.58
131.64
97.52
113.43
114.83
113.70
130.84
134.44
131.64
130.84
147.90
92.11
132.44
170.59
207.81
247.14
282.98
321.81
356.31
394.71
433.08
471.44
509.84
173.63
207.81
286.47
321.81
360.67
283.32
209.88
244.12
247.14
244.71
281.59
289.34
283.32
281.59
318.31
a/B means the enthalpy of vaporization was determined from eq. (a) using term B; values in bold are experimental values within ±10 and
±25% of values taken from the literature; values in italics are the experimental values within ±50% of values taken from the literature
- 87 -
Table VIII
Molar heat capacity values (Cp) calculated from the fitting terms B or C of eq. (III) by use of experimental gas chromatographic data
(DB-5, Tc = 373K) and implementation of the enthalpy of vaporization values derived from eqs (a)–(i) (terms A, B, or C)
Analyte
Term, eq. (III)
Tc = 323K
Methanol
Ethanol
1-Propanol
1-Butanol
1-Pentanol
1-Hexanol
1-Heptanol
1-Octanol
1-Nonanol
1-Decanol
1-Undecanol
1-Dodecanol
2-Propanol
2-Butanol
2-Hexanol
2-Heptanol
2-Octanol
3-Hexanol
2-Methyl-1-propanol
2-Methyl-1-butanol
3-Methyl-1-butanol
2-Methyl-2-butanol
2-Methyl-1-pentanol
4-Methyl-1-pentanol
2-Methyl-3-pentanol
3-Methyl-3-pentanol
2,4-Dimethyl-3-pentanol
a/B
B
a/C
C
B
C
Cp values (kJ mol–1) calculated by use of the fitting terms of eq:
b/B
b/C
c/B
c/C
B
C
B
C
B
C
B
C
d/B
B
201.73
182.99
173.59
167.68
163.81
161.09
158.99
157.40
156.04
154.86
154.00
154.00
176.46
150.29 321.28 135.49 289.64 150.81 322.40 136.24 291.26 171.50 366.63 197.30 421.77 168.54
162.59
160.05
159.25
162.08
169.11
163.57
165.49
165.59
161.06
163.46
161.39
161.06
158.73
- 88 -
d/C
C
B
C
431.24
391.19
371.10
358.46
350.20
344.37
339.89
336.49
333.58
331.05
329.22
329.22
377.23
360.30
347.59
342.15
340.45
346.48
361.51
349.67
353.77
354.00
344.30
349.45
345.02
344.30
339.33
183.42
166.38
157.84
152.46
148.95
146.47
144.56
143.12
141.88
140.80
140.02
140.02
160.45
153.24
147.84
145.52
144.80
147.37
153.76
148.72
150.47
150.57
146.44
148.63
146.75
146.44
144.32
392.10
355.68
337.42
325.93
318.41
313.12
309.04
305.95
303.30
301.00
299.34
299.34
342.99
327.60
316.04
311.09
309.55
315.04
328.70
317.93
321.66
321.87
313.05
317.73
313.71
313.05
308.53
Analyte
Term, eq. (III)
Tc = 323K
Methanol
Ethanol
1-Propanol
1-Butanol
1-Pentanol
1-Hexanol
1-Heptanol
1-Octanol
1-Nonanol
1-Decanol
1-Undecanol
1-Dodecanol
2-Propanol
2-Butanol
2-Hexanol
2-Heptanol
2-Octanol
3-Hexanol
2-Methyl-1-propanol
2-Methyl-1-butanol
3-Methyl-1-butanol
2-Methyl-2-butanol
2-Methyl-1-pentanol
4-Methyl-1-pentanol
2-Methyl-3-pentanol
3-Methyl-3-pentanol
2,4-Dimethyl-3-pentanol
e/B
e/C
B
C
B
C
203.63
184.72
175.23
169.27
165.36
162.61
160.49
158.89
157.52
156.32
155.46
155.46
178.13
170.13
164.13
161.56
160.76
163.61
170.70
165.11
167.05
167.16
162.58
165.01
162.92
162.58
160.23
435.32
394.89
374.61
361.85
353.51
347.63
343.10
339.67
336.73
334.18
332.33
332.33
380.80
363.70
350.87
345.38
343.67
349.76
364.92
352.98
357.12
357.35
347.55
352.75
348.29
347.55
342.53
186.80
169.45
160.74
155.27
151.69
149.17
147.22
145.75
144.49
143.40
142.60
142.60
163.40
156.07
150.56
148.20
147.47
150.08
156.59
151.46
153.24
153.34
149.14
151.37
149.45
149.14
146.98
399.33
362.24
343.63
331.93
324.28
318.88
314.73
311.59
308.89
306.55
304.85
304.85
349.31
333.63
321.86
316.82
315.25
320.84
334.75
323.79
327.59
327.80
318.82
323.58
319.49
318.82
314.21
Cp values (kJ mol–1) calculated by use of the fitting terms of eq:
f/B
f/C
g/B
h/A
h/B
B
C
B
C
B
C
B
C
B
C
229.45
208.14
197.45
190.72
186.33
183.23
180.84
179.04
177.48
176.14
175.16
175.16
200.71
191.70
184.94
182.04
181.14
184.35
192.35
186.05
188.23
188.35
183.19
185.93
183.58
183.19
180.54
490.51
444.95
422.10
407.72
398.32
391.70
386.60
382.73
379.42
376.55
374.46
374.46
429.07
409.81
395.36
389.17
387.24
394.10
411.19
397.72
402.39
402.65
391.62
397.47
392.44
391.62
385.96
265.19
240.56
228.21
220.43
215.35
211.77
209.01
206.92
205.13
203.58
202.45
202.45
231.98
221.56
213.75
210.40
209.36
213.07
222.31
215.03
217.55
217.69
211.73
214.89
212.17
211.73
208.67
566.91
514.26
487.85
471.24
460.37
452.71
446.82
442.35
438.52
435.20
432.79
432.79
495.91
473.65
456.94
449.79
447.56
455.49
475.24
459.68
465.07
465.37
452.62
459.38
453.57
452.62
446.08
44.62
61.63
75.34
86.91
98.33
107.59
117.18
125.02
132.25
140.36
147.85
155.98
79.88
91.20
114.23
121.52
130.47
113.53
90.06
99.53
99.89
104.05
109.36
116.81
115.52
116.31
126.16
95.38
131.75
161.05
185.78
210.20
230.00
250.50
267.27
282.71
300.06
316.07
333.44
170.76
194.97
244.20
259.78
278.92
242.71
192.53
212.78
213.55
222.44
233.78
249.72
246.94
248.64
269.70
41.32
55.56
67.61
78.11
88.65
96.56
105.10
111.54
118.57
125.48
131.18
88.34
118.77
144.54
166.97
189.50
206.42
224.68
238.45
253.47
268.26
280.43
43.97
60.13
74.19
86.76
99.49
109.54
120.29
128.74
137.95
146.99
154.80
94.00
128.55
158.60
185.48
212.68
234.16
257.15
275.21
294.90
314.23
330.92
70.73
80.35
100.86
108.27
116.17
96.09
151.20
171.78
215.61
231.46
248.34
205.41
77.10
88.66
113.64
123.17
133.33
109.12
164.82
189.54
242.94
263.31
285.02
233.28
88.37
84.27
92.68
97.57
103.76
100.89
101.02
110.19
188.91
180.15
198.13
208.58
221.81
215.67
215.96
235.55
98.99
95.60
102.77
110.32
116.47
113.40
113.38
124.60
211.61
204.38
219.71
235.85
248.99
242.43
242.38
266.37
i/A
i/B
B
C
B
C
34.94
50.24
64.71
78.82
93.74
107.34
122.07
135.15
149.72
164.27
178.82
193.39
65.86
78.82
108.66
122.07
136.80
107.47
79.61
92.60
93.74
92.82
106.81
109.75
107.47
106.81
120.74
74.69
107.39
138.33
168.51
200.40
229.46
260.95
288.92
320.06
351.18
382.28
413.42
140.79
168.51
232.29
260.95
292.45
229.74
170.18
197.95
200.40
198.43
228.34
234.61
229.74
228.34
258.11
43.95
63.19
81.39
99.15
117.92
135.01
153.54
170.00
188.32
206.63
224.93
243.26
82.84
99.15
136.68
153.54
172.08
135.18
100.14
116.48
117.92
116.76
134.35
138.05
135.18
134.35
151.87
93.95
135.08
174.00
211.96
252.08
288.63
328.24
363.42
402.59
441.73
480.85
520.02
177.10
211.96
292.20
328.24
367.87
288.98
214.07
249.00
252.08
249.60
287.22
295.11
288.98
287.22
324.67
a/B means the enthalpy of vaporization was determined from eq. (a) using term B; values in bold are experimental values within ±10 and
±25% of values taken from the literature; values in italics are the experimental values within ±50% of values taken from the literature
- 89 -
Table IX
Molar heat capacity values (Cp) calculated from the fitting terms B or C of eq. (I) by use of experimental gas chromatographic data
(DB-1, Tc = 373K) and implementation of the enthalpy of vaporization values derived from eqs (a)–(i) (terms A, B, or C)
Analyte
Term, eq. (III)
Tc = 323K
Methanol
Ethanol
1-Propanol
1-Butanol
1-Pentanol
1-Hexanol
1-Heptanol
1-Octanol
1-Nonanol
1-Decanol
1-Undecanol
1-Dodecanol
2-Propanol
2-Butanol
2-Hexanol
2-Heptanol
2-Octanol
3-Hexanol
2-Methyl-1-propanol
2-Methyl-1-butanol
3-Methyl-1-butanol
2-Methyl-2-butanol
2-Methyl-1-pentanol
4-Methyl-1-pentanol
2-Methyl-3-pentanol
3-Methyl-3-pentanol
2,4-Dimethyl-3-pentanol
a/B
B
a/C
C
B
C
Cp values (kJ mol–1) calculated by use of the fitting terms of eq:
b/B
b/C
c/B
c/C
B
C
B
C
B
C
B
C
d/B
B
325.31
295.09
279.94
270.40
264.17
259.78
256.39
253.83
251.63
249.73
248.34
248.34
284.56
239.46 440.06 240.55 442.06 238.93 439.09 244.34 449.03 233.04 428.26 280.99 516.37 271.79
262.20
258.10
256.82
261.37
272.70
263.77
266.87
267.04
259.72
263.60
260.27
259.72
255.97
- 90 -
d/C
C
B
C
597.82
542.29
514.45
496.92
485.47
477.39
471.17
466.47
462.43
458.92
456.38
456.38
522.95
499.47
481.85
474.31
471.95
480.32
501.15
484.74
490.42
490.74
477.29
484.43
478.30
477.29
470.40
339.37
307.85
292.04
282.09
275.59
271.00
267.47
264.80
262.51
260.52
259.08
259.08
296.86
283.54
273.54
269.25
267.92
272.67
284.49
275.17
278.40
278.58
270.95
275.00
271.52
270.95
267.03
623.66
565.73
536.68
518.40
506.45
498.03
491.54
486.63
482.42
478.76
476.11
476.11
545.55
521.06
502.68
494.81
492.35
501.08
522.81
505.69
511.62
511.96
497.92
505.37
498.97
497.92
490.73
Analyte
Term, eq. (III)
Tc = 323K
Methanol
Ethanol
1-Propanol
1-Butanol
1-Pentanol
1-Hexanol
1-Heptanol
1-Octanol
1-Nonanol
1-Decanol
1-Undecanol
1-Dodecanol
2-Propanol
2-Butanol
2-Hexanol
2-Heptanol
2-Octanol
3-Hexanol
2-Methyl-1-propanol
2-Methyl-1-butanol
3-Methyl-1-butanol
2-Methyl-2-butanol
2-Methyl-1-pentanol
4-Methyl-1-pentanol
2-Methyl-3-pentanol
3-Methyl-3-pentanol
2,4-Dimethyl-3-pentanol
e/B
e/C
B
C
B
C
325.60
295.36
280.19
270.65
264.41
260.01
256.62
254.06
251.86
249.95
248.57
248.57
284.82
272.04
262.44
258.33
257.05
261.61
272.95
264.01
267.11
267.28
259.96
263.84
260.50
259.96
256.20
598.36
542.78
514.91
497.37
485.91
477.82
471.60
466.89
462.85
459.34
456.80
456.80
523.42
499.92
482.29
474.74
472.38
480.75
501.60
485.18
490.87
491.19
477.72
484.87
478.73
477.72
470.82
347.20
314.95
298.77
288.60
281.94
277.26
273.64
270.91
268.56
266.53
265.05
265.05
303.71
290.08
279.84
275.46
274.10
278.96
291.05
281.52
284.82
285.01
277.20
281.34
277.78
277.20
273.19
638.05
578.78
549.06
530.36
518.13
509.51
502.88
497.86
493.54
489.80
487.09
487.09
558.13
533.08
514.27
506.22
503.71
512.64
534.87
517.35
523.42
523.76
509.41
517.02
510.48
509.41
502.05
Cp values (kJ mol–1) calculated by use of the fitting terms of eq:
f/B
f/C
g/B
h/A
h/B
B
C
B
C
B
C
B
C
B
C
309.38
280.65
266.23
257.17
251.24
247.06
243.84
241.41
239.31
237.50
236.19
236.19
270.63
258.48
249.37
245.46
244.24
248.57
259.35
250.86
253.80
253.97
247.01
250.70
247.53
247.01
243.44
568.55
515.75
489.26
472.60
461.70
454.02
448.11
443.63
439.79
436.46
434.04
434.04
497.35
475.02
458.26
451.09
448.85
456.81
476.61
461.01
466.41
466.72
453.93
460.71
454.88
453.93
447.37
376.73
341.74
324.19
313.15
305.93
300.84
296.92
293.95
291.41
289.20
287.60
287.60
329.55
314.75
303.65
298.90
297.41
302.68
315.81
305.47
309.05
309.25
300.78
305.27
301.41
300.78
296.43
692.32
628.02
595.76
575.47
562.20
552.85
545.65
540.20
535.52
531.47
528.52
528.52
605.61
578.42
558.02
549.28
546.56
556.24
580.36
561.36
567.94
568.32
552.74
561.00
553.90
552.74
544.75
73.78
101.93
124.57
143.69
162.59
177.93
193.80
206.73
218.71
232.13
244.52
257.90
132.09
150.83
188.93
200.94
215.76
187.72
148.94
164.58
165.19
172.06
180.85
193.14
191.01
192.34
208.63
135.59
187.32
228.93
264.07
298.80
326.98
356.15
379.91
401.92
426.58
449.35
473.94
242.75
277.18
347.20
369.26
396.50
344.98
273.71
302.46
303.58
316.19
332.35
354.93
351.02
353.46
383.40
63.76
86.54
105.58
123.00
139.41
152.25
165.81
175.94
188.21
117.18
159.03
194.03
226.04
256.20
279.79
304.71
323.33
345.87
69.95
96.43
119.32
140.55
161.16
177.96
195.71
209.56
225.83
128.54
177.21
219.27
258.29
296.17
327.04
359.65
385.11
415.01
112.36
127.82
160.08
171.80
183.79
156.90
145.36
141.72
140.46
152.51
154.27
163.40
158.59
159.79
173.59
206.49
234.90
294.18
315.72
337.74
288.33
267.13
260.45
258.12
280.27
283.51
300.29
291.43
293.65
319.01
125.50
144.67
185.47
201.15
217.42
182.15
159.42
162.70
162.05
172.02
179.57
188.85
183.67
184.44
202.24
230.63
265.86
340.84
369.65
399.56
334.74
292.97
298.99
297.81
316.11
329.99
347.04
337.52
338.95
371.66
i/A
i/B
B
C
B
C
58.50
84.11
108.34
131.98
156.96
179.72
204.38
226.28
250.67
275.05
299.40
323.79
110.27
131.98
181.94
204.38
229.05
179.93
133.29
155.04
156.96
155.41
178.84
183.75
179.93
178.84
202.16
107.50
154.57
199.10
242.54
288.44
330.26
375.59
415.84
460.66
505.45
550.22
595.04
202.65
242.54
334.35
375.59
420.93
330.66
244.95
284.92
288.44
285.60
328.65
337.68
330.66
328.65
371.50
76.44
109.91
141.57
172.46
205.11
234.85
267.07
295.70
327.57
359.42
391.25
423.12
144.10
172.46
237.75
267.07
299.32
235.13
174.18
202.60
205.11
203.09
233.70
240.12
235.13
233.70
264.17
140.48
201.99
260.17
316.94
376.93
431.58
490.80
543.41
601.98
660.51
719.01
777.57
264.81
316.94
436.91
490.80
550.06
432.10
320.09
372.32
376.93
373.22
429.47
441.28
432.10
429.47
485.47
a/B means the enthalpy of vaporization was determined from eq. (a) using term B; values in bold are experimental values within ±10 and
±25% of values taken from the literature; values in italics are the experimental values within ±50% of values taken from the literature
- 91 -
(c)
- 92 -
2-Meth-3-pent
4-Meth-2-pent
2-Meth-1-pent
2-Meth-1-but
3-Meth-1-but
2-Meth-2-but
2-Meth-1-prop
3-Hex
2-Meth-3-pent
4-Meth-2-pent
2-Meth-1-pent
2-Meth-1-but
3-Meth-1-but
2-Meth-2-but
2-Meth-1-prop
3-Hex
2-Oct
2-Hept
2-Hex
2-But
2-Prop
1-Dodec
1-Undec
1-Dec
1-Non
1-Oct
1-Hept
1-Hex
1-Pent
0
2-Oct
2-Hept
2-Hex
2-But
2-Prop
1-Dodec
1-Undec
1-Dec
1-Non
1-Oct
1-Hept
1-Hex
1-Pent
1-But
1-Prop
Eth
1-But
1-Prop
2-Meth-3-pent
4-Meth-2-pent
2-Meth-1-pent
2-Meth-1-but
3-Meth-1-but
2-Meth-2-but
2-Meth-1-prop
3-Hex
2-Oct
2-Hept
2-Hex
2-But
2-Prop
1-Dodec
1-Undec
1-Dec
1-Non
1-Oct
1-Hept
1-Hex
1-Pent
1-But
1-Prop
Eth
Meth
(a)
Eth
Meth
molar heat capacity [J/(mol K)]
(b)
Meth
molar heat capacity [J/(mol K)]
molar heat capacity [J/(mol K)]
700
600
500
400
300
200
100
0
0
Exp. T = 323K
Ref. +/- 10%
Ref. +/- 25%
Ref. +/- 50%
700
600
500
400
300
200
100
Exp. T = 373K
Ref. +/- 10%
Ref. +/- 25%
Ref. +/- 50%
700
600
500
400
300
200
100
Exp. T = 423K
Ref. +/- 10%
Ref. +/- 25%
Ref. +/- 50%
Fig. 2
Molar heat capacity (Cp) values calculated from experimental gas chromatographic data by
use of fitting term B from eq. (I), with the indicated ranges of the literature data (DB-Wax)
(The enthalpy of vaporization values originated from eq. (i), term A). (a) Tc = 323 K, (b)
Tc = 373 K, (c) Tc = 423 K
(c)
- 93 -
2-Meth-3-pent
4-Meth-2-pent
2-Meth-1-pent
2-Meth-1-but
3-Meth-1-but
2-Meth-2-but
2-Meth-1-prop
3-Hex
1-But
2-Meth-3-pent
4-Meth-2-pent
2-Meth-1-pent
2-Meth-1-but
3-Meth-1-but
2-Meth-2-but
2-Meth-1-prop
3-Hex
2-Oct
2-Hept
2-Hex
2-But
2-Prop
1-Dodec
1-Undec
1-Dec
1-Non
1-Oct
1-Hept
1-Hex
1-Pent
0
2-Oct
2-Hept
2-Hex
2-But
2-Prop
1-Dodec
1-Undec
1-Dec
1-Non
1-Oct
1-Hept
1-Hex
1-Pent
1-But
1-Prop
Eth
Eth
1-Prop
2-Meth-3-pent
4-Meth-2-pent
2-Meth-1-pent
2-Meth-1-but
3-Meth-1-but
2-Meth-2-but
2-Meth-1-prop
3-Hex
2-Oct
2-Hept
2-Hex
2-But
2-Prop
1-Dodec
1-Undec
1-Dec
1-Non
1-Oct
1-Hept
1-Hex
1-Pent
1-But
1-Prop
Eth
Meth
(a)
Meth
molar heat capacity [J/(mol K)]
(b)
Meth
molar heat capacity [J/(mol K)]
molar heat capacity [J/(mol K)]
700
600
500
400
300
200
100
0
0
Exp. DB-1
Ref. +/- 10%
Ref. +/- 25%
Ref. +/- 50%
700
600
500
400
300
200
100
Exp. DB-5
Ref. +/- 10%
Ref. +/- 25%
Ref. +/- 50%
700
600
500
400
300
200
100
Exp. DB-Wax
Ref. +/- 10%
Ref. +/- 25%
Ref. +/- 50%
Fig 3
Molar heat capacity (Cp) values calculated from experimental gas chromatographic data
by use of fitting term B from eq. (III), with the indicated ranges of the literature data (Tc =
348 K) (the enthalpy of vaporization values originated from eq. (i), term A). (a) DB-1, (b)
DB-5, (c) DB-Wax
re of vaporization was similar to the process of retention seems to predominate. The least polar stationary phase, DB-1, furnishes retention data
that result in molar heat capacity values which deviate most from the reference data. This is another confirmation that Nature apparently favours
intermolecular interactions among similar species.
Models I and III proved to be those enabling prediction of the most
accurate values of molar heat capacity. The good performance was independent of the stationary phase used and the fitting term B for both performed better than the fitting term C (probably because its full physical
description includes the working temperature, Tc, which does not appear
in C). The worst results were obtained from model II; irrespective of the
stationary phase used the thermodynamic data obtained from its use deviated most from the reference values.
An analogous ranking can be applied to the equations used for determination of the enthalpies of vaporization of the test analytes. Irrespective of the stationary phase used, eqs (g)–(i) proved to be the best performing. For DB-Wax eqs (d)–(f) also performed very well. With this series of
relationships term C afforded better results than B (irrespective of the stationary phase and model used).
An important relationship was noticed between the enthalpies of
vaporization used for the computations performed in step 2 and the resulting molar heat capacities – the less the enthalpies of vaporization deviated
from the reference data, the better were the heat capacities. The opposite
was also noticed – enthalpies of vaporization that deviated strongly from
the reference data usually resulted in poor molar heat capacity values. Very sporadically the opposite behaviour was observed and can be regarded
as a meaningless effect of the numbers.
CONCLUSIONS
The mathematical models used proved physicochemically sound
and performed well statistically. Their usefulness for prediction of retention
data and thermodynamic values to some extent fulfilled our expectations.
The models used performed best for experimental data derived from the
most polar stationary phase (i.e. DB-Wax) and the best coincidence of our
results and reference data was observed for the lowest working temperatures used in this study. Models (I) and (III) proved best for determination
of molar heat capacities, and B proved to be the best fitting term.
- 94 -
The enthalpies of vaporization derived from eqs (g)–(i) resulted in
the best numerical values of molar heat capacity for the alcohols studied
(i.e. the values closest to the reference data). Now term C was found to
perform better than term B).
Combination of capillary gas chromatography with mathematical
models has once again proved an effective means of acquisition the thermodynamic data. This time the approach was used to determine the molar
heat capacities of aliphatic alcohols, relatively polar analytes. This approach
is certainly a good alternative to traditional, well established calorimetric
methods.
REFERENCES
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16, 119 (2006)
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15, 97 (2005)
[3] K. Ciążyńska-Halarewicz, E. Borucka, and T. Kowalska,
Acta Chromatogr., 12, 49 (2002)
[4] T. Kowalska, Acta Chromatogr., 11, 7 (2001)
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[7] K. Ciążyńska-Halarewicz, M. Helbin, P. Korzenecki,
and T. Kowalska, Mathematical models of solute retention in gas
chromatography as sources of thermodynamic data. Part IV.
Alcohols as the test analytes (paper in preparation)
[8] CRC Handbook of Chemistry and Physics, 81st Edition, CRC Press,
2000
[9] E.S. Domalski and E.D. Hearing, J. Phys. Chem. Ref. Data,
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[10] M. Zábranský, V. Růžička, and V. Majer, J. Phys. Chem. Ref. Data,
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[12] Poradnik fizykochemiczny, WNT, Warszawa, 1974
- 95 -
[13] P. Korzenecki, An alternative approach to determination
of the thermodynamic data for the homologues and congeners
from the retention data derived by means of the capillary gas
chromatography, combined with the semi-empirical mathematical
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- 96 -