Differential thermal analysis under quasi-isothermal, quasi-isobaric conditions (Q-DTA): Part IV. Latent error in the determination of the decomposition heat of salt hydrates decomposing congruently and incongruently

Article abstract of DOI:10.1016/j.tca.2005.08.005

The authors disclosed by the simultaneous Q-DTA, Q-TG method a latent, till now not known error in determining the decomposition heat of salt hydrates decomposing congruently or incongruently. This error cannot be shown by the traditional calorimetric or thermoanalytical methods owing to overlapping of the processes taking part in the heat decomposition, it can only be detected and eliminated by applying the simultaneous Q-DTA, Q-TG method of very high resolution and selectivity. A calculation technique is elaborated for the elimination of this error.

Full text of DOI:10.1016/j.tca.2005.08.005

Thermochimica Acta 438 (2005) 76–82
Differential thermal analysis under quasi-isothermal,
quasi-isobaric conditions (Q-DTA)
Part IV. Latent error in the determination of the decomposition
heat of salt hydrates decomposing congruently and incongruently
F. Paulik∗, E. Bessenyey-Paulik, K. Walther-Paulik
Institute for General and Analytical Chemistry, Technical University Budapest, 1521, H-1022 Budapest, Boga´r str. 18/B., Hungary
Received 25 February 2005; received in revised form 27 July 2005; accepted 3 August 2005
Available online 29 September 2005
Abstract
The authors disclosed by the “simultaneous Q-DTA, Q-TG” method a latent, till now not known error in determining the decomposition
heat of salt hydrates decomposing congruently or incongruently.
This error cannot be shown by the traditional calorimetric or thermoanalytical methods owing to overlapping of the processes taking part in
the heat decomposition, it can only be detected and eliminated by applying the “simultaneous Q-DTA, Q-TG” method of very high resolution
and selectivity.
A calculation technique is elaborated for the elimination of this error.
© 2005 Elsevier B.V. All rights reserved.
Keywords: Simultaneous Q-DTA, Q-TG method; Transformation-governed heating control; Self-generated atmosphere; Decomposition heat of salt hydrates
1. Introduction
elaborated. The present paper deals with the results of this
research work.
In a recent work, the authors studied the decomposition
mechanism of several salt hydrates decomposing congruently
or incongruently [1,2] by using their “simultaneous Q-DTA,
Q-TG” method [3–6]. They established that in contrast to tra-
ditional DTA or DSC methods, by applying this measuring
technique, the elementary processes of the complex transfor-
mations of salt hydrates can be fully separated, even if these
processes overlap each other totally (Figs. 1–4).
In the course of their research work, the authors noted
an error unknown until now, observable curiously enough
mainly in the case of salt hydrates consisting of more ele-
mentary reactions and dissolving congruently, as well as in
case of salt hydrates dissolving incongruently. In order to
eliminate this error, a correction calculation method has been
2. Experimental conditions
The salt hydrates CuSO4·5H2O, MnSO4·5H2O,
Mg(NO3)2·6H2O and Na2SO4·10H2O have been stud-
ied earlier [2] for determining their heat decomposition
mechanism. In the present paper, the objective was the
determination of the decomposition heats of the same salt
hydrates. Therefore, their stoichiometric composition (crys-
n
tal water) was measured (Q-TGT curve) very carefully, and
the smaller deviations found were corrected by calculation.
s
Samples were studied by using the instrument Derivato-
graph C (Hungarian Optical Works, Budapest, system Paulik,
Paulik, Erdey). This instrument was made applicable recently
in addition for recording “simultaneous TG, DTG, DTA,
EGA” [7] and “quasi-isothermal, quasi-isobaric thermo-
∗
Corresponding author. Tel.: +36 1 3268167; fax: +36 1 3268167.
E-mail address: bessenyey.paulik@axelero.hu (F. Paulik).
0040-6031/$ – see front matter © 2005 Elsevier B.V. All rights reserved.
doi:10.1016/j.tca.2005.08.005

F. Paulik et al. / Thermochimica Acta 438 (2005) 76–82
77
Fig. 3. Mg(NO3)2·6H2O. Curves recorded with the conventional DTA and
TG (a) and the simultaneous Q-DTA, Q-TG (b) methods: section a–b:
Fig. 1. CuSO0·5H2O. Curves recorded with the conventional DTA
Mg(NO3)2·6H2O → L1unsat;sectionc–d:L1
→ L2unsat + xH2Og↑;point
unsat
and TG (a) and simultaneous Q-DTA, Q-TG (b) methods: sec-
unsat
sat
d: L2
→ L1sat; section d–e: L1 → Mg(NO3)2·2H2Os↓ + yH2Og↑; sec-
sat
tion a–b: CuSO4·5H2Os → (1 − x)CuSO4·3H2Os + L1
; section b–c:
tion f–g: Mg(NO3)2·2H2Os → Mg(NO3)2s + 2H2Og↑.
sat
(1 − x)CuSO4·3H2O + L1 → (1 − y)CuSO4·3H2Os + L2sat; section c–d:
(1 − y)CuSO4·3H2Os + L2 → CuSO4·3H2Os↓ + 2H2Og↑; section e–f:
sat
Tables 1–4, the reaction heats (ꢀrH205 ◦C) calculated from
the standard formation heats at 25 ◦C (ꢀf H205 ◦C), whereas in
CuSO4·3H2Os → CuSO4·H2Os + 2H2Og↑.
n
gravimetry” (Q-TG) curves [7a,b],also for carrying out alter-
natively “simultaneous Q-DTA, Q-TG” [3–6] measurements,
columns C and D the values of the enthalpy changes (ꢀHT
)
measured by the simultaneous Q-DTA, Q-TG instrument asre
shown. In columns E and F the corrected values are to be
found.
n
n
i.e. for taking Q-TAT and Q-TGT curves (Figs. 1b–4b), as
s
s
well.
In Figs. 1a–4a traditional DTA and TG curves are shown.
Figs. 1b–4b illustrate the course of the corrected enthalpy
changes of samples (s) recorded in function of the tem-
perature (Ts) measured under normalized conditions (n)
The enthalpy change values measured directly by the
Q-DTA, Q-TG instrument are obtained directly for 1 g of
the sample in kJ g−1 (column C) which are then trans-
formed into kJ mol−1 values (columns D), which is conform
with the usual practice. For example, in different physico-
chemical tables [8–10] the formation heats, transformation
heats, molecular heats, etc. are given in kJ mol−1. Therefore,
the values for the salt hydrates obtained in kJ g−1 (column
C) are all multiplied by the molecular mass (M1) of the com-
pounds studied (columns D).
n
n
(Q-TAT ) (curve 3), whereas the curve Q-TGT (curve 4)
s
shows the weight change of the sample. Thes results for
enthalpy changes readable from curve 3 are also included
in Tables 1–4 (column E).
On curve 3, as well as in the columns A of Tables 1–4,
subsequent elementary processes of the transformations are
indicated by sections a–b and c–d, etc. In columns B of
However, it turned out that we are only correct if the
enthalpychangevaluesofeveryelementaryprocess(columns
Fig. 2. MnSO4·5H2O. Curves recorded with the conventional DTA
and TG (a) and the simultaneous Q-DTA, Q-TG (b) methods: sec-
tion a–b: MnSO4·5H2Os → (1 − x)MnSO4·4H2Os + L1sat; section c–d:
Fig. 4. Na2SO4·10H2O. Curves recorded with the conventional DTA
sat
(1 − x)MnSO4·4H2Os + L1 → (1 − y)MnSO4·4H2Os + L2sat; section e–f:
and TG (a) and the simultaneous Q-DTA, Q-TG (b) methods:
(1 − y)MnSO4·H2Os + L2 → MnSO4·H2Os↓ + 4H2Og↑; section f–g:
section a–b: Na2SO4·10H2Os → (1 − x)Na2SO4s + L1
; section c–d:
sat
sat
MnSO4·H2Os → MnSO4s + H2Og↑.
(1 − x)Na2SO4s + L1 → Na2SO4 ↓ + 10H2Og↑.
sat
s

78
F. Paulik et al. / Thermochimica Acta 438 (2005) 76–82
Table 1
CuSO4·5H2O
A
B
ꢀH205
C
ꢀHT
D
E
F
n
◦
C
s
Theoretical
kJ Mol−1
Measured
kJ g−1
Corrected (kJ Mol−1
)
kJ Mol−1
1
2
3
4
5
a–b
c–d
e–f
a–f
−0.215
−0.391
−0.696
−54
−98
M1
M1
M1
−54
−14
M1
M2
M3
−54
M1
Q
M3
−13
−174
−149
−149
−227
−326
−217
E − B − 4
−216
F − B − 5
0
n
Deviation of ꢀHT from ꢀH25 in %
D − B + 44
◦
C
s
M1 = MCuSO ·5H O, M2 = M2H O, M3 = MCuSO ·3H O, Q = evaporation heat: 2.425 kJ g−1 × weight of evaporated H2O: 0.1442 g × M2H O
.
4
2
2
4
2
2
Table 2
MnSO4·5H2O
A
B
ꢀH205
C
ꢀHT
D
E
F
n
◦
C
s
Theoretical
kJ mol−1
Measured
kJ g−1
Corrected (kJ Mol−1
)
kJ mol−1
1
2
3
4
5
6
a–b
c–d
e–f
g–h
a–h
−0.112
−0.235
−1.641
−0.386
−27
−57
M1
M1
M1
M1
−27
−52
M1
M2
M3
M4
−27
−52
−52
−65
M1
M2
Q
−396
−93
−118
−65
M4
−278
−573
−262
E − B − 6
−196
0
n
Deviation of ꢀHT from ꢀH25 in %
D − B + 106
F − B − 29
◦
C
s
M1 = MMnSO ·5H O
,
M2 = MMnSO ·4H O
,
M3 = M4H O
,
M4 = MMnSO ·H O
,
Q = evaporation heat: 2.425 kJ g−1 × weight of evaporated H2O:
4
2
4
2
2
4
2
0.2986 g × M4H O
.
2
Table 3
Mg(NO3)2·6H2O
A
B
ꢀH205
C
ꢀHT
D
E
F
n
◦
C
s
Theoretical
kJ mol−1
Measured
kJ g−1
Corrected (kJ Mol−1
)
kJ mol−1
1
2
3
4
5
6
a–b
c–d
d–e
f–g
a–g
−0.273
−1.012
−0.645
−0.825
−70
−259
−165
−212
M1
M1
M1
M1
−70
−73
M1
M2
M2
M3
−70
M1
Q1
Q2
M3
−29
−20
−46
−152
−152
−370
−706
D − B + 91
−341
E − B − 8
−271
0
n
Deviation of ꢀHT from ꢀH25 in %
F − B − 27
◦
C
s
M1 = MMg(NO ) ·6H O, M2 = M4H O, M3 = MMg(NO ) ·2H O, Q1/Q2 = evaporation heat: 2.425 kJ g−1 × weight of evaporated water: 0.1686/0.1124 g × M4H O
.
2
3
2
2
3
2
2
2
Table 4
Na2SO4·10H2O
A
B
ꢀH205
C
ꢀHT
D
E
F
n
◦
C
s
Theoretical
kJ mol−1
Measured
kJ g−1
Corrected (kJ Mol−1
)
kJ mol−1
1
2
3
4
a–b
c–d
a–d
−0.262
−2.479
−84
M2
M1
−84
M1
M2
−84
M1
Q
−799
−446
−244
−521
−883
−530
−328
0
n
Deviation of ꢀHT from ꢀH25 in %
D − B + 70
E − B + 2
F − B − 37
◦
C
s
M1 = MNa SO ·10H O, M2 = M10H O, Q = evaporation heat: 2.425 kJ g−1 × weight of evaporated water: 0.5587 g × M10H O
.
2
2
4
2
2

F. Paulik et al. / Thermochimica Acta 438 (2005) 76–82
79
C) are multiplied with the molecular mass (M1, M2, M3 . . .)
of the respective starting compound, or if the corrected results
of the measurement (columns E) are recorded as functions of
them (Figs. 1b–4b, curves 3).
earlier concerning the interpretability of traditional DTA and
DSC curves. Unambiguous answers are given to these ques-
tions by the curves of Fig. 1b.
At 96 ◦C, CuSO4·5H2O was melted in its own crystal
water, and the solution contained solid CuSO4·3H2Os and
a saturated solution containing trihydrate (Fig. 1b, curve 3,
section a–b). At 103 ◦C, the solution started to boil, then it
evaporated isothermally (section c–d). Before reaching the
Thus, taking CuSO4·5H2O as an example, in the elemen-
tary reaction a–b, M1 = MCuSO ·5H O, in reaction c–d, M2 =
4
2
2 × MH O, in e–f, M3 = MCuSO ·3H O molecular masses
2
4
2
should be taken as multiplication factors. In the case of
the evaporation of the solution phase, the number of water
molecules leaving the system has also to be taken into
account.
boiling point, the weight of the sample remained strictly
s
n
constant (curve Q-TGT ). The solid CuSO4·3H2O rem-
nant decomposed at 116s◦C to solid CuSO4·H2Os and water
In order to prove the correctness of this calculation
method, it was also calculated what amount of heat (Q) was
needed for the evaporation of the liquid water liberated in the
process (c–d). Therefore, by taking again CuSO4·5H2O as an
example, the amount of evaporated water was read from the
Q-TG curve (Fig. 1b, curve 4) (ꢀm = 0.1442 g) and this was
multiplied by the evaporation heat of water (2.425 kJ g−1),
by the molecular mass of water, and by the number of water
vapour (section e–f).
3.1.2. Determination of the decomposition heat of
CuSO4·5H2O
In section a–d of curve 3 in Fig. 1b (CuSO4·5H2O →
CuSO4·3H2O) an enthalpy change of −152 kJ mol−1
,
whereas in section d–f (CuSO4·3H2O → CuSO4·H2O) that
of −174 kJ mol−1 was measured by the authors (Table 1, col-
umn D, lines 1–3). In order to check the values measured, the
authors looked for earlier data but no reliable data could be
found in the literature.
molecules evaporated (2 × MH O) (Table 1, column F, line
2
2).
The correctness of the above calculation is supported also
by comparing the measured (column D) and the corrected
enthalpy change values (columns E and F) with the one cal-
culated from the standard formation heats of the reaction
partners resulting in standard reaction heats which can be
considered a theoretical value (column B) (ꢀrH205 ◦C). The
percentual differences between theoretical, measured and
corrected values (D–B, E–B, F–B) are given in the last lines
(lines 4–6) of Tables 1–4.
3.1.3. Earlier results
At the beginning (1910–1960), the decomposition heat
of CuSO4·5H2O was determined mainly by calorimet-
ric measurements (dehydration and rehydration heats, dis-
solution heat, etc.) and by determining the change in
vapour pressure [19]. The most probable values seemed to
be, among many different ones for both transformations,
for CuSO4·5H2O → CuSO4·3H2O −249 kJ mol−1, and for
CuSO4·3H2O → CuSO4·H2O −249 kJ mol−1, respectively
[20].
The value of the reaction heat changes with the temper-
ature (Kirchoff”s law). Therefore, the question may arise
what error is made if we compare the measured and corrected
n
enthalpy changes (ꢀHT ) of partial reactions taking place at
In the fifties, Kissinger [21], by publishing his equation
derived from the Arrhenius relationship brought into fash-
ion to apply reaction kinetic parameter calculations. The
famous experiment of Borhardt and Daniels [22] seemed
to justify the findings of Kissinger. After that, thermo-
analytical experts determined the transformation heats of
every compound, also the dehydration heat of CuSO4·5H2O
[23–28] almost exclusively [29] by calculating reaction
kinetic parameters, in spite of the fact that the results scat-
tered between −180 and −360 kJ mol−1 for the reaction
CuSO4·5H2O → CuSO4·H2O.
s
temperatures different (Ts) from ambient (25 ◦C) temperature
(Tables 1–4, columns D, E and F) with the standard reac-
tion heats valid at 25 ◦C (ꢀrH205 ◦C) (columns B). The newer
physico-chemical tables [8–10] contain also the changes of
formation heats with temperature. Thus, the values of stan-
dard reaction heats were recalculated to the characteristic
temperatures of the elementary reactions, and this was com-
pared with the similarly recalculated measured and corrected
values of the reaction heats for the elementary reactions. The
differences determined by these types of calculations were
found so small that they did not modified essentially the latent
error. Therefore, such kinds of corrections were neglected in
later calculations.
This fad remained alive almost up to now, in spite of
the fact that it turned out already at the beginning that the
parameter calculation is unsuitable for determining reaction
heats.
Attention to this fact was called, e.g. by the inventors of
the Q-TG method as soon as in 1971 [30]. Later on, they
and their coworkers supported this criticism also by practical
examples [7d,31–34].
Accordingtotheiropinion, theArrheniusrelationshipcan-
not be criticized in its own place, but it is not applicable for
determining the activation enthalpy of reactions leading to
equilibrium by using a non-isothermal heating program and
3. Discussion
3.1. CuSO4·5H2O
3.1.1. Decomposition mechanism of CuSO4·5H2O
According to publications cited in the References without
striving for completeness [7c,11–18], many questions arose

80
F. Paulik et al. / Thermochimica Acta 438 (2005) 76–82
open sample holder for taking the DTA, DSC and TG curves
being the basis for parameter calculation.
result of this calculation (−5%) (column F, line 5) hardly dif-
fers from the values measured and corrected (column E, line
5) what makes also probable that the correction calculation
is right.
The dehydration heats of other salt hydrates having dif-
ferent decomposition mechanisms than that of CuSO4·5H2O
have also been measured by the “simultaneous Q-DTA,
Q-TG” method. In these cases the latent error was even
bigger.
It is namely well-known that the traditional experimental
conditions are capable of modifying the course of curves TG,
DTA and DSC to such an extent that they are characteristic
rather for the experimental conditions and not for the reaction
itself [7e].
3.1.4. Determination of the reaction heat of
CuSO4·5H2O by the “simultaneous Q-DTA, Q-TG
method”
As the authors did not find reliable comparative data in
the literature, they calculated the sums of standard reaction
heat (ꢀrH205 ◦C) of the two-step decomposition process, of
3.2. MnSO4·5H2O
n
n
According to the curves Q-TAT and Q-TGT in Fig. 2b,
MnSO4·5H2O was melted incongsruently in itss own crys-
tal water at 35 ◦C by forming solid MnSO4·4H2Os and
a saturated solution (L1sat) (curve 3, section a–b). At
55 ◦C, MnSO4·4H2O also decomposed, and an intermediate,
MnSO4·H2Os and also a saturated solution of the monohy-
drate (L2sat) was formed (section c–d). The later saturated
solution started to boil at 102 ◦C, then it evaporated isother-
mally. In the same time, the dissolved MnSO4·H2Os pro-
portional to the evaporating water, precipitated. At 270 ◦C,
CuSO4·5H2O from the standard formation heats (ꢀf H205 ◦C
)
of the reaction partners formed [8–10] according to thermo-
chemical rules (Table 1, column B, line 4). This was then
compared with the enthalpy change measured (column D,
line 4, Fig. 1b, curve 3). A difference of 44% has been found
between the measured and the theoretical values (columns
D–B, line 5).
In order to disclose the reason for this deviation, the
dehydration heats of other salt hydrates (MnSO4·5H2O,
Mg(NO3)2·6H2O, Na2SO4·10H2O) were also determined,
and even bigger differences (+70, +91, +106) were found
between the theoretical and measured values (columns D–B).
Curiously, these unprobably big deviations helped to find the
reason for a latent, till now unknown error.
s
the remaining MnSO4·H2Os decomposed to MnSO4 and
water vapour. This process was originally also isothermal,
but due to a delayed nucleus formation, the temperature of
the monohydrate increased temporarily to 275 ◦C (section
f–g). According to experience [1,2,7f], the beak-like course
of curve 3 and is a sign for delayed nucleus formation.
n
n
It turned out, namely, that the error was caused by the fact
that the authors calculated the enthalpy values of the elemen-
tary reactions measured in kJ g−1, e.g. for the CuSO4·5H2O
in the traditional way, by multiplying it with the molecular
mass (M1) of the original compound (CuSO4·5H2O) into the
dimension of kJ mol−1 (column D).
The f–f section of the Q-TAT and Q-TGT curves is also
s
s
worth of attention. This indicates that in this temperature
range the sample took up a small amount of heat by loosing
at the same time a little weight. Between 100 and 270 ◦C
the concentration of the residual solution increased again,
because the solubility of the monohydrate increased rapidly
with rising temperature. It can be supposed that towards the
end of evaporation, from the large amount of MnSO4·H2Os,
microcrystals precipitated, and from the syrup-like, concen-
trated solution a mush-like pulp was formed, at the surface
of which a crust could be developed [7g] which hindered the
removal of the last remnants of water.
In case of the MnSO4·5H2O, there is a big difference
(+106%) (line 6, columns D–B) between the theoretical (col-
umn B, line 5) and the measured and traditionally calculated
(column D, line 5) values. This big difference could be
decreased to −6% (columns E–B, line 6) by the correction
calculation proposed (column E). The difference between the
theoretical and corrected enthalpy changes (columns F–B,
line 6), however, increased to −29% when the evaporation
heat of pure water was used instead of that of the saturated
solution measured in calculating the absorbed amount of heat
(Q). This later way of calculation is only an approaching one
because it let out of consideration that between 50 and 250 ◦C
further different kind of exothermal and endothermal elemen-
tary processes (e.g. change of heat capacity) took place. Due
to this can be explained the difference between the two cor-
rected values (−6 and −29%).
It also turned out that it would have been correct to handle
the elementary processes of the dehydration of CuSO4·5H2O
(section a–b, etc.) as independent processes from the view-
point of the calculations, and the enthalpy values obtained in
the dimension of kJ g−1(Table 1, column C) should have been
multiplied by the molecular masses of the respective starting
compounds (M1, M2, M3) and by the number of the partici-
pating molecules, which are in case of CuSO4·5H2O: M1 =
MCuSO ·5H O, M2 = 2 × MH O, M3 = M3 = MCuSO ·3H O
.
4
2
2
4
2
The results are obtained in this case in kJ mol−1, but in a
corrected value (column E, lines 1–3). The sum of the reac-
tion heats thus corrected (column E, line 4) shows a difference
of only −4% (columns E–B, line 5) when compared with the
theoretical value.
Though the satisfactory agreement has a supporting value,
another way was also found to control the correctness of the
calculation method. It was calculated, e.g. what amount of
heat (Q) was taken up, later during the evaporation of the
saturated solution (section c–d). The weight of the water
n
evaporated according to curve Q-TGT was multiplied by the
s
evaporation heat of water, by the molecular mass of water and
by the number of molecules taking part in section c–d. The

F. Paulik et al. / Thermochimica Acta 438 (2005) 76–82
81
3.3. Mg(NO3)2·6H2O
(2) This deteriorating effect of material- and heat-transport
processes are totally eliminated by using the “simultane-
ous Q-DTA, Q-TG measuring technique”. The explana-
tion for this is that the experiment is carried out under
optimum experimental conditions which are not equal,
but very near to those required by thermodynamics deter-
mined by theoretical considerations. This approximation
of the ideal conditions is made possible by the use of
the “labyrinth crucible” instead of traditional open sam-
ple holders and the “transformation-governed heating
control” instead of a non-isothermal heating program.
The former generates in its inside a pure, “self-generated
atmosphere” of 100 kPa pressure, whereas the latter, on a
feed-back principle, regulates the sample temperature so
that the difference in the temperature between the sam-
ple and the reference material (ꢀT) is always such that
the transformation takes place with a constant rate being
by orders of magnitude smaller than the traditional one
(dHt/dt ∼ dm/dt). The result:
Following information can be read from curves
n
n
Q-TAT and Q-TGT in Fig. 3.
s
s
Mg(NO3)2·6H2O melted congruently at 90 ◦C in its own
crystal water (section a–b), and an unsaturated solution was
formed (section b–c), which started to boil at 130 ◦C. From
the boiling solution water vapour was evaporated (curve
n
Q-TGT ), and at the same time, both the boiling tempera-
ture ansd, to a proportional extent, the concentration of the
solution increased continuously (section c–d). The solution
became saturated at 280 ◦C. From then on, parallelly, water
n
vapour left the solution (curve Q-TGT ), and in a proportional
s
amount, solid Mg(NO3)2·2H2Os precipitated at a constant
temperature. The water loss of an unsaturated solution is
always non-isothermal, whereas that of saturated solutions
is isothermal [1,2]. The dihydrate decomposed at 370 ◦C to
Mg(NO3)2s and water vapour.
Table 3 also proves that in calculating the enthalpy
changes, the above described correction calculation should be
applied. Withoutthiscorrection, namely, theerrorwouldhave
been also in this case very large, +91% (columns D–B, line
5), whereas the difference with using the corrected enthalpy
change makes only −8% (columns E–B).
(3) By applying the “simultaneous Q-DTA, Q-TG method”:
(3a) Transformations leading to equilibrium and free
of every additional elementary processes or other
effects take place always in a strictly isothermal
way at a temperaure characteristic for the transfor-
mation (Figs. 1b–4b).
3.4. Na2SO4·10H2O
(3b) The course of equilibrium transformations is mod-
ified to non-isothermal on sections of the process
where some foreign effect leading also to equilib-
rium appears (e.g. change of the boiling point in
multicomponent systems with changing composi-
tion (Fig. 3b, curves 3 and 4, section c–d) or change
in the melting point [7], or in cases where additional
elementary processes of non-equilibrium nature
(e.g. nucleus formation) take also place (Fig. 2b,
curves 3 and 4, section f–g), or an increase of the
crust thickness of the newly formed phase hinder-
ing the free removal of the gaseous decomposition
products plays a role (Fig. 2b, curves 3 and 4, sec-
tion f–f).
Dehydration of Na2SO4·10H2O is a simple, well inter-
pretable process.
According to curve 3 in Fig. 4b, the salt hydrate melted in
its own crystal water at 32 ◦C, and water-free Na2SO4 and
s
a saturated solution were formed. The latter evaporated at
104 ◦C with boiling without any temperature change forming
s
precipitated Na2SO4 .
As Table 4 shows, a difference between the theoreti-
cal and measured enthalpy change values of +70% found
(columns D–B, line 4), whereas in case of the corrected
and non-corrected values this difference was only +2%
(columns E–B, line 4) and −37% (columns F–B, line 4),
respectively.
(3c) Reactions not leading to equilibrium (e.g. thermal
decomposition of organic compounds) run in a non-
isothermal way. The repetition of the studies pro-
n
n
4. Conclusions
vides (Q-TAT and Q-TGT curves of unchanged
course characsteristic for the given compound. In
s
(1) The course of traditional DTA, DSC, TG, EGA, etc.
curves is the resultant of partly the enthalpy and weight
changes accompanying the chemical and physical trans-
formations, and partly are influenced by the effects of
additional elementary processes modifying their course
(e.g. nucleus formation), as well as by the effects of
material- and heat-transport, which are, however, out of
our interest. The latter effects are also functions of the
experimental conditions, but sometimes they modify the
course of the curves to such an extent that they are charac-
teristic for material- and heat-transport processes rather
than for the transformation studied.
these cases, the course of thermal decomposition is
independent of the partial pressure of the gaseous
decomposition product. Use of a labyrinth crucible
or inert gas is advisable, but only for protecting the
sample from the oxidative effect of air.
(4) To the contrary of using traditional methods, the extraor-
dinary resolution capability and selectivity of the simul-
taneous Q-DTA, Q-TG method allow to separate the
subsequent elementary processes in simple and com-
plex systems, and to identify them by their characteristic
course, as well as to determine their enthalpy and weight
changes separately.

82
F. Paulik et al. / Thermochimica Acta 438 (2005) 76–82
(5) The large resolution and selectivity of the simultaneous
Q-DTA, Q-TGmethodmadepossibletodiscoveralatent,
till now unknown hidden mistake in the static (calorimet-
ric) and dynamic (DTA, DDC, DSC) determination of
the enthalpy changes in complex transformations lead-
ing to equilibrium. Until now, it was usual to multiply the
results obtained in kJ g−1 dimension by the molecular
mass of the starting material, obtaining thus the result in
kJ mol−1 as given in, e.g. physico-chemical tables. How-
ever, the right way is to consider the partial processes as
series of individual processes, and the results obtained in
kJ g−1 are multiplied by the molecular mass of the start-
ing materials of the partial process, and then, by summing
(f) F. Paulik, Special Trends in Thermal Analysis, Wiley & Sons,
Chichester, 1995, p. 193;
(g) F. Paulik, Special Trends in Thermal Analysis, Wiley & Sons,
Chichester, 1995, p. 215.
[8] O. Knacke, O. Kubaschewski, H. Heeselmann (Eds.), Thermochem-
ical Properties of Inorganic Substances III, Springer Verlag, Berlin,
1991.
[9] CRC Handbook of Chemistry and Physics, CRC Press, Boca Raton,
Boston, 1998.
[10] R.H. Perry (Ed.), Perry’s Chemical Engineer’s Handbook, McGraw-
Hill, 1998.
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[12] W.W. Wendlandt, Thermochim. Acta 1 (1970) 419.
[13] W.W. Wendlandt, Thermochim. Acta 9 (1974) 456.
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(1974) 381.
[15] K. Nagase, H. Yokobayashi, Thermochim. Acta 23 (1978) 283.
[16] M.I. Pope, D.I. Sutton, Thermochim. Acta 23 (1978) 188.
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.
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