Eyring parameters of dehydration processes

Article abstract of DOI:10.1016/S0040-6031(03)00125-4

Thermogravimetry was used in the study of the kinetics of dehydration of MnSO₄·5H₂O, CuSO₄·5H ₂O and 3CDSO₄·8H₂O under static air atmosphere. The values of the kinetic and thermodynamic par

Full text of DOI:10.1016/S0040-6031(03)00125-4

Thermochimica Acta 405 (2003) 171–181
Eyring parameters of dehydration processes
Magdalena Olszak-Humienik∗, Janina Moz˙ejko
Institute of Chemistry and Environmental Protection, Technical University of Szczecin, Al. Piastów 42, 71-065 Szczecin, Poland
Abstract
Thermogravimetry was used in the study of the kinetics of dehydration of MnSO4·5H2O, CuSO4·5H2O and 3CdSO4·8H2O
under static air atmosphere. The values of the kinetic and thermodynamic parameters for each stage of thermal dehydration
were calculated from α(T) data by using the integral method, applying the Coats–Redfern approximation. The best model for
all stages of dehydration is random nucleation model F1. The dependencies of enthalpy on entropy of activated complexes for
different kinetic models were described. The linear relation was calculated between the Gibbs energy of activated complexes
and the maximum dehydration rate temperature for analysed dehydration processes.
© 2003 Elsevier Science B.V. All rights reserved.
Keywords: Kinetics of thermal dehydration; Thermodynamic functions of activated complexes; Decomposition of hydrates of cadmium;
Copper and manganese sulphates
1. Introduction
hydrophilic surface and may participate in the restruc-
turing of the solid material, while such surface bonded
water molecules may be mobile in an adsorbed state
[2]. In the salt hydrates water molecules may be asso-
ciated with the metal atoms or with anions and other
water molecules, the metal ions may be surrounded
by several different water molecules (they do not have
the same environment, e.g. NiSO4·7H2O) while two
kinds of metal ions with different environments may
exist in hydrates (8CdSO4·3H2O). Hydroxyl bonds are
formed in hydrated oxy-salts. The geometry of hydrate
structures may determine their behaviour.
Dehydrations of crystalline solids together repre-
sent an important group of heterogeneous reactions.
In one set of reactions, water, which is present as
a ligand coordinated to (usually) a transition-metal
cation, is released on heating. Other dehydrations are
accompanied by the structural reorganization of the
lattice, which is destabilized by the removal of con-
stituent hydrogen-bonded water. There may also be
hydroxyl groups that combine to give oxide and water
[3]. The step-by-step character of thermal dehydration
Hydrates have been known from the earliest days
of chemistry, well-known minerals have interesting
physical properties and have always played an impor-
tant role in various technologies. A characteristic of
all hydrates is that the lattice collapses when water
is removed from the crystals and the structure of the
anhydrous material bearing no simple relation to that
of the hydrate. There are certain crystals which have
the ability to absorb water which may be subsequently
removed without radically altering the crystal. If the
crystal consist of a rigid framework in which there are
cavities or tunnels, then reversible hydration and de-
hydration may take place [1]. The water product is in-
herently volatile, but a proportion is adsorbed on the
∗
Corresponding author. Tel.: +48-91-449-45-35/48-12;
fax: +48-91-433-33-70.
E-mail addresses: magol@carbon.tuniv.szczecin.pl
(M. Olszak-Humienik), mozejko@carbon.tuniv.szczecin.pl
(J. Moz˙ejko).
0040-6031/$ – see front matter © 2003 Elsevier Science B.V. All rights reserved.
doi:10.1016/S0040-6031(03)00125-4

172
M. Olszak-Humienik, J. Moz˙ejko / Thermochimica Acta 405 (2003) 171–181
and cadmium hydrated sulphates. The hydrates have a
different associated water molecules and crystallised
in the various space groups.
Nomenclature
A
E
pre-exponential Arrhenius factor (min−1
apparent activation energy (kJ mol−1
)
)
The octahedral coordination group around a cop-
per atom in CuSO4·5H2O is composed of four wa-
f(α) conversion function dependent on
2−
mechanism of the reaction
ter molecules and two oxygen atoms of SO4 ions.
F
Snedecor’s variable
The odd water molecule is held by hydroxyl bonds
between water molecules coordinated to metal atoms
and oxygen atoms of SO4 ions. In contrast to pen-
g(α) integral form of the conversion function
ꢀG∗ Gibbs free energy of activated
2−
complexes (kJ mol−1
)
tahydrate, in the trihydrate of copper sulphate all water
molecules are coordinated to the copper atom. The co-
ordination group around a metal is composed of three
ꢀH∗ enthalpy of activated complex (kJ mol−1
k(T) rate constant
)
linear rate of heating (K min−1
correlation coefficient
gas constant (kJ mol−1 K−1
)
2−
q
r2
R
water molecules and an oxygen atom of SO4 ions
[1]. Dehydration of this salt was studied by many au-
thors [5–10].
)
ꢀS∗ entropy of activated complexes
The hydrate cadmium sulphate has a complex
structure and contains four crystallographic different
groups of water molecules [1]. The decomposition of
3CdSO4·8H2O and properties of its intermediates has
been the subject of numerous investigations [11–15].
The rate of a dehydration under non-isothermal con-
ditions has been represented by the relation:
(kJ mol−1 K−1
time (min)
)
t
T
absolute temperature (K)
Tm maximum dehydration rate temperature
Greek letter
α
transformation degree
dα
= k(T)f(α)
(1)
dt
is often connected in different studies with the vari-
ous strengths of molecular bonding lost from the ini-
tial compound structure: weakly bonded molecules
are removed in the early stages, and more strongly
bonded ones later. Coordinated and non-coordinated
water molecules are stepwise removed from hydrates.
The dehydration temperature depends on the strength
of the water bonding. Longvinenko [4] says that there
is no correlation between the composition and the
structure of the intermediate phase and the existence
of weakly and strongly bonded water molecules in
starting hydrate. The dehydration steps’ independence
from the starting structure, and the great influence of
the equilibrium shift is well known. The entropy term
controls the reaction of intermediate hydrate forma-
tion.
Many sulphates crystallize with odd numbers of
molecules of water of crystallization. Dehydration of
these hydrates to the monohydrate stage is easy, but
the last molecule of water is not removed until tem-
peratures between 200 and 300 ◦C are reached.
The present paper reports a kinetic and thermody-
namic study of the dehydration of copper, manganese
where α is the transformation degree, t the time (min),
k(T) is the rate constant, f(α) the conversion function
dependent on mechanism of the reaction, and T the
absolute temperature (K).
k(T) can be described by the Arrhenius equation:
ꢀ
ꢁ
E
k(T) = A exp −
(2)
RT
where R is the gas constant (kJ mol−1 K−1), E the
apparent activation energy (kJ mol−1), and A the
pre-exponential Arrhenius factor (min−1).
These equations imply a strong correlation between
kinetic parameters. The rate constant can also be de-
scribed by Eyring equation [16]:
ꢀ
∗ ꢁ
ꢀ
∗ ꢁ
kBT
h
ꢀS
R
ꢀH
k(T) =
exp
exp −
(3)
RT
where kB is the Boltzmann constant, h the Planck’s
constant, ꢀH∗ the enthalpy of activated complex
(kJ mol−1), ꢀS∗ the entropy of activated complexes
(kJ mol−1 K−1), and ꢀG∗ the Gibbs free energy of
activated complexes (kJ mol−1).

M. Olszak-Humienik, J. Moz˙ejko / Thermochimica Acta 405 (2003) 171–181
173
Fig. 1. TG curves for particular hydrated sulphates: CuSO4·5H2O, MnSO4·5H2O and 3CdSO4·8H2O.
After integrating Eq. (1), we have:
The correlation coefficient, r2 and Snedecor’s vari-
able, F were calculated to aid the selection of the g(α)
function best describing the experimental results.
ꢂ
ꢂ
α
t
dα
g(α) =
=
k(T) dt
(4)
f(α)
0
0
where g(α) is the integral form of conversion function.
In the present study, the kinetics of thermal decom-
position of hydrates was followed by integral method
by applying the Coats–Redferns approximation:
2. Experimental
These investigations of thermal dehydration of
choice hydrated sulphates (MnSO4·5H2O, CuSO4·
5H2O and 3CdSO4·8H2O) were carried out in static
air atmosphere, at a heating rate of 2–10 K min−1, in
the temperature range 293–600 K, with derrivatograph
ꢃ
ꢀ
ꢁꢄ
g(α)
T2
AR
qE
2RT
E
ln
= ln
1 −
−
(5)
E
RT
where q is the rate of heating a sample.
A plot of ln(g(α)/T2) versus 1/T gives a straight line
if the model relation is correct.
Table 1
Characteristic parameters of particular dehydration steps of hy-
drated sulphates at heating rate 10 K min−1
The thermodynamic functions of activated com-
plexes can be calculated via the equations:
Stage
Trange (K)
Tm (K)
Mass loss (%)
Found
Theoretical
ꢀH∗ = E − RT
(6)
(7)
(8)
MnSO4·5H2O
ꢀ
ꢁ
hA
1
2
3
4
336–370
362.7
385.4
516.9
549.4
12.47
26.75
35.16
37.50
13.07
28.01
35.48
37.34
ꢀS∗ = R ln
− 1
370–399
487–530
530–556
kBT
ꢀG∗ = ꢀH∗ − T ꢀS∗
CuSO4·5H2O
1
2
3
327–380
380–421
505–553
368.1
407.0
541.2
14.15
28.49
35.94
14.42
28.84
36.05
The application of these equations to systems of con-
densed phases can be justifiable by employing a canon-
ical ensemble approach. From the above equations it
seems that the correlation between the enthalpy and
entropy of activated complexes will be similar to the
correlation between parameters E and ln A.
3CdSO4·8H2O
1
2
361–441
415–515
404.0
496.0
11.54
18.58
11.70
18.72

174
M. Olszak-Humienik, J. Moz˙ejko / Thermochimica Acta 405 (2003) 171–181
Table 2
Kinetic, thermodynamic and statistic parameters of MnSO4·5H2O thermal dehydration
Model
E (kJ mol−1
)
A (min−1
)
r2
F
ꢀS∗ (J mol−1 K−1
)
ꢀH∗ (kJ mol−1
)
ꢀG∗ (kJ mol−1
)
Stage 1
D1
D2
D3
D4
F1
A2
A3
R1
162.6
186.1
217.8
196.4
123.5
58.8
37.2
78.3
98.2
106.0
3.16 × 1016
6.82 × 1026
1.75 × 1031
8.98 × 1027
1.46 × 1018
2.49 × 108
1.17 × 105
1.32 × 1011
1.68 × 1014
2.75 × 1015
86.0
89.2
92.8
90.5
95.2
94.7
94.1
85.0
90.7
92.4
312
421
655
488
1006
909
817
290
499
620
161.2
225.0
309.4
246.5
59.1
−127.9
−191.6
−75.8
−16.4
6.9
159.6
183.1
214.9
193.5
120.6
55.9
34.3
75.4
95.2
103.0
102.7
103.7
105.7
106.5
99.8
101.0
101.9
102.1
101.0
100.6
R2
R3
Stage 2
D1
D2
D3
D4
F1
A2
A3
R1
93.6
130.6
207.0
153.5
153.5
73.5
46.9
43.6
81.0
100.3
2.02 × 1012
2.11 × 1017
4.06 × 1027
1.21 × 1020
1.23 × 1021
7.33 × 109
1.13 × 106
2.38 × 105
6.68 × 1010
3.76 × 1013
84.1
89.8
97.1
92.8
99.8
99.8
99.8
82.1
94.1
96.9
175
289
1112
427
18238
16551
14962
151
−53.7
42.4
239.3
95.2
114.5
−100.4
−173.4
−186.4
−82.1
−29.4
90.5
127.5
203.8
150.3
150.3
70.4
43.7
40.4
77.8
97.1
110.9
111.4
112.9
114.1
106.8
108.5
109.6
111.2
109.0
108.3
R2
R3
525
1041
Stage 3
D1
D2
D3
D4
F1
A2
A3
R1
277.5
314.5
360.2
329.6
200.1
95.8
1.13 × 1028
5.14 × 1031
1.25 × 1036
6.94 × 1032
2.69 × 1020
3.00 × 109
5.68 × 105
2.27 × 1013
4.09 × 1016
6.62 × 1017
94.9
96.2
97.5
96.7
98.3
98.2
98.0
94.6
96.8
97.4
723
988
245.4
315.4
399.4
337.0
99.4
−110.3
−181.5
−36.0
26.3
273.3
310.3
355.9
325.4
195.9
91.6
148.7
150.1
153.1
154.2
145.4
147.6
149.1
148.6
147.0
146.5
1510
1138
2281
2086
1900
679
61.1
56.9
134.5
164.6
175.9
130.3
160.4
171.6
R2
R3
1169
1437
49.5
Stage 4
D1
D2
D3
D4
F1
A2
A3
R1
304.7
385.0
517.6
426.9
334.8
162.9
105.5
147.8
221.5
254.3
7.75 × 1028
3.38 × 1036
1.16 × 1049
1.48 × 1040
1.92 × 1032
3.01 × 1015
6.34 × 109
5.78 × 1013
1.28 × 1021
2.24 × 1024
93.2
96.2
99.2
97.5
99.9
99.9
99.9
92.8
98.1
99.1
480
883
4095
260.8
407.1
647.1
476.8
325.8
4.1
−104.6
−28.8
111.8
173.9
300.2
380.5
513.1
422.4
330.3
158.3
101.0
143.3
217.0
249.8
158.6
159.5
161.7
163.5
153.4
156.1
157.8
158.9
156.3
155.3
1356
128600
121502
114606
451
1761
3946
R2
R3
MOM-PC (Hungary). All hydrates used in the present
study after recrystallization from water were an an-
alytical grade materials and were supplied by PPH
Polskie Odczynniki Chemiczne, Gliwice, Poland. The
sample mass was 20 mg.
3. Results and discussion
The thermal decomposition of particular anal-
ysed hydrates is characterised by several stages. The
changes in the TG run at 10 K min−1 are shown in

M. Olszak-Humienik, J. Moz˙ejko / Thermochimica Acta 405 (2003) 171–181
175
Table 3
Kinetic, thermodynamic and statistic parameters of CuSO4·5H2O thermal dehydration
Model
E (kJ mol−1
)
A (min−1
)
r2
F
ꢀS∗ (J mol−1 K−1
)
ꢀH∗ (kJ mol−1
)
ꢀG∗ (kJ mol−1
)
Stage 1
D1
D2
D3
D4
F1
A2
A3
R1
120.4
144.5
179.9
155.9
107.2
50.6
31.7
57.2
78.2
86.9
9.89 × 1016
2.47 × 1020
1.96 × 1025
4.49 × 1021
3.38 × 1015
1.10 × 107
1.40 × 104
6.30 × 107
1.19 × 1011
2.62 × 1012
92.7
95.5
98.2
96.6
99.5
99.4
99.3
91.9
96.9
98.1
291
36.5
101.6
195.4
125.7
8.5
−154.0
−209.4
−139.5
−76.8
−51.1
117.4
141.5
176.9
152.9
104.2
47.6
28.7
54.2
75.2
83.9
104.3
105.0
106.7
107.8
101.2
102.9
103.9
104.3
102.8
102.3
484
1272
652
4533
3990
3488
262
R2
R3
728
1183
Stage 2
D1
D2
D3
D4
F1
A2
A3
R1
105.4
131.5
175.9
145.4
112.1
52.7
32.9
49.4
73.6
84.6
1.77 × 1013
3.98 × 1016
1.74 × 1022
1.11 × 1018
4.62 × 1014
3.76 × 106
7.02 × 103
7.15 × 105
1.99 × 109
6.94 × 1010
79.8
85.3
92.4
88.0
96.6
96.1
95.6
77.6
88.6
91.8
111
162
339
205
788
693
604
97
−35.9
28.3
136.3
56.0
102.2
128.3
172.7
142.2
108.9
49.5
29.7
46.1
70.4
81.4
116.2
117.3
119.5
120.4
112.3
113.3
114.1
115.3
113.8
113.3
8.8
−163.6
−216.6
−177.4
−111.5
−82.0
R2
R3
218
313
Stage 3
D1
D2
D3
D4
F1
A2
A3
R1
182.3
227.9
307.7
252.6
200.6
95.9
60.9
86.7
129.5
149.4
1.98 × 1017
4.97 × 1021
2.29 × 1029
5.58 × 1023
4.40 × 1019
1.15 × 109
2.89 × 105
7.38 × 107
2.18 × 1012
2.48 × 1014
84.6
89.6
95.9
92.1
98.9
98.8
98.7
83.3
93.0
95.7
176
275
748
39.2
123.5
270.2
162.7
84.1
−118.5
−187.4
−141.3
−55.7
−16.3
178.0
223.5
303.4
248.3
196.3
91.5
56.6
82.4
125.2
145.1
157.5
159.2
162.6
163.5
152.5
153.3
154.2
156.0
154.2
153.6
371
2964
2691
2433
159
425
704
R2
R3
Fig. 1. The values of characteristic parameters of
dehydration processes are presented in Table 1.
Analysis of the weight losses changes suggests the
following scheme for the dehydration processes of
analysed compounds:
3. CuSO4 · H2O → CuSO4 + H2O.
For 3CdSO4·8H2O:
1. 3CdSO4 · 8H2O → 3CdSO4 · H2O + 5H2O;
2. CdSO4 · H2O → CdSO4 + H2O.
For MnSO4·5H2O:
The dehydration steps of 3CdSO4·8H2O under ex-
perimental conditions are not at all connected with this
different bonding of the water molecules; there is no
step of loss for the two weakly bonded uncoordinated
water molecules. This hydrate decomposes with the
formation of only one stable phase—monohydrate.
Decompositions of the all examined hydrates were
endothermic processes. The variable α was calculated
from the fractional mass loss (TG).
1. MnSO4·5H2O → MnSO4·3.25H2O+1.75H2O;
2. MnSO4·3.25H2O → MnSO4·1.25H2O+2H2O;
3. MnSO4 ·1.25H2O → MnSO4 ·0.25H2O+H2O;
4. MnSO4 · 0.25H2O → MnSO4 + 0.25H2O.
For CuSO4·5H2O:
1. CuSO4 · 5H2O → CuSO4 · 3H2O + 2H2O;
2. CuSO4 · 3H2O → CuSO4 · H2O + 2H2O;

176
M. Olszak-Humienik, J. Moz˙ejko / Thermochimica Acta 405 (2003) 171–181
Table 4
Kinetic, thermodynamic and statistic parameters of 3CdSO4·8H2O thermal dehydration
Model
E (kJ mol−1
)
A (min−1
)
r2
F
ꢀS∗ (J mol−1 K−1
)
ꢀH∗ (kJ mol−1
)
ꢀG∗ (kJ mol−1
)
Stage 1
D1
D2
D3
D4
F1
A2
A3
R1
217.3
240.1
273.2
250.7
152.5
73.0
1.54 × 1028
1.19 × 1031
1.51 × 1035
1.17 × 1032
1.26 × 1020
2.31 × 109
5.18 × 105
3.03 × 1013
1.85 × 1016
2.59 × 1017
91.3
93.9
96.9
95.0
98.7
98.6
98.5
90.8
95.4
96.8
87
570
249.9
305.2
383.8
324.2
95.1
−110.4
−180.3
−31.6
21.7
214.0
236.8
269.8
247.4
149.2
69.7
114.2
115.1
116.7
118.1
111.3
113.7
115.1
114.7
113.2
112.6
1169
709
2886
2622
32373
364
46.5
43.2
105.4
125.1
133.3
102.1
121.8
130.0
R2
R3
771
1110
43.7
Stage 2
D1
D2
D3
D4
F1
A2
A3
R1
267.7
288.1
317.6
297.6
172.0
82.0
1.41 × 1028
1.66 × 1030
1.40 × 1033
6.82 × 1030
2.22 × 1018
2.69 × 108
1.13 × 105
2.63 × 1013
3.10 × 1015
2.21 × 1016
85.2
87.6
90.9
88.7
93.6
93.0
92.3
84.4
88.9
90.5
386
473
672
528
981
888
800
363
535
637
247.7
287.4
343.4
299.1
60.1
−129.8
−194.4
−34.2
5.4
263.8
284.2
313.6
293.6
168.1
78.1
146.1
147.7
150.5
151.5
139.5
139.7
140.4
142.2
141.0
140.5
52.0
48.1
129.9
147.5
154.8
125.9
143.6
150.9
R2
R3
21.8
The α–temperature curves from non-isothermal TG
experiments were used to determine the mechanism of
the individual stages and were fitted by well-known ki-
netic models [16]. The values of kinetic and thermody-
namic parameters obtained at heating rate 10 K min−1
from different g(α) functions for particular stages of
analysed hydrates are shown in Tables 2–4.
The best model was chosen at heating rate
10 K min−1 on the basis of statistic parameters
values—r2 and F. From Tables 2–4, it can be seen that
the most suitable expressions for the all dehydration
stages are those of the random nucleation model F1
over the widest α range and an activation energies for
this model were in the range from 107 (the first stage
for CuSO4·5H2O) to 335 kJ mol−1 (the last stage for
MnSO4·5H2O). The highest values of E for the last
dehydration stages reflect the fact that the final wa-
ter molecule is most strongly bound. The hydrates:
MnSO4·5H2O and CuSO4·5H2O decompose at ap-
proximately equal temperatures, have approximately
equal values of Gibbs energies of activated complexes
but the entropy term contribution is higher in the case
of MnSO4·5H2O.
The dependencies of the enthalpy of activation on
the entropy of transient state for different kinetic mod-
els are shown in Figs. 2–4 and can be described as
follows:
Stage
ꢀH∗
r2
MnSO4·5H2O
1
2
3
4
362.4 ꢀS∗ + 101.9
385.4 ꢀS∗ + 110.3
516.9 ꢀS∗ + 148.0
549.4 ꢀS∗ + 156.7
0.9994
0.9984
0.9996
0.9996
CuSO4·5H2O
1
2
3
368.1 ꢀS∗ + 104.3
407.0 ꢀS∗ + 116.5
541.0 ꢀS∗ + 156.3
0.9989
0.9982
0.9989
3CdSO4·8H2O
1
2
404.0 ꢀS∗ + 113.9
496.5 ꢀS∗ + 142.0
0.9995
0.9995
Table 5 lists the kinetic and thermodynamic pa-
rameters for dehydration of all analysed salts at dif-

M. Olszak-Humienik, J. Moz˙ejko / Thermochimica Acta 405 (2003) 171–181
177
Table 5
Characteristic parameters of dehydration at different heating rates (F1 model)
β (K min−1
)
E (kJ mol−1
)
ln A (min−1
)
Tmax (K)
ꢀS∗ (J mol−1 K−1
)
ꢀH∗ (kJ mol−1
)
ꢀG∗ (kJ mol−1
)
MnSO4
Stage 1
2.5
186.2
166.5
144.7
123.5
65.5
57.8
49.8
41.8
334
342
346
353
256.3
192.0
125.4
59.1
183.5
163.7
141.8
120.6
97.9
98.0
98.5
99.8
5
7.5
10
Stage 2
2.5
5
7.5
10
238.6
212.3
189.6
153.5
78.1
69.0
60.6
48.6
361
363
374
380
360.7
285.2
214.9
114.5
235.6
209.3
186.5
150.3
105.3
105.8
106.1
106.8
Stage 3
2.5
5
7.5
10
293.0
261.8
230.6
200.1
70.9
62.7
54.0
47.0
486
491
519
508
298.1
230.1
157.1
99.4
289.0
257.8
226.3
195.9
144.2
144.7
144.8
145.4
Stage 4
2.5
5
7.5
10
381.8
379.9
357.0
334.8
87.2
85.8
80.0
74.3
523
532
536
543
432.9
421.5
373.0
325.8
377.4
375.5
352.5
330.3
150.8
151.5
152.5
153.4
CuSO4
Stage 1
2.5
162.6
150.3
128.0
107.2
55.9
51.2
42.8
35.8
347
351
359
359
176.3
136.8
66.8
8.5
159.7
147.4
125.1
104.2
98.6
99.4
101.1
101.2
5
7.5
10
Stage 2
2.5
5
7.5
10
217.7
183.0
150.0
112.1
69.0
57.2
46.0
33.8
373
379
387
390
284.9
186.6
93.1
−8.8
214.6
179.9
146.7
108.9
108.4
109.1
110.8
112.3
Stage 3
2.5
5
7.5
10
248.5
234.3
213.6
200.6
58.2
54.4
49.1
45.2
498
506
515
521
192.3
160.4
116.4
84.1
244.4
230.0
209.3
196.3
148.6
148.8
149.4
152.5
CdSO4
Stage 1
2.5
166.7
162.8
159.9
152.5
53.2
51.0
49.8
46.3
354
362
369
399
153.7
135.5
125.1
95.1
163.8
159.7
156.8
149.2
109.3
110.7
110.6
111.3
5
7.5
10
Stage 2
2.5
5
7.5
10
219.0
206.4
192.8
172.0
57.0
52.8
48.8
42.2
431
443
440
475
183.2
148.2
115.0
60.1
215.4
202.7
189.2
168.1
136.4
137.0
138.5
139.5

178
M. Olszak-Humienik, J. Moz˙ejko / Thermochimica Acta 405 (2003) 171–181
Table 5 (Continued )
β (K min−1
)
E (kJ mol−1
)
ln A (min−1
)
Tmax (K)
ꢀS∗ (J mol−1 K−1
)
ꢀH∗ (kJ mol−1
)
ꢀG∗ (kJ mol−1
)
CdSO4
Stage 1
2.5
166.7
162.8
159.9
152.5
53.2
51.0
49.8
46.3
354
362
369
399
153.7
135.5
125.1
95.1
163.8
159.7
156.8
149.2
109.3
110.7
110.6
111.3
5
7.5
10
Stage 2
2.5
5
7.5
10
219.0
206.4
192.8
172.0
57.0
52.8
48.8
42.2
431
443
440
475
183.2
148.2
115.0
60.1
215.4
202.7
189.2
168.1
136.4
137.0
138.5
139.5
Fig. 2. Dependence between the enthalpy and entropy of activated complexes created in thermal dehydration of MnSO4·5H2O.
Fig. 3. Dependence between the enthalpy and entropy of activated complexes created in thermal dehydration of CuSO4·5H2O.

M. Olszak-Humienik, J. Moz˙ejko / Thermochimica Acta 405 (2003) 171–181
179
Fig. 4. Dependence between the enthalpy and entropy of activated complexes created in thermal dehydration of 3CdSO4·8H2O.
ferent heating rates (F1 model). From these data it
seems that the apparent kinetic energies, the logarithm
of pre-exponential factor, the enthalpy and the en-
tropy for the particular steps of dehydration decrease
with a rise in heating rate. The maximum dehydra-
tion rate temperature and the Gibbs free energy of
activated complexes increase with a rise in heating
rate.
Table 6 lists the characteristic parameters values of
dehydration which were calculated by an extrapolation
of functions and Tmax, respectively, at zero heating
rate (under isothermal conditions).
The dependence of Gibbs free energy of activated
complexes calculated for F1 model on the maximum
dehydration rate temperature can be described by
equation
Figs. 5 and 6 show the example dependencies of
ꢀS∗ and ꢀH∗ on heating rates for dehydration of man-
ganese sulphate.
ꢀG∗ = 0.29 Tm − 0.4697
and is shown in Fig. 7.
r2 = 0.963
Fig. 5. Correlation between the entropy of activated complexes and the heating rate for MnSO4.

180
M. Olszak-Humienik, J. Moz˙ejko / Thermochimica Acta 405 (2003) 171–181
Fig. 6. Correlation between the enthalpy of activated complexes and the heating rate for MnSO4.
Table 6
Extrapolated values of characteristic parameters of dehydration
Stage
E0 (kJ mol−1
)
ln A0 (min−1
)
T0 max (K)
ꢀS0∗ (J mol−1 K−1
)
ꢀH0∗ (kJ mol−1
)
ꢀG∗0 (kJ mol−1
)
MnSO4
1
2
3
4
207.7
268.0
323.9
404.3
73.5
88.4
78.7
92.9
328.5
352.8
477.4
517.7
322.7
446.0
363.5
480.8
205.0
265.1
319.9
400.0
99.0
107.7
146.4
151.1
CuSO4
1
2
3
184.2
253.2
265.3
63.6
80.8
62.8
342.4
367.4
490.7
240.5
382.5
230.4
181.3
250.1
261.3
99.0
109.6
148.2
CdSO4
1
2
171.8
236.2
55.6
62.2
335.7
415.3
174.0
227.2
169.0
232.7
110.7
138.4
Fig. 7. Correlation between the Gibbs free energy of activated complexes and the maximum dehydration rate temperature.

M. Olszak-Humienik, J. Moz˙ejko / Thermochimica Acta 405 (2003) 171–181
181
4. Conclusion
References
[1] A.F. Wells, Strukturalna chemia nieorganiczna, WNT
Warszawa, 1993.
The course of thermal dehydration of all salts in-
vestigated under experimental conditions in this study
can be described by the F1 kinetic model.
This work supports the claim that the different bond-
ing of water molecules in the structure of starting hy-
drates is not always reflected in stepwise character of
thermal dissociation. All these investigated hydrates
had fewer stages of thermal dehydration than the var-
ious bonding water molecules.
The apparent kinetic energies, the logarithm of
pre-exponential factor, the enthalpy and the entropy
for the particular steps of dehydration decrease with
a rise in heating rate. The maximum dehydration
rate temperature and the Gibbs free energy of ac-
tivated complexes increase with a rise in heating
rate.
The Gibbs free energy of activated complexes
formed in investigating thermal dehydration processes
is the lineal function of the maximum dehydration
rate temperature.
[2] A.K. Galwey, J. Thermal Anal. 41 (1994) 267–286.
[3] A.K. Galwey, Thermochim. Acta 355 (2000) 181–238.
[4] V. Longvinenko, J. Thermal Anal. 36 (1990) 1743–1749.
[5] A.K. Galwey, G.M. Laverty, Solid State Ionics 38 (1990) 155.
[6] V.V. Pechkovski, A.G. Zvezdin, T.J. Beresneva, Kinet. Katal.
4 (1963) 208.
[7] A.N. Ketov, Z. Prikl. Chim. 4 (1961) 517.
[8] W.W. Wendlandt, J. Inorg. Nucl. Chem. 25 (1963) 833.
[9] J. Straszko, M. Olszak-Humienik, J. Moz˙ejko, Przem. Chem.
74 (4) (1995) 146–149.
[10] N.Z. Laykov, A.P. Chupakhin, V.P. Isupov, V.V. Boldyrev,
Kinet. Katal. 19 (1977) 84.
[11] B. Lorant, Z. Anal. Chem. 219 (1966) 256.
[12] P. Herpin, J.M. Brégeault, Bull. Soc. Fr. Minéral. Cristallogr.
91 (1968) 296.
[13] H. Lipson, Proc. Roy. Soc. (London), A 156 (1936) 463.
[14] G. Pannetier, J.M. Brégeault, J. Guenot, Bull. Soc. Chim. Fr.
(1962) 2158.
[15] L. Walter-Lévy, D. Groult, J. Visser, Bull. Soc. Chim. Fr. 34
(1974) 383.
[16] J. Straszko, M. Olszak-Humienik, J. Moz˙ejko, Thermochim.
Acta 292 (1997) 145–150.