Thermodynamic properties of potassium nitrate-magnesium nitrate compound [2KNO3·Mg(NO3)2]

Article abstract of DOI:10.1016/j.tca.2011.12.010

The Mg(NO₃)₂-KNO₃ binary system phase diagram has a congruent melting compound, 2KNO₃·Mg(NO ₃)₂. The thermodynamic properties for this compound are not available in the literature. In this study, the nitrate compound was synthesized and the melting point and heat capacity were determined using differential scanning calorimetry (DSC). Two endothermic peaks were observed at 404.8 K and 468.83 K corresponding to solid state transition and melting of the compound with the enthalpies of transitions as 2.71 kJ/mol and 20.73 kJ/mol, respectively. The heat capacity data as function of temperature are fit to polynomial function and thermodynamic properties like enthalpy, entropy and Gibbs energies of the compound as function of temperature are subsequently deduced.

Full text of DOI:10.1016/j.tca.2011.12.010

Thermochimica Acta 531 (2012) 6–11
Contents lists available at SciVerse ScienceDirect
Thermochimica Acta
journal homepage: www.elsevier.com/locate/tca
Thermodynamic properties of potassium nitrate–magnesium nitrate compound
[2KNO3·Mg(NO3)2]
Ramana G. Reddy∗, Tao Wang, Divakar Mantha
Department of Metallurgical and Materials Engineering, The University of Alabama, Tuscaloosa, AL 35487-0202, USA
a r t i c l e i n f o
a b s t r a c t
Article history:
Received 10 April 2011
Received in revised form 8 December 2011
Accepted 14 December 2011
Available online 24 December 2011
The Mg(NO3)2–KNO3 binary system phase diagram has
a
congruent melting compound,
2KNO3·Mg(NO3)2. The thermodynamic properties for this compound are not available in the liter-
ature. In this study, the nitrate compound was synthesized and the melting point and heat capacity
were determined using differential scanning calorimetry (DSC). Two endothermic peaks were observed
at 404.8 K and 468.83 K corresponding to solid state transition and melting of the compound with the
enthalpies of transitions as 2.71 kJ/mol and 20.73 kJ/mol, respectively. The heat capacity data as function
of temperature are fit to polynomial function and thermodynamic properties like enthalpy, entropy and
Gibbs energies of the compound as function of temperature are subsequently deduced.
© 2011 Elsevier B.V. All rights reserved.
Keywords:
DSC
Mg(NO3)2–KNO3 binary system
2KNO3·Mg(NO3)2 compound
Melting point
Heat capacity
Thermodynamic properties
1. Introduction
The phase diagram of Mg(NO3)2–KNO3 binary system
has two eutectics and one congruently melting solid phase,
Molten salts have been used as thermal energy storage media
for solar energy applications. Nitrates are being used in the solar
energy applications for their low melting point, low unit cost, high
heat capacity, high thermal stability, negligible vapor pressure and
high energy storage density [1]. Solar salt (NaNO3/KNO3: 60/40)
is the most popular thermal energy storage medium which is cur-
rently being used with the freezing point of 494.15 K [2]; another
ternary system HITEC which contains NaNO3, KNO3 and NaNO2
has freezing point of 414.15 K [3]. Newer nitrate salt mixtures are
being studied and projected as potential candidates for thermal
energy storage (TES) and heat transfer (HT) applications. Based on
these favorable features, molten salt can work directly as the energy
storage medium below 773.15 K [1]. Development and synthesis of
newer molten salt mixtures with freezing point lower than those
currently used for thermal energy storage applications is necessary
for sustained utilization of solar energy. The approach to develop
lower freezing point molten salt mixtures is by the prediction of
new eutectic mixtures and also by the development of new nitrate
compounds. In this context, the congruently melting compound,
2KNO3·Mg(NO3)2 can be a promising additive.
2KNO3·Mg(NO3)2. The compound 2KNO3·Mg(NO3)2 will be
labeled as MgKN in this article. The two eutectic points appear on
either side of the congruently melting solid. The melting point of
the congruently melting compound, MgKN that can be read from
the phase diagram is 498 K [4]. However, no experimental data are
available in the literature on the accuracy of this melting point.
Thermodynamic properties such as heat capacity, enthalpy, and
entropy and Gibbs energy are also not available in the literature.
In this paper, we determine the melting point and heat capacity of
MgKN using the differential scanning calorimetry (DSC) technique
to re-verify the melting point given in the phase diagram and
also to deduce the thermodynamic parameters as function of
temperature.
2. Experimental
2.1. Materials
The MgKN compound is synthesized from magnesium nitrate
hexahydrate (98%, Alfa Aesar) and potassium nitrate (ACS,
99.0% min, Alfa Aesar). Potassium nitrate is used without fur-
ther purification whereas the magnesium nitrate hexahydrate
is dehydrated before synthesizing the 2KNO3·Mg(NO3)2 com-
pound. The synthesized 2KNO3·Mg(NO3)2 compound has 98% of
purity.
∗
Corresponding author. Tel.: +1 205 348 4246; fax: +1 205 348 2164.
E-mail address: rreddy@eng.ua.edu (R.G. Reddy).
0040-6031/$ – see front matter © 2011 Elsevier B.V. All rights reserved.
doi:10.1016/j.tca.2011.12.010

R.G. Reddy et al. / Thermochimica Acta 531 (2012) 6–11
7
2.2. Dehydration of Mg(NO3)2·6H2O
Weighted amount of magnesium nitrate hexahydrate was taken
in a stainless steel crucible and placed on a hot plate in argon atmo-
sphere. Temperature of the salt is measured with a thermocouple
immersed in the salt. The salt was held at 523.15 K for 2 h after
which the salt solidifies to a white mass. The temperature is then
raised slowly to 573.15 K to remove any traces of moisture from the
salt and to ensure complete dehydration. The complete removal of
water is ascertained by weight loss.
2.3. Apparatus and calibration
Perkin-Elmer Diamond differential scanning calorimeter (DSC)
was use to measure the melting point and heat capacity of the
MgKN compound. Endothermic heat flow and temperature can be
recorded in the instrument with an accuracy of 0.0001 mW and
0.01 K, respectively. Before the actual measurements, pure indium,
zinc metal were used to calibrate the DSC temperature as well as
the heat flow curve based on the GEFTA calibration procedure [5,6].
The measurements were made under purified nitrogen atmosphere
Fig. 1. Endothermic peaks of 2KNO3·Mg(NO3)2 compound determined by Diamond
DSC showing solid state phase transition and melting.
with a flow rate of 20 cc min−1 and at a heating rate of 5 K min−1
.
heat capacity of the sample, heat flow curve for the baseline of
the empty sample pan also needs to be obtained immediately fol-
lowing the identical “iso-scan-iso” steps which were used for the
actual sample run. The difference of heat flow between the actual
crimpled sample and the empty sample pan is the absolute heat
absorbed by the test sample.
2.4. Salt preparation
The 2KNO3·Mg(NO3)2 nitrate salt compound is composed of
66.67 mol% KNO3 and 33.33 mol% Mg(NO3)2. Potassium nitrate and
dehydrated magnesium nitrate are the two salt components that
are used to synthesize the MgKN compound. Weighed amounts
of the two salts according to the above mentioned stoichiometry
are measured to an accuracy of 0.1 mg with the electrical balance
and mixed thoroughly in a stainless steel crucible. The mixture is
heated up to a certain temperature, which is about 50 K more than
the melting temperature of the salt mixture. At this temperature the
salt mixture was held for about 30 min. The salt mixture is allowed
to air cool to ambient temperature. This procedure is repeated 3–4
times to get a homogeneous MgKN compound.
3. Results and discussion
3.1. Melting point determination
Differential scanning calorimetry (DSC) was used to determine
the melting point and any solid state phase transitions of the
2KNO3·Mg(NO3)2 compound. A low scanning rate was chosen to
record the heat flow curve as function of temperature in order
to improve the sensitivity of detection. It helps to pick up any
small endothermic peaks and also reduces the temperature dif-
ference between the internal furnace and sample. Fig. 1 shows
the DSC plot of one run (sixth cycle) for the MgKN compound.
DSC plots for the compound were collected for at least three runs
(each run with fresh MgKN preparation) to ensure the reproducibil-
ity. Two endothermic peaks were identified in the figure. The first
endothermic peak refers to solid state phase transition of the MgKN
compound. The onset of phase transition begins at 403.48 0.20 K
and the peak transition temperature is 404.80 0.18 K. Fig. 2 shows
the DSC plot of endothermic peaks of the heating cycle in KNO3.
Two endothermic peaks appear in the figure, the first refers to solid
state phase transition and the second peak refers to the melting of
KNO3. Solid state phase transition from ␣-KNO3 to ␤-KNO3 occurs
at a peak temperature of 407.38 0.12 K and melting peak occurs
at 610.38 0.10 K. Similar to the solid state phase transition that
occurs in KNO3, a solid state phase transition too occurs in the
MgKN compound. The temperature of solid state phase transition
in the MgKN compound occurs at 404.80 K which is about 2.6 K
lower than that in the KNO3 compound. The enthalpy of solid state
phase transition determined from the area under the endothermic
peak is 2.71 0.03 kJ/mol. No information on the solid state phase
transition of MgKN compound is available in the literature. In this
study, we label the two solid states of MgKN compound as solid
state ˛ and solid state ˇ for convenience.
2.5. Experimental procedure
Standard aluminum pan with lid used for DSC measurements
are weighed before the experiment. For the determination of melt-
ing point and heat capacity of the synthesized MgKN compound
20–25 mg of the sample was used. The salt compound is placed
carefully in the aluminum pan and closed with the lid. The lid is
crimped by a sample press and the pan is weighed. The weight of
the sample is determined by removing the weight of the pan and
lid. The crimped ample pan was immediately put inside the sam-
ple chamber of DSC after preparation and held at 523.15 K for 10 h
to remove the trace amount of moisture that might have possibly
caught in the process of loading sample and also to ensure a homo-
geneous mixture. In the experimental procedure for melting point
determination, a temperature range from 298.15 K to 523.15 K was
set with a heating rate of 5 K min−1 followed by a cooling cycle at
the same rate. This cycle is repeated for at least 6 times to ensure
good mixture of the sample and reproducibility of the results.
For heat capacity measurement, the same procedure as that
followed for melting point determination is employed with addi-
tion of ‘iso-scan-iso’ steps to the heating–cooling cycles program.
The iso-scan-iso steps with a step width of 25 K are introduced
into the program cycle after five temperature-scan cycles. Start-
ing from 298.15 K, the temperature was held for 5 min before and
after each scanning step. The small temperature scan range is cho-
sen to decrease the thermal resistance between the device and the
sample. The upper limit for the heat capacity (Cp) measurement
was set to 623.15 K in our experiments. To get the value of molar
The second endothermic peak refers to the melting of the MgKN
compound with an onset temperature of 465.41 K and peak tem-
perature of 468.83 K. Normally, the onset temperature of transition

8
R.G. Reddy et al. / Thermochimica Acta 531 (2012) 6–11
Table 1
Temperatures and enthalpies of phase transitions in the 2KNO3·Mg(NO3)2
compound.
Compound
Transition
Temperature (K)
Enthalpy (kJ/mol)
2KNO3·Mg(NO3)2
Solid ␣–solid ␤
Solid ␤–liquid
404.8
468.83
2.71
20.73
congruent point on each side of the phase diagram and the melting
temperatures are all found to be lower than the congruent temper-
ature while higher than those of the eutectic points. As a result of
that, the congruent temperature determined using DSC technique
was verified. Moreover, the melting temperatures of two composi-
tion points beyond the portion of the partial phase diagram limited
by two eutectic points were also tested. Each point shows higher
melting temperatures than that of the eutectic point on the same
side, which indicates the validity of the measured eutectic temper-
atures. The enthalpy of fusion of the MgKN compound determined
from the area under the melting endothermic peak is 20.73 kJ/mol.
Table 1 lists the peak transition temperatures and the correspond-
ing enthalpies for the MgKN compound.
Fig. 2. Endothermic peaks of KNO3 determined by Diamond DSC showing solid state
phase transition and melting.
3.2. Heat capacity measurement
is taken as the experimental transition point for any metallic sam-
ple. However, in case of molten salts mixtures, since the thermal
conductivity is low, the complete transition is ensured only at the
peak transition temperature. The thermal gradient which exists
due to the low thermal conductivity of the salt results in internal
heat flow which enhances the mixing in the salt. Thus, the tran-
sition temperature is defined as the peak temperature of phase
transition. The peak values of temperatures for all transitions of
the MgKN compound are taken as the transition temperatures.
The only possible melting point data of the MgKN compound that
can be found prior to our study was from the previously reported
binary Mg(NO3)2–KNO3 phase diagram [4] which showed 30 K
higher melting point than that obtained in this study. To ensure
the validity of the congruent temperature of the MgKN compound,
the Mg(NO3)2–KNO3 phase diagram between two eutectic points
were reproduced using melting temperatures of the binary sys-
tem with different constituent salt compositions. The partial phase
diagram is illustrated in Fig. 3, the melting points of two eutectic
composition were determined as 461.2 0.1 K and 463.1 0.3 K.
Two points were chosen between eutectic composition and
In the DSC equipment, the heat flow through the sample is tested
as function of temperature. In the heating process, the temperature
profile can be expressed in (K) as:
Tt = To + h
(1)
where To is the initial temperature in K, h is the set heating
rate (K min−1) and Tt is the temperature in K at a certain time t
(min). Based on the thermodynamic definition, heat capacity is the
amount of heat required to change a body’s temperature by a given
amount. Combined with the equation above, the expression for Cp
(J/K mol) can be shown as follows: [7]
ꢂ
ꢃ
ꢀ
ꢁ
ꢀ
ꢁ
1
m
dH
dT
1
m
dH/dt
dT/dt
1
m
ꢀP
ˇ
Cp
=
=
=
(2)
where the ꢀP is the actual DSC heat flow signal which has the unit
as mW, m is the mass for the sample of interest. This way the heat
capacity with the DSC heat flow data are calculated.
The molar heat capacity of the MgKN compound was measured
by the DSC equipment from room temperature to 623.15 K. The
heat flow is recorded as a function of temperature in “iso-scan-iso”
steps at intervals of 25 K. The ‘iso stage’ refers to isothermal hold-
ing at a particular temperature, ‘scan stage’ refers to the heat flow
recording at a heating rate of 5 K min−1 up to a an increment of
25 K, followed by another isothermal holding stage. This is a stan-
dard procedure followed in the measurement of heat capacity of
materials using the DSC equipment. This procedure of heat capacity
measurement has two advantages; (i) any heat fluctuations during
the recording are avoided by the isothermal steps and (ii) any phase
transition can be highlighted by the choice of temperature range.
The absolute heat flow to the sample is determined by subtracting
the heat flow collected by running a baseline curve with an empty
pan. Fig. 4 shows the heat capacity of the MgKN compound mea-
sured as function of temperature in the range 298.15–623.15 K. The
figure shows two phase transitions corresponding to the solid state
phase transition and melting of the MgKN compound. Table 2 lists
the values of heat capacity as function of temperature for the entire
temperature range of this study.
The heat capacity data can be divided into three sections; (i)
solid state ␣ (298.15–403.15) K (ii) solid state ␤ (415.15–458.15) K
(iii) liquid state (478.15–623.15) K. Accordingly, the heat capacity
data are fit to three separate polynomial equations corresponding
to the three phases of the compound.
Fig. 3. Phase diagram of KNO3–Mg(NO3)2 binary system.

R.G. Reddy et al. / Thermochimica Acta 531 (2012) 6–11
9
Table 2
Heat capacity of 2KNO3.Mg(NO3)2 at different temperatures (298.15–623.15 K).
T (K)
Cp (J/K mol)
T (K)
Cp (J/K mol)
T (K)
Cp (J/K mol)
T (K)
Cp (J/K mol)
298.15
300
305
310
315
320
325
330
335
340
345
350
355
360
365
370
375
380
385
390
395
400
403
404
315.1
315.4
316.3
317.7
319.4
321.5
324.0
326.9
330.2
333.8
337.9
342.3
347.1
352.3
357.9
363.8
370.2
376.9
384.0
391.5
399.4
407.7
412.8
811.0
405
406
407
408
409
410
411
412
413
414
415
420
425
430
435
440
445
450
455
458
459
460
461
462
1042.3
900.2
714.4
611.1
562.5
518.0
464.1
426.3
409.2
403.6
402.9
408.4
407.7
410.9
418.2
429.6
444.9
464.3
487.6
511.7
532.4
561.4
606.9
680.8
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
485
490
495
500
505
510
515
520
806.8
1030.1
1503.6
2552.2
4003.0
3432.5
2955.4
2419.9
1683.9
1106.4
770.0
542.5
510.0
480.6
469.0
455.6
454.5
458.0
461.6
465.1
468.6
472.2
475.7
479.2
525
530
535
540
545
550
555
560
565
570
575
580
585
590
595
600
605
610
615
620
623.15
482. 8
486.3
489.9
493.4
496.9
500.5
504.0
507.5
511.1
514.6
518.1
521.7
525.2
528.7
532.3
535.8
539.3
542.9
546.4
549.9
552.2
Table 3
3.2.1. Heat capacity of solid state ˛: (298.15–403.15) K
Thermodynamic properties of 2KNO3·Mg(NO3)2 compound in solid state
␣
The heat capacity data for MgKN compound in the solid state 1
in the temperature range of 298.15–403.15 K is given in Table 3. The
data are fit to a second order polynomial equation. Eq. (3) gives the
polynomial equation along with the least square fit parameter (R2)
in the temperature range for the solid state ␣ of the compound.
(298.15–403.15 K).
T (K)
Cp (J/mol K)
ꢀS (J/mol K)
ꢀH (kJ/mol)
ꢀG (kJ/mol)
298.15
300
305
310
315
320
325
330
335
340
345
350
355
360
365
370
375
380
385
390
395
400
403.15
315.1
315.4
316.3
317.7
319.4
321.5
324.0
326.9
330.2
333.8
337.9
342.3
347.1
352.3
357.9
363.8
370.2
376.9
384.0
391.5
399.4
407.7
412.8
0.00
2.02
7.28
0.00
0.61
2.20
3.74
5.35
0.00
0.00
−0.03
−0.07
−0.15
−0.25
−0.38
−0.52
−0.70
−0.90
−1.12
−1.37
−1.65
−1.94
−2.26
−2.60
−2.98
−3.37
−3.79
−4.24
−4.71
−5.20
−5.53
Cp(soild state ␣)(J/K mol) = 7.69 × 10−3T2 − 4.46T + 961.27;
12.31
17.47
22.57
27.58
32.51
37.35
42.34
47.15
52.10
57.06
61.85
66.81
71.60
76.58
81.52
86.46
91.53
96.61
101.56
104.82
× (298.15 − 403.15) K, R2 = 0.9712
(3)
6.98
8.59
10.21
11.82
13.50
15.15
16.87
18.62
20.33
22.13
23.89
25.74
27.61
29.50
31.46
33.46
35.42
36.73
3.2.2. Heat capacity of solid state ˇ: (415.15–458.15) K
The heat capacity data for MgKN compound in the solid state ␤
in the temperature range of 415.15–458.15 K is given in Table 4. The
data are fit to a second order polynomial equation. Eq. (4) gives the
Table 4
Thermodynamic properties of 2KNO3·Mg(NO3)2 compound in solid state
␤
(415.15–458.15 K).
T (K)
Cp (J/mol K)
ꢀS (J/mol K)
ꢀH (kJ/mol)
ꢀG (kJ/mol)
415.15
420
425
430
435
440
445
450
455
402.9
408.4
407.7
410.9
418.2
429.6
444.9
464.3
487.6
511.7
123.84
128.58
133.41
138.25
142.90
147.77
152.73
157.83
162.93
166.36
44.51
46.50
48.54
50.62
52.64
54.78
56.98
59.27
61.59
63.16
−6.91
−7.51
−8.16
−8.84
−9.52
−10.24
−10.99
−11.76
−12.54
−13.05
458.15
Fig. 4. Heat capacity of 2KNO3·Mg(NO3)2 compound as function of temperature
determined by Diamond DSC.

10
R.G. Reddy et al. / Thermochimica Acta 531 (2012) 6–11
Table 5
below:
Thermodynamic properties of 2KNO3·Mg(NO3)2 compound in liquid state
ꢄ
T
ꢀ
ꢁ
t
CP
T
ꢀHt
Tt
(478.15–623.15 K).
ST ◦ − S298.15
=
dT +
◦
T (K)
Cp (J/mol K)
ꢀS (J/mol K)
ꢀH (kJ/mol)
ꢀG (kJ/mol)
298.15
ꢄ
ꢄ
T
T
ꢀ
ꢁ
ꢀ
ꢁ
m
478.15
485
490
495
500
505
510
515
520
525
530
535
540
545
550
555
560
565
570
575
580
585
590
595
600
605
610
615
620
623.15
455.6
454.5
458.0
461.6
465.1
468.6
472.2
475.7
479.2
482.8
486.3
489.9
493.4
496.9
500.5
504.0
507.5
511.1
514.6
518.1
521.7
525.2
528.7
532.3
535.8
539.3
542.9
546.4
549.9
552.2
231.70
238.13
242.81
247.47
252.13
256.78
261.41
266.03
270.65
275.25
279.84
284.43
289.00
293.56
298.12
302.66
307.20
311.72
316.24
320.75
325.25
329.75
334.23
338.71
343.18
347.64
352.09
356.54
360.98
363.77
93.79
96.89
99.17
−16.99
−18.60
−19.81
−21.03
−22.28
−23.55
−24.85
−26.17
−27.51
−28.87
−30.26
−31.67
−33.11
−34.56
−36.04
−37.54
−39.07
−40.61
−42.18
−43.78
−45.39
−47.03
−48.69
−50.37
−52.08
−53.80
−55.55
−57.32
−59.12
−60.26
Cp
T
CP
ꢀHm
Tm
+
dT +
+
dT
(6)
T
T
T
m
t
101.47
103.78
106.12
108.47
110.84
113.23
115.63
118.06
120.50
122.95
125.43
127.92
130.43
132.96
135.51
138.07
140.66
143.26
145.87
148.51
151.16
153.83
156.52
159.22
161.95
164.69
166.42
ꢄ
T
t
HT ◦ − H298.15
=
CpdT + ꢀHt
◦
298.15
ꢄ
ꢄ
T
m
T
+
CpdT + ꢀHm
+
CpdT
(7)
(8)
T
T
m
t
GT ◦ − G298.15 = (HT ◦ − H298.15◦) − T(ST ◦ − S298.15
◦
◦
)
The standard thermodynamic properties, entropy, enthalpy
and Gibbs energies as function of temperature for the three
phases of the MgKN compound are expressed in the following
sections.
3.3.1. Solid state ˛ (298.15–403.15) K
Standard entropy as a function of temperature of the MgKN
compound in the solid state ␣ is given by:
ꢄ
T
ꢀ
ꢁ
Cp
T
dT = 3.85 × 10−3T2 − 4.46T
◦
◦
ST = S298.15
=
298.15
+ 961.27 ln T − 4488.93 J/K mol
(9)
Standard enthalpy as a function of temperature of the MgKN
compound in the solid state ␣ is given by:
polynomial equation along with the least square fit parameter (R2)
in the temperature range for the solid state ␤ of the compound.
ꢄ
T
HT ◦ − H298.15
=
CpdT = 2.56 × 10−3T3 − 2.23T2
◦
298.15
Cp(solid state ␤)(J/K mol) = 8.04 × 10−2T2 − 68.086T
+ 961.27T − 156219.47 J/mol
(10)
+ 14821.96; (415.15 − 458.15) K, R2 = 0.9676
(4)
Standard Gibbs energy as a function of temperature of the MgKN
compound in the solid state ␣ is given by:
GT ◦ − G298.15 = (HT ◦ − H298.15◦) − T(ST ◦ − S298.15◦) = 1.28
◦
3.2.3. Heat capacity of liquid state: (478.15–623.15) K
The heat capacity data for MgKN compound in the liquid state
in the temperature range of 478.15–623.15 K is given in Table 5.
The data are fit to a linear equation. Eq. (5) gives the polynomial
equation along with the least square fit parameter (R2) in the tem-
perature range for the liquid state of the compound.
× 10−3T3 + 2.23T2 + (5450.20 − 961.27 ln T)T
−156219.47 J/mol
(11)
Cp(liquid)(J/K mol) = 7.07 × 10−1T + 111.60;
3.3.2. Solid state ˇ (415.15–458.15) K
Standard entropy as a function of temperature of the MgKN
compound in the solid state ␤ is given by:
× (478.15 − 623.15) K, R2 = 0.985
(5)
ꢄ
ꢄ
T
T
ꢀ
ꢁ
ꢀ
ꢁ
t
Cp
T
Cp
T
ꢀHt
Tt
ST ◦ − S298.15
=
dT +
+
dT = 4.02
◦
Heat capacity data of the MgKN compound in the two solid states
follows a second order polynomial curve whereas the heat capacity
is linear in the liquid state.
298.15
T
t
× 10−2T2 − 68.09T + 14821.96 ln T − 67893.31 J/K mol
(12)
3.3. Thermodynamic properties
The standard thermodynamic properties such as entropy,
enthalpy, and Gibbs energy for MgKN compound are determined
from the experimental data of heat capacity as function of tem-
perature for each phase of the compound. In thermodynamics,
all these three properties are expressed in terms of heat capac-
ity as function of temperature [8]. In the present study, the
expressions for the standard thermodynamic properties are given
Standard enthalpy as a function of temperature of the MgKN
compound in the solid state ␤ is given by:
ꢄ
ꢄ
T
T
t
◦
HT ◦ − H298.15
=
CpdT + ꢀHt +
CpdT = 2.68
T
t
298.15
× 10−2T3 − 34.04T2 + 14821.96T − 2159715.28 J/mol
(13)

R.G. Reddy et al. / Thermochimica Acta 531 (2012) 6–11
11
of the enthalpy has a linear relationship with temperature. These
curves are all smooth in the three temperature ranges.
Standard Gibbs energy as a function of temperature of the MgKN
compound in the solid state ␤ is given by:
4. Conclusions
GT ◦ − G298.15 = (HT ◦ − H298.15◦) − T(ST ◦ − S298.15◦) = −1.34
◦
× 10−2T3 + 34.04T2 + (82715.27 − 14821.96 ln T)T
The melting point and heat capacity of the 2KNO3·Mg(NO3)2
compound were experimentally determined by DSC. There exists a
solid state phase transition in the compound. Solid state phase tran-
sition occurs at 404.80 K and melting of the compound takes place
at 468.83 K. Heat capacity data showed two endothermic peaks cor-
responding to the phase transitions of the MgKN compound. Heat
capacity data in the entire temperature range of study were fit to
three polynomials corresponding to the three phases of the com-
pound. Thermodynamic properties such as entropy, enthalpy, and
Gibbs energy of the MgKN compound were deduced from the heat
capacity expressions.
− 2159715.28 J/mol
(14)
3.3.3. Liquid state (478.15–623.15) K
Standard entropy as a function of temperature of the MgKN
compound in the liquid state is given by:
ꢄ
ꢄ
T
T
m
ꢀ
ꢁ
ꢀ
ꢁ
t
Cp
T
Cp
T
ꢀHt
Tt
ꢀHm
Tm
ST ◦ − S298.15
=
dT +
+
dT +
◦
298.15
T
t
ꢄ
T
ꢀ
ꢁ
Cp
+
= 7.07 × 10−1T + 111.60 ln T−794.92 J/K mol
Acknowledgements
T
T
m
(15)
The authors are pleased to acknowledge the financial sup-
port from DOE, Grant No. DE-FG36-08GO18153, for this research
project. We also thank the University of Alabama for providing the
experimental facilities.
Standard enthalpy as a function of temperature of the MgKN
compound in the liquid state is given by:
ꢄ
ꢄ
T
T
m
t
References
◦
HT ◦ − H298.15
=
CpdT + ꢀHt +
CpdT
298.15
T
t
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T
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T
m
(16)
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GT ◦ − G298.15 = (HT ◦ − H298.15◦) − T(ST ◦ − S298.15◦) = −3.54
◦
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modynamic properties for solid ␣; Eqs. (12)–(14) refer to the
thermodynamic properties for solid ␤; Eqs. (15)–(17) refer to ther-
modynamic properties of the liquid. The entropy and Gibbs energy
curves have logarithmic dependence with temperature while that
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