# Heat Capacity and Thermodynamic Property of Cesium Tetraborate Pentahydrate

Authors: Kangrui Sun; Kaiyu Zhao; Long Li; Yafei Guo; Tianlong Deng
Journal: Journal of Chemistry
 (2019)

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## Abstract

In order to recover cesium tetraborate pentahydrate (Cs2O·2B2O3·5H2O) from the high concentration cesium-containing salt lake brines and geothermal water resources, the molar heat capacity of Cs2O·2B2O3·5H2O has been measured with a precision calorimeter at the temperature from 303 to 349 K. It was found that there is no phase transition and thermal anomalies. The molar heat capacity of cesium tetraborate pentahydrate is fitted as Cp,m (J·mol−1·K−1) = 593.85705 + 48.0694[T − (Tmax + Tmin)/2]/(Tmax − Tmin)/2] + 24.86395[(T − (Tmax + Tmin)/2)/(Tmax − Tmin)/2]2 + 0.53077[(T − (Tmax + Tmin)/2)/(Tmax − Tmin)/2]3, and the relevant thermodynamic functions of enthalpy, entropy, and Gibbs free energy of cesium tetraborate pentahydrate are also obtained at intervals of 2 K from 303 to 349 K.


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## Body

## 1. Introduction

The demands for cesium and its compounds have been sharply increased for their excellent properties and crucially commercial values in recent years [1]. Cesium ion with the biggest hydration in the periodic table determines its prominent properties and applications, such as large solubility and weak hydration in alkali borates. In addition, cesium compounds are applied in many modern high-tech fields owing to tremendous actinochemistry and excellent photo-electrical effect, and cesium borates also serve as the basic materials in new hybrid nonlinear optical materials [2]. Cesium resources were distributed and dispersed in the crust, associated with other minerals [3]; hence, the study of thermodynamic properties for cesium borates was necessary for synthesizing materials and extracting cesium borates from salt lake brines.Heat capacity is a significant parameter to study the chemical engineering thermodynamics, which reflects the ability of matter to absorb or release heat without phase change [4], and it is beneficial to optimize the process route and improve the separation technology. There have been reported on the standard molar enthalpy of formation as well as the thermodynamic properties of aqueous solutions of Cs2O·2B2O3·5H2O with the group contribution method [5]. Sun [2] also accurately determined its density, electrical conductivity, and pH at 298.15 and 333.15 K. The crystal structure of Cs2O·2B2O3·5H2O has been analyzed from single-crystal X-ray diffraction [6]. Zhang et al. [7] measured the molar heat capacity of aqueous Li2B4O7 solution with a precision automated adiabatic calorimeter from 80 to 356 K, and the heat capacity of lithium pentaborate pentahydrate has been reported previously in the range from 297 to 375 K using the SETARAM BT 2.15 adiabatic calorimeter [8]. However, there is no report on the molar heat capacity of solid minerals of Cs2B4O7·5H2O in the literature till now.In this paper, in order to make full use of Cs2O·2B2O3·5H2O as well as its potential value, the heat capacity of cesium tetraborate pentahydrate was measured in the range 303 to 349 K, and the relevant thermodynamic functions of enthalpy, entropy, and Gibbs free energy were also carried out for the first time.


## 2. Experimental

### 2.1. Synthesis of Cs2B4O7·5H2O

The compound of Cs2O·2B2O3·5H2O was synthesized according to the literature [9]. Briefly, a certain amount of H3BO3, Cs2CO3, and deionized distilled water (DDW) was added accurately in a beaker, and then heated at 323.15 K and stirred for at least more than 30 min at 150 rpm until dissolved completely. Then, the solution was filtered in an attemperator, and the clear solution was crystallized in a thermostat water bath at 303 K. Finally, the solid phase was separated after washing three times with DDW and absolute ethyl alcohol separately, and then dried in a desiccator before use.


### 2.2. Identification and Analytical Methods of Cs2O·2B2O3·5H2O

The power X-ray diffraction pattern of the synthesized compound in Figure1 was obtained by using a PERSEE XD-3 polycrystalline X-ray diffractometer with Cu-Kα radiation at 4 min−1, which corresponds to Cs2O·2B2O3·5H2O. TG and DSC were characterized by using a SETARAM LABSYS thermal analyzer under an N2 atmosphere with a heating rate of 10 K·min−1 from 298.15 to 823.15 K. The TG-DSC curve in Figure 2 shows that the weight loss of 17.42% corresponds to the loss of five water molecules, which is in good agreement with the calculated value of 17.60%.Figure 1
The X-ray diffraction pattern of Cs2O·2B2O3·5H2O.Figure 2
The TG curve of Cs2O·2B2O3·5H2O.The concentration of B2O3 was determined by the gravimetric method with sodium hydroxide standard solution in the presence of mannitol and double indicator of methyl red and phenolphthalein, and the uncertainty of the results was less than 0.0005 in mass fraction [10]. The cesium ion content was obtained by using an inductively coupled plasma optical emission spectrometer (Prodigy, Leman Corporation, America) with a precision of ±0.005 in mass fraction. The H2O content was analyzed by the differential subtraction. The chemical analysis results are shown in Table 1. The results, along with X-ray power diffraction analysis and TG curve, show that the compound has high purity and is suitable for thermodynamic experiments.Table 1
Chemical analytical results of Cs2O·2B2O3·5H2O in mass fractiona.
Cs2O
B2O3
H2O
n (Cs2O : B2O3 : H2O)
Experimental
0.5533
0.2724
0.1742
1.00 : 1.99 : 4.93
Theoretical
0.5515
0.2724
0.1761
1.00 : 2.00 : 5.00
aStandard uncertainties u are u(Cs2O) = 0.0053, u(B2O3) = 0.0005, and u(H2O) = 0.0055 in mass fraction.


### 2.3. Calorimetry and Experiment Method

The high-precision SETARAM LABSYS (France) was used for heat capacity experiment, which requires three groups of experiments, namely, blank experiment, reference experiment and sample experiment, and alumina as reference experiment. To verify the performance, the heat capacity of KCl was measured, and the average experimental value for five times of 0.6860 J·g−1·K−1 was in accordance with 0.6879 J·g−1·K−1 reported in the literature [11], for which the deviation was 0.0028. The heat capacity of sample was carried out in the range 303 to 349 K with a heating rate of 1 K/min, putting about 250 mg of samples in the crucible weighted with an accuracy of 0.00001 g, and the flow rate of N2 was 20 mL/min.


## 2.1. Synthesis of Cs2B4O7·5H2O

The compound of Cs2O·2B2O3·5H2O was synthesized according to the literature [9]. Briefly, a certain amount of H3BO3, Cs2CO3, and deionized distilled water (DDW) was added accurately in a beaker, and then heated at 323.15 K and stirred for at least more than 30 min at 150 rpm until dissolved completely. Then, the solution was filtered in an attemperator, and the clear solution was crystallized in a thermostat water bath at 303 K. Finally, the solid phase was separated after washing three times with DDW and absolute ethyl alcohol separately, and then dried in a desiccator before use.


## 2.2. Identification and Analytical Methods of Cs2O·2B2O3·5H2O

The power X-ray diffraction pattern of the synthesized compound in Figure1 was obtained by using a PERSEE XD-3 polycrystalline X-ray diffractometer with Cu-Kα radiation at 4 min−1, which corresponds to Cs2O·2B2O3·5H2O. TG and DSC were characterized by using a SETARAM LABSYS thermal analyzer under an N2 atmosphere with a heating rate of 10 K·min−1 from 298.15 to 823.15 K. The TG-DSC curve in Figure 2 shows that the weight loss of 17.42% corresponds to the loss of five water molecules, which is in good agreement with the calculated value of 17.60%.Figure 1
The X-ray diffraction pattern of Cs2O·2B2O3·5H2O.Figure 2
The TG curve of Cs2O·2B2O3·5H2O.The concentration of B2O3 was determined by the gravimetric method with sodium hydroxide standard solution in the presence of mannitol and double indicator of methyl red and phenolphthalein, and the uncertainty of the results was less than 0.0005 in mass fraction [10]. The cesium ion content was obtained by using an inductively coupled plasma optical emission spectrometer (Prodigy, Leman Corporation, America) with a precision of ±0.005 in mass fraction. The H2O content was analyzed by the differential subtraction. The chemical analysis results are shown in Table 1. The results, along with X-ray power diffraction analysis and TG curve, show that the compound has high purity and is suitable for thermodynamic experiments.Table 1
Chemical analytical results of Cs2O·2B2O3·5H2O in mass fractiona.
Cs2O
B2O3
H2O
n (Cs2O : B2O3 : H2O)
Experimental
0.5533
0.2724
0.1742
1.00 : 1.99 : 4.93
Theoretical
0.5515
0.2724
0.1761
1.00 : 2.00 : 5.00
aStandard uncertainties u are u(Cs2O) = 0.0053, u(B2O3) = 0.0005, and u(H2O) = 0.0055 in mass fraction.


## 2.3. Calorimetry and Experiment Method

The high-precision SETARAM LABSYS (France) was used for heat capacity experiment, which requires three groups of experiments, namely, blank experiment, reference experiment and sample experiment, and alumina as reference experiment. To verify the performance, the heat capacity of KCl was measured, and the average experimental value for five times of 0.6860 J·g−1·K−1 was in accordance with 0.6879 J·g−1·K−1 reported in the literature [11], for which the deviation was 0.0028. The heat capacity of sample was carried out in the range 303 to 349 K with a heating rate of 1 K/min, putting about 250 mg of samples in the crucible weighted with an accuracy of 0.00001 g, and the flow rate of N2 was 20 mL/min.


## 3. Results and Discussion

### 3.1. Heat Capacity

The heat capacity of sample was measured in the range 303 K to 349 K with a heating rate of 1 K/min using the calorimeter with the standard uncertainty 0.05 J·mol−1·K−1. The resulting molar heat capacity of Cs2O·2B2O3·5H2O is listed in Table 2 and shown in Figure 3. It can be seen from Figure 3 that the specific heat capacity gradually increases with the increase of temperature, increases slowly from 303 to 330 K, and increases fast after 330 K. No phase change was observed within the temperature range of the experiment and no other thermal abnormalities occurred.Table 2
Molar heat capacity of Cs2O·2B2O3·5H2O (molecular mass (M) = 511.127 g·mol−1).
T/Ka
C
p,m J·mol−1·K−1
T/K
C
p,m J·mol−1·K−1
T/K
C
p,m J·mol−1·K−1
303.33
570.00
319.35
581.92
335.24
617.95
304.18
570.56
320.20
583.56
336.2
621.95
305.19
570.62
321.23
585.56
337.8
624.74
306.28
571.10
322.32
586.09
338.35
627.63
307.37
571.23
323.15
587.36
339.35
629.92
308.49
571.49
324.24
589.06
340.31
631.70
309.34
572.79
325.24
591.47
341.42
635.84
310.26
572.65
326.19
593.77
342.4
637.49
311.19
572.73
327.20
596.56
343.23
640.9
312.29
573.54
328.28
599.75
344.32
644.88
313.18
574.82
329.19
602.72
345.58
652.60
314.19
575.47
330.27
605.53
346.27
656.45
315.26
576.57
331.18
607.64
347.28
662.18
316.32
577.17
332.19
611.02
348.55
669.30
317.29
578.53
333.17
612.41
318.36
579.41
334.33
614.99
aUncertainty of temperature u(T) = 0.01 K and the molar heat capacity uncertainty u(Cp,m) = 0.05 J·mol−1·K−1.Figure 3
Experimental and fitting molar heat capacity of Cs2O·2B2O3·5H2O in the range of 303 to 349 K.For the sake of observing the heat capacity data and getting a heat capacity at a temperature quickly, the molar heat capacity of Cs2O·2B2O3·5H2O obtained from the experiment was fitted, which can be expressed in the following polynomial equation (1) with the correlation coefficient r = 0.9987 and be drawn in Figure 3.(1)Cp,mJ·mol−1·K−1=593.85705+48.0694T−Tmax+Tmin/2Tmax−Tmin/2+24.86395T−Tmax+Tmin/2Tmax−Tmin/22+0.53077T−Tmax+Tmin/2Tmax−Tmin/23,where Cp,m is the molar heat capacity of Cs2O·2B2O3·5H2O, T is the absolute temperature in kelvin, and Tmax and Tmin express the maximum and minimum temperatures, i.e., 349 and 303, respectively. The molar heat capacity of Cs2O·2B2O3·5H2O at 303 K can be calculated as 370 J·mol−1·K−1 according to the above equation, and all deviations between the experimental values, Cp,exp, and the fitted values, Cp,fit, were within 0.005, as shown in Figure 4.Figure 4
The deviations of the experimental and fitting values.


### 3.2. Enthalpy, Entropy, and Gibbs Free Energy

The thermodynamic functions of Cs2O·2B2O3·5H2O were obtained by the following thermodynamic equations:(2)HT–H303=∫303TCp,mdT,(3)ST−S303=∫303TCp,mTdT,(4)GT−G303=∫303TCp,mdT−T∫303TCp,mTdT.The values of the molar heat capacity and thermodynamic functions of (HT−H303), (ST−S303), and (GT−G303) are listed in Table 3 at an interval of 2 K. As can be seen from Table 3, the molar heat capacity and thermodynamic functions of (HT−H303) and (GT−G303) are increased with the rise of temperature, but the entropy (ST−S303) is decreased.Table 3
Molar heat capacity and thermodynamic functions of Cs2O·2B2O3·5H2O.
T/K
C
p,m J·mol−1·K−1
H
T
−
H
303 kJ·mol−1
S
T
−
S
303 J·mol−1·K−1
G
T
−
G
303 kJ·mol−1
303
570.12
0
0
0
305
570.29
6.763
−6.940
8.880
307
570.82
13.468
−14.009
17.769
309
571.69
20.114
−21.203
26.666
311
572.93
26.703
−28.520
35.572
313
574.53
33.232
−35.957
44.487
315
576.49
39.704
−43.512
53.410
317
578.82
46.117
−51.182
62.342
319
581.51
52.473
−58.965
71.283
321
584.58
58.770
−66.859
80.232
323
588.01
65.010
−74.861
89.190
325
591.81
71.192
−82.969
98.157
327
595.99
77.317
−91.181
107.133
329
600.55
83.384
−99.493
116.117
331
605.48
89.394
−107.905
125.110
333
610.80
95.346
−116.414
134.112
335
616.50
101.242
−125.017
143.122
337
622.59
107.080
−133.713
152.142
339
629.07
112.862
−142.500
161.169
341
635.93
118.587
−151.374
170.206
343
643.18
124.255
−160.335
179.250
345
650.83
129.868
−169.380
188.304
347
658.88
135.424
−178.507
197.366


## 3.1. Heat Capacity

The heat capacity of sample was measured in the range 303 K to 349 K with a heating rate of 1 K/min using the calorimeter with the standard uncertainty 0.05 J·mol−1·K−1. The resulting molar heat capacity of Cs2O·2B2O3·5H2O is listed in Table 2 and shown in Figure 3. It can be seen from Figure 3 that the specific heat capacity gradually increases with the increase of temperature, increases slowly from 303 to 330 K, and increases fast after 330 K. No phase change was observed within the temperature range of the experiment and no other thermal abnormalities occurred.Table 2
Molar heat capacity of Cs2O·2B2O3·5H2O (molecular mass (M) = 511.127 g·mol−1).
T/Ka
C
p,m J·mol−1·K−1
T/K
C
p,m J·mol−1·K−1
T/K
C
p,m J·mol−1·K−1
303.33
570.00
319.35
581.92
335.24
617.95
304.18
570.56
320.20
583.56
336.2
621.95
305.19
570.62
321.23
585.56
337.8
624.74
306.28
571.10
322.32
586.09
338.35
627.63
307.37
571.23
323.15
587.36
339.35
629.92
308.49
571.49
324.24
589.06
340.31
631.70
309.34
572.79
325.24
591.47
341.42
635.84
310.26
572.65
326.19
593.77
342.4
637.49
311.19
572.73
327.20
596.56
343.23
640.9
312.29
573.54
328.28
599.75
344.32
644.88
313.18
574.82
329.19
602.72
345.58
652.60
314.19
575.47
330.27
605.53
346.27
656.45
315.26
576.57
331.18
607.64
347.28
662.18
316.32
577.17
332.19
611.02
348.55
669.30
317.29
578.53
333.17
612.41
318.36
579.41
334.33
614.99
aUncertainty of temperature u(T) = 0.01 K and the molar heat capacity uncertainty u(Cp,m) = 0.05 J·mol−1·K−1.Figure 3
Experimental and fitting molar heat capacity of Cs2O·2B2O3·5H2O in the range of 303 to 349 K.For the sake of observing the heat capacity data and getting a heat capacity at a temperature quickly, the molar heat capacity of Cs2O·2B2O3·5H2O obtained from the experiment was fitted, which can be expressed in the following polynomial equation (1) with the correlation coefficient r = 0.9987 and be drawn in Figure 3.(1)Cp,mJ·mol−1·K−1=593.85705+48.0694T−Tmax+Tmin/2Tmax−Tmin/2+24.86395T−Tmax+Tmin/2Tmax−Tmin/22+0.53077T−Tmax+Tmin/2Tmax−Tmin/23,where Cp,m is the molar heat capacity of Cs2O·2B2O3·5H2O, T is the absolute temperature in kelvin, and Tmax and Tmin express the maximum and minimum temperatures, i.e., 349 and 303, respectively. The molar heat capacity of Cs2O·2B2O3·5H2O at 303 K can be calculated as 370 J·mol−1·K−1 according to the above equation, and all deviations between the experimental values, Cp,exp, and the fitted values, Cp,fit, were within 0.005, as shown in Figure 4.Figure 4
The deviations of the experimental and fitting values.


## 3.2. Enthalpy, Entropy, and Gibbs Free Energy

The thermodynamic functions of Cs2O·2B2O3·5H2O were obtained by the following thermodynamic equations:(2)HT–H303=∫303TCp,mdT,(3)ST−S303=∫303TCp,mTdT,(4)GT−G303=∫303TCp,mdT−T∫303TCp,mTdT.The values of the molar heat capacity and thermodynamic functions of (HT−H303), (ST−S303), and (GT−G303) are listed in Table 3 at an interval of 2 K. As can be seen from Table 3, the molar heat capacity and thermodynamic functions of (HT−H303) and (GT−G303) are increased with the rise of temperature, but the entropy (ST−S303) is decreased.Table 3
Molar heat capacity and thermodynamic functions of Cs2O·2B2O3·5H2O.
T/K
C
p,m J·mol−1·K−1
H
T
−
H
303 kJ·mol−1
S
T
−
S
303 J·mol−1·K−1
G
T
−
G
303 kJ·mol−1
303
570.12
0
0
0
305
570.29
6.763
−6.940
8.880
307
570.82
13.468
−14.009
17.769
309
571.69
20.114
−21.203
26.666
311
572.93
26.703
−28.520
35.572
313
574.53
33.232
−35.957
44.487
315
576.49
39.704
−43.512
53.410
317
578.82
46.117
−51.182
62.342
319
581.51
52.473
−58.965
71.283
321
584.58
58.770
−66.859
80.232
323
588.01
65.010
−74.861
89.190
325
591.81
71.192
−82.969
98.157
327
595.99
77.317
−91.181
107.133
329
600.55
83.384
−99.493
116.117
331
605.48
89.394
−107.905
125.110
333
610.80
95.346
−116.414
134.112
335
616.50
101.242
−125.017
143.122
337
622.59
107.080
−133.713
152.142
339
629.07
112.862
−142.500
161.169
341
635.93
118.587
−151.374
170.206
343
643.18
124.255
−160.335
179.250
345
650.83
129.868
−169.380
188.304
347
658.88
135.424
−178.507
197.366


## 4. Conclusions

The heat capacity of cesium tetraborate pentahydrate was measured ranging from 303 to 349 K with a heating rate of 1 K/min using the high-precision calorimeter without phase transition and thermal anomaly, which were fitted and shown asCp,m(J·mol−1·K−1) = 593.85705 + 48.0694[T − (Tmax + Tmin)/2]/(Tmax − Tmin)/2] + 24.86395[(T − (Tmax + Tmin)/2)/(Tmax − Tmin)/2]2 + 0.53077[(T − (Tmax + Tmin)/2)/(Tmax − Tmin)/2]3. The molar heat capacity and thermodynamic functions of (HT−H303), (ST−S303), and (GT−G303) are obtained with the temperature of 2 K interval.



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*Source: 9371328-2019-02-26.xml*