# Heat Capacity and Thermodynamic Property of Lithium Pentaborate Pentahydrate

Authors: Wanjing Cui; Long Li; Yafei Guo; Sisi Zhang; Tianlong Deng
Journal: Journal of Chemistry
 (2018)

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## Abstract

The heat capacity of lithium pentaborate pentahydrate has been measured using an adiabatic calorimeter at the temperature from 297 to 375 K. No phase transition and thermal anomalies were observed. The molar heat capacity of LiB5O8·5H2O can be expressed as Cp,m (J·mol−1·K−1) = 396.79376 + 35.87528 [T-(Tmax+Tmin)/2]/[(Tmax-Tmin)/2] + 0.16494[T-(Tmax+Tmin)/2]/[(Tmax-Tmin)/2]2 + 8.3083[T-(Tmax+Tmin)/2]/[(Tmax-Tmin)/2]3, where T is the temperature in Kelvin, Tmax=375K, and Tmin=297K. The thermodynamic functions of (HT-H298.15), (ST-S298.15), and (GT-G298.15) of LiB5O8·5H2O are obtained via the molar heat capacity at the temperature of 5 K intervals.


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## Body

## 1. Introduction

Studies of alkali borates have attracted much interest in recent years because some of these compounds especially the alkali pentaborates show significant physical interest, such as nonlinear optical behavior [1]. The [B5O10]2− boron oxycyclic structure of the alkali metal pentaborate crystal contains the BO3 group, which has a strong macro frequency effect and can be used in the field of nonlinear optical materials [2]. In addition, the lithium pentaborate (LiB5O8·5H2O) also can be used in special glass, lubricating oil additives, and production of boron oxide [3, 4].Heat capacity is one of the important parameters of thermodynamic properties to optimize the producing process. And reliable calculation of such thermodynamic functions of entropy, enthalpy, and Gibbs free energy requires data on heat capacity [5]. Furthermore, heat capacity is inherent characteristic of crystals, closely related to the specific features of their composition and structure. To better understand the industrial application of LiB5O8·5H2O and perform the corresponding theoretical studies, the thermodynamic properties of this compound are essential. Li et al. [6] reported the standard molar enthalpy of formation of LiB5O8·5H2O. Ge et al. [7] determined the physicochemical properties of LiB5O8 solutions, including the density, viscosity, conductivity, and pH. However, there is no data reported on the heat capacity of LiB5O8·5H2O in the literature. In this paper, the heat capacity of LiB5O8·5H2O has been determined using an adiabatic calorimeter in the temperature range from 297 to 375 K, and the values of the thermodynamic functions, heat capacity, entropy, enthalpy, and Gibbs free energy, were calculated at temperature 5 K intervals.


## 2. Experimental

### 2.1. Synthesis

The chemical of LiB5O8·5H2O was synthesized in our laboratory according to the phase diagram of system Li2O-B2O3-H2O [8]. Certain amounts of H3BO3 and LiOH·H2O were dissolved in the quantificational deionized water under stirring for 24 h at 333.15 K. Then, the product was filtered by suction filtration and washed three times with deionized water and absolute ethyl alcohol, respectively. Finally, the samples were dried until the weight was constant and stored in the desiccators for use.


### 2.2. Characterization and Analytical Methods

The synthesized chemical of LiB5O8·5H2O was identified by X-ray powder diffraction (PERSEE XD-3 polycrystalline X-ray diffractometer with Cu-Kα radiation at 4° min−1) and thermogravimetric (TG) (performed on a SETARAM LABSYS thermal analyzer under argon atmosphere with a heating rate of 10 K min−1). The X-ray powder pattern of the synthesized LiB5O8·5H2O in Figure 1 shows that the diffraction peaks on patterns correspond well in position, indicating the phase purity of the synthesized samples. The weight loss of 32.26% from the TG curve in Figure 2 corresponds to the loss of five water molecules and can be compared with the calculated value of 32.26%.Figure 1
The X-ray diffraction pattern of LiB5O8⋅5H2O.Figure 2
The TG curve of LiB5O8⋅5H2O.The B2O3 concentration was analyzed using gravimetric method with sodium hydroxide standard solution in the presence of mixture indicators of methyl red plus phenolphthalein and the excessive mannitol conditions, and the standard uncertainty u(BO2-) was 0.0005 in mass fraction [9]. The lithium ion content was measured by inductively coupled plasma optical emission spectrometer (Prodigy, Leman Corporation, America) with precision of ±0.5%. The crystallized water content was calculated through subtraction. The chemical analytical result of LiB5O8·5H2O is listed in Table 1.Table 1
Chemical analytical result of lithium pentaborate pentahydrate in mass fraction.
Li2O
B2O3
H2O
n (Li2O : B2O3 : H2O)
Experimental
0.0538
0.6262
0.3200
1.00 : 4.99 : 9.87
Theoretical
0.0536
0.6239
0.3226
1.00 : 5.00 : 10.00


### 2.3. Adiabatic Calorimetry and Experiment Method

Heat capacity measurements were carried out in a high-precision SETARAM BT 2.15 adiabatic calorimeter. The BT 2.15 calorimeter comprises a calorimetric chamber, electrical or pneumatic peripherals, and the liquid nitrogen supply. The calorimetric chamber can receive the heat capacity cell, which is provided with a syringe for sample introduction. The sample mass used for the heat capacity measurement was 8877.74 mg. The performance of this calorimetric apparatus has been verified by measuring the heat capacity of KCl where the average result is 0.6877 J·g−1·K−1 in seven times and the deviation of the results is 0.0007, compared with the reference data of 0.6879 J·g−1·K−1 [10]. The heat capacity Cp,m of the sample was measured ranging from 297 to 375 K by an adiabatic continuous heating technique with a heating rate of 0.1 K/min.


## 2.1. Synthesis

The chemical of LiB5O8·5H2O was synthesized in our laboratory according to the phase diagram of system Li2O-B2O3-H2O [8]. Certain amounts of H3BO3 and LiOH·H2O were dissolved in the quantificational deionized water under stirring for 24 h at 333.15 K. Then, the product was filtered by suction filtration and washed three times with deionized water and absolute ethyl alcohol, respectively. Finally, the samples were dried until the weight was constant and stored in the desiccators for use.


## 2.2. Characterization and Analytical Methods

The synthesized chemical of LiB5O8·5H2O was identified by X-ray powder diffraction (PERSEE XD-3 polycrystalline X-ray diffractometer with Cu-Kα radiation at 4° min−1) and thermogravimetric (TG) (performed on a SETARAM LABSYS thermal analyzer under argon atmosphere with a heating rate of 10 K min−1). The X-ray powder pattern of the synthesized LiB5O8·5H2O in Figure 1 shows that the diffraction peaks on patterns correspond well in position, indicating the phase purity of the synthesized samples. The weight loss of 32.26% from the TG curve in Figure 2 corresponds to the loss of five water molecules and can be compared with the calculated value of 32.26%.Figure 1
The X-ray diffraction pattern of LiB5O8⋅5H2O.Figure 2
The TG curve of LiB5O8⋅5H2O.The B2O3 concentration was analyzed using gravimetric method with sodium hydroxide standard solution in the presence of mixture indicators of methyl red plus phenolphthalein and the excessive mannitol conditions, and the standard uncertainty u(BO2-) was 0.0005 in mass fraction [9]. The lithium ion content was measured by inductively coupled plasma optical emission spectrometer (Prodigy, Leman Corporation, America) with precision of ±0.5%. The crystallized water content was calculated through subtraction. The chemical analytical result of LiB5O8·5H2O is listed in Table 1.Table 1
Chemical analytical result of lithium pentaborate pentahydrate in mass fraction.
Li2O
B2O3
H2O
n (Li2O : B2O3 : H2O)
Experimental
0.0538
0.6262
0.3200
1.00 : 4.99 : 9.87
Theoretical
0.0536
0.6239
0.3226
1.00 : 5.00 : 10.00


## 2.3. Adiabatic Calorimetry and Experiment Method

Heat capacity measurements were carried out in a high-precision SETARAM BT 2.15 adiabatic calorimeter. The BT 2.15 calorimeter comprises a calorimetric chamber, electrical or pneumatic peripherals, and the liquid nitrogen supply. The calorimetric chamber can receive the heat capacity cell, which is provided with a syringe for sample introduction. The sample mass used for the heat capacity measurement was 8877.74 mg. The performance of this calorimetric apparatus has been verified by measuring the heat capacity of KCl where the average result is 0.6877 J·g−1·K−1 in seven times and the deviation of the results is 0.0007, compared with the reference data of 0.6879 J·g−1·K−1 [10]. The heat capacity Cp,m of the sample was measured ranging from 297 to 375 K by an adiabatic continuous heating technique with a heating rate of 0.1 K/min.


## 3. Results and Discussion

### 3.1. Heat Capacity

According to the experimental method, the heat capacityCp of LiB5O8·5H2O was measured using the adiabatic calorimeter from 297 to 375 K with standard uncertainty 0.05 J·mol−1·K−1, and the result of the molar heat capacity of LiB5O8·5H2O is shown in Table 2 and Figure 3.Table 2
Molar heat capacity of LiB5O8⋅5H2O (molecular mass M = 278.99 g mol−1).
T/K
C
p
,
m
T/K
C
p
,
m
T/K
C
p
,
m
J⋅mol−1⋅K−1
J⋅mol−1⋅K−1
J⋅mol−1⋅K−1
297.44
350.85
324.19
385.60
350.08
410.17
298.38
353.23
325.32
386.75
351.22
411.46
299.13
355.08
326.23
387.85
352.36
412.27
300.21
357.20
327.24
388.59
353.39
414.08
302.18
361.25
328.58
389.95
354.39
415.41
303.19
363.14
329.53
390.38
355.37
416.69
304.28
364.46
330.19
391.17
356.16
417.34
305.11
365.22
331.15
392.06
357.13
418.45
306.21
366.60
332.13
392.83
358.21
419.13
307.28
367.77
333.16
393.24
359.31
420.45
308.16
369.14
334.14
394.20
360.23
421.34
309.21
370.16
335.16
395.38
361.34
422.37
310.16
371.33
336.21
396.66
362.26
423.94
311.18
372.58
337.16
397.30
363.12
425.24
312.29
373.40
338.21
398.18
364.13
426.12
313.20
374.52
339.19
399.46
365.21
427.13
314.18
375.55
340.17
400.85
366.28
428.43
315.31
376.60
341.29
401.88
367.53
429.91
316.24
377.63
342.16
402.22
368.19
431.01
317.18
378.66
343.15
403.16
369.33
432.70
318.40
379.72
344.15
404.66
370.49
433.92
319.35
380.80
345.41
405.60
371.18
435.44
320.18
381.48
346.10
406.09
372.12
436.70
321.26
382.09
347.10
407.30
373.09
437.91
322.15
383.11
348.30
408.37
374.18
439.08
323.16
384.23
349.39
409.37
Note. Standard uncertainty of temperature u(T)=0.01 K, and the molar heat capacity u(Cp,m) = 0.05 J⋅mol−1⋅K−1.Figure 3
Experimental molar heat capacity of LiB5O8⋅5H2O in the range of 297 to 375 K.In Figure3, it is shown that the heat capacity of LiB5O8·5H2O sample increases smoothly with the increasing of temperature in the range between 297 and 375 K without any phase transition and thermal anomaly.On the basis of the Debye Law [11], the molar heat capacity of LiB5O8·5H2O determined in this work has been fitted and shown in (1). On the basis of (1), the molar heat capacity of LiB5O8·5H2O at 298.15 K can be obtained as 354.54 J·mol−1·K−1.(1)Cp,mJ·mol-1·K-1=396.79376+35.87528T-Tmax⁡+Tmin⁡/2Tmax⁡-Tmin⁡/2+0.16494T-Tmax⁡+Tmin⁡/2Tmax⁡-Tmin⁡/22+8.3083T-Tmax⁡+Tmin⁡/2Tmax⁡-Tmin⁡/23,where T is the absolute temperature in Kelvin, Tmax⁡ is the upper temperature (375 K), and Tmin⁡ is the lower temperature (297 K). The deviations between the experimental and the fitted values are within 0.005 and shown in Figure 4.Figure 4
Plot of deviations of experimental data from fitted.


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

The thermodynamic functions of LiB5O8·5H2O relative to the standard status, that is, 298.15 K and 0.1 MPa, can be derived based on the following thermodynamic equations:(2)HT-H298.15=∫298.15TCp,mdT,ST-S298.15=∫298.15TCp,mTdT,GT-G298.15=∫298.15TCp,mdT-T∫298.15TCp,mTdT.The results of the molar heat capacity and thermodynamic functions of(HT-H298.15), (ST-S298.15), and (GT-G298.15) are obtained and listed in Table 3 with a temperature of 5 K interval. From the entropy function data in Table 3, it is shown that the molar heat capacity and the changes of enthalpy (HT-H298.15) and entropy (ST-S298.15) are increased with the increasing of temperature from 298.15 K to 375 K and the changes of free energy (GT-G298.15) are just the opposite.Table 3
Calculated molar heat capacities and thermodynamic functions of LiB5O8⋅H2O.
T/K
C
p
,
m
H
T
-
H
298.15
S
T
-
S
298.15
G
T
-
G
298.15
J⋅mol−1⋅K−1
kJ⋅mol−1
J⋅mol−1⋅K−1
kJ⋅mol−1
298.15
354.54
0
0
0
300
357.28
0.6590
2.2035
−0.0020
305
364.21
2.465
8.17
−0.0280
310
370.49
4.303
14.15
−0.0838
315
376.23
6.172
20.13
−0.1695
320
381.53
8.068
26.10
−0.2851
325
386.50
9.990
32.06
−0.4305
330
391.25
11.936
38.01
−0.6057
335
395.87
13.906
43.93
−0.8105
340
400.48
15.898
49.83
−1.0449
345
405.18
17.915
55.72
−1.3088
350
410.08
19.955
61.59
−1.6021
355
415.27
22.020
67.45
−1.9247
360
420.87
24.112
73.30
−2.2766
365
426.98
26.234
79.15
−2.6577
370
433.70
28.387
85.01
−3.0681
375
441.14
30.576
90.89
−3.5079


## 3.1. Heat Capacity

According to the experimental method, the heat capacityCp of LiB5O8·5H2O was measured using the adiabatic calorimeter from 297 to 375 K with standard uncertainty 0.05 J·mol−1·K−1, and the result of the molar heat capacity of LiB5O8·5H2O is shown in Table 2 and Figure 3.Table 2
Molar heat capacity of LiB5O8⋅5H2O (molecular mass M = 278.99 g mol−1).
T/K
C
p
,
m
T/K
C
p
,
m
T/K
C
p
,
m
J⋅mol−1⋅K−1
J⋅mol−1⋅K−1
J⋅mol−1⋅K−1
297.44
350.85
324.19
385.60
350.08
410.17
298.38
353.23
325.32
386.75
351.22
411.46
299.13
355.08
326.23
387.85
352.36
412.27
300.21
357.20
327.24
388.59
353.39
414.08
302.18
361.25
328.58
389.95
354.39
415.41
303.19
363.14
329.53
390.38
355.37
416.69
304.28
364.46
330.19
391.17
356.16
417.34
305.11
365.22
331.15
392.06
357.13
418.45
306.21
366.60
332.13
392.83
358.21
419.13
307.28
367.77
333.16
393.24
359.31
420.45
308.16
369.14
334.14
394.20
360.23
421.34
309.21
370.16
335.16
395.38
361.34
422.37
310.16
371.33
336.21
396.66
362.26
423.94
311.18
372.58
337.16
397.30
363.12
425.24
312.29
373.40
338.21
398.18
364.13
426.12
313.20
374.52
339.19
399.46
365.21
427.13
314.18
375.55
340.17
400.85
366.28
428.43
315.31
376.60
341.29
401.88
367.53
429.91
316.24
377.63
342.16
402.22
368.19
431.01
317.18
378.66
343.15
403.16
369.33
432.70
318.40
379.72
344.15
404.66
370.49
433.92
319.35
380.80
345.41
405.60
371.18
435.44
320.18
381.48
346.10
406.09
372.12
436.70
321.26
382.09
347.10
407.30
373.09
437.91
322.15
383.11
348.30
408.37
374.18
439.08
323.16
384.23
349.39
409.37
Note. Standard uncertainty of temperature u(T)=0.01 K, and the molar heat capacity u(Cp,m) = 0.05 J⋅mol−1⋅K−1.Figure 3
Experimental molar heat capacity of LiB5O8⋅5H2O in the range of 297 to 375 K.In Figure3, it is shown that the heat capacity of LiB5O8·5H2O sample increases smoothly with the increasing of temperature in the range between 297 and 375 K without any phase transition and thermal anomaly.On the basis of the Debye Law [11], the molar heat capacity of LiB5O8·5H2O determined in this work has been fitted and shown in (1). On the basis of (1), the molar heat capacity of LiB5O8·5H2O at 298.15 K can be obtained as 354.54 J·mol−1·K−1.(1)Cp,mJ·mol-1·K-1=396.79376+35.87528T-Tmax⁡+Tmin⁡/2Tmax⁡-Tmin⁡/2+0.16494T-Tmax⁡+Tmin⁡/2Tmax⁡-Tmin⁡/22+8.3083T-Tmax⁡+Tmin⁡/2Tmax⁡-Tmin⁡/23,where T is the absolute temperature in Kelvin, Tmax⁡ is the upper temperature (375 K), and Tmin⁡ is the lower temperature (297 K). The deviations between the experimental and the fitted values are within 0.005 and shown in Figure 4.Figure 4
Plot of deviations of experimental data from fitted.


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

The thermodynamic functions of LiB5O8·5H2O relative to the standard status, that is, 298.15 K and 0.1 MPa, can be derived based on the following thermodynamic equations:(2)HT-H298.15=∫298.15TCp,mdT,ST-S298.15=∫298.15TCp,mTdT,GT-G298.15=∫298.15TCp,mdT-T∫298.15TCp,mTdT.The results of the molar heat capacity and thermodynamic functions of(HT-H298.15), (ST-S298.15), and (GT-G298.15) are obtained and listed in Table 3 with a temperature of 5 K interval. From the entropy function data in Table 3, it is shown that the molar heat capacity and the changes of enthalpy (HT-H298.15) and entropy (ST-S298.15) are increased with the increasing of temperature from 298.15 K to 375 K and the changes of free energy (GT-G298.15) are just the opposite.Table 3
Calculated molar heat capacities and thermodynamic functions of LiB5O8⋅H2O.
T/K
C
p
,
m
H
T
-
H
298.15
S
T
-
S
298.15
G
T
-
G
298.15
J⋅mol−1⋅K−1
kJ⋅mol−1
J⋅mol−1⋅K−1
kJ⋅mol−1
298.15
354.54
0
0
0
300
357.28
0.6590
2.2035
−0.0020
305
364.21
2.465
8.17
−0.0280
310
370.49
4.303
14.15
−0.0838
315
376.23
6.172
20.13
−0.1695
320
381.53
8.068
26.10
−0.2851
325
386.50
9.990
32.06
−0.4305
330
391.25
11.936
38.01
−0.6057
335
395.87
13.906
43.93
−0.8105
340
400.48
15.898
49.83
−1.0449
345
405.18
17.915
55.72
−1.3088
350
410.08
19.955
61.59
−1.6021
355
415.27
22.020
67.45
−1.9247
360
420.87
24.112
73.30
−2.2766
365
426.98
26.234
79.15
−2.6577
370
433.70
28.387
85.01
−3.0681
375
441.14
30.576
90.89
−3.5079


## 4. Conclusions

The heat capacity of LiB5O8·5H2O was measured using an adiabatic calorimeter at temperatures from 297 to 375 K, and it did not contain anomalous contributions at the experimental temperature regions. The molar heat capacity of LiB5O8·5H2O obeys a polynomial of Cp,m (J·mol−1·K−1) = 396.79376+35.87528[T-(Tmax⁡+Tmin⁡)/2]/[(Tmax⁡-Tmin⁡)/2] + 0.16494{[T-(Tmax⁡+Tmin⁡)/2]/[(Tmax⁡-Tmin⁡)/2]}2 + 8.3083{[T-(Tmax⁡+Tmin⁡)/2]/[(Tmax⁡-Tmin⁡)/2]}3. The molar heat capacity and thermodynamic functions of (HT-H298.15), (ST-S298.15), and (GT-G298.15) for LiB5O8·5H2O are obtained for the first time.



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*Source: 7962739-2018-01-17.xml*