# Heat Capacities and Thermodynamic Properties of Pinnoite and Inderite

Authors: Hanyu Zheng; Kangrui Sun; Long Li; Yafei Guo; Tianlong Deng
Journal: Journal of Chemistry
 (2020)

---

## Abstract

In this paper, in order to understand the thermodynamic properties of natural minerals of pinnoite (MgB2O4·3H2O, Pin) and inderite (Mg2B6O11·15H2O, Ind) deposited in salt lakes, heat capacities of two minerals were measured using a precision calorimeter at temperatures from 306.15 to 355.15 K after the high purity was synthesized. It was found that there are no phase transitions and thermal anomalies for the two minerals, and the molar heat capacities against temperature for Pin and Ind were fitted as Cp,m,pin = −2029.47058 + 16.94666T − 0.04396T2 + 3.89409×10−5T3 and Cp,m,Ind = −30814.43795 + 282.68108T − 0.85605T2 + 8.70708×10−4T 3, respectively. On the basis of molar heat capacities (Cp,m) of Pin and Ind, the thermodynamic functions of entropy, enthalpy, and Gibbs free energy at the temperature of 1 K interval for the two minerals were obtained for the first time.


---

## Body

## 1. Introduction

Magnesium borates are widely used in many fields such as chemical industry, glass and ceramics industries, and superconducting materials because of the excellent performance [1–4], and the extensive application of magnesium borate also makes it a great resource to be developed and utilized in the world today. Fortunately, six natural hydrated magnesium borate minerals 2MgO·3B2O3·15H2O (inderite), 2MgO·3B2O3·15H2O (kurnakovite), 2MgO·2B2O3·MgCl2·14H2O (chloropinnoite), MgO·B2O3·3H2O (pinnoite), MgO·2B2O3·9H2O (hungchaoite), and MgO·3B2O3·7.5H2O (mcallisterite) have been found in the Qaidam Basin, China [5, 6]. It is well known that thermodynamic properties are the theoretical foundation for the exploitation of brine resources; hence, in order to provide useful information for synthesizing materials and extracting magnesium borates in salt lake brines, the study of thermodynamic properties for magnesium borates is necessary.Heat capacity which refers to the energy absorbed or released when the unit mass changes per unit temperature [7] is one of the important thermodynamic properties for optimizing the production process, and it can be used for reliable calculation of enthalpy, entropy, and Gibbs free energy [8, 9]. In addition, heat capacity is the inherent characteristic of crystals, which is closely related to its unique composition and crystal structure. In order to understand the thermodynamic properties of natural minerals of pinnoite (MgB2O4·3H2O, Pin) and inderite (Mg2B6O11·15H2O, Ind) deposited in salt lakes, the heat capacities of minerals pinnoite and inderite were measured using the calorimeter at temperatures from 306.15 to 355.15 K after the high purity was synthesized [10], and the relative thermodynamic functions of entropy, enthalpy, and Gibbs free energy were also carried out according to the thermodynamic equations for the first time.


## 2. Experimental

### 2.1. Recrystallizations or Synthesizations and Characterizations for Pinnoite and Inderite

For pinnoite purification, 30.00 g of the MgB2O4·H2O purchased products was taken and dissolved in 100.00 g of fresh CO2-free deionized distilled water (DDW), and the pH was adjusted to 8 with 50% (v/v) hydrochloric acid, and then, the solution was stirred at 200 rpm for about one week at room temperature until the solution reaches equilibrium. Next, the precipitates were filtered and washed with DDW three times as well as once with anhydrous ethanol and then dried at 25°C in a vacuum drying box and characterized before use. The synthesis of inderite was done as described previously [11, 12]. Briefly, 40.00 g borax was dissolved in 400.00 g of fresh CO2-free deionized distilled water (DDW) under the condition of stirring at 343.15 K. After the borax dissolved completely, the temperature was decreased to 323.15 K to add 40.00 g of MgSO4·7H2O, and then the solution was stirred at 200 rpm for 12 hours. The precipitate was filtered in attemperator and then recrystallized in a thermostat water bath at 303 K. Similarly, it was filtered in an attemperator and washed three times with DDW and once with anhydrous ethanol and then dried in a desiccator before use.The pinnoite and inderite were identified by X-ray diffraction analysis (MSAL XD-3, Beijing Purkinje General Instrument Co. Ltd., China), and the results are shown in Figure1, and it showed that the diffraction peaks on patterns correspond well with the standard Atlas database. Figure 2 shows the method for the identification of pinnoite and inderite by TG-DSC (Labsys, Setaram, France), respectively. The thermal analysis curve results of pinnoite showed that the total weight loss rate of the sample is 33.21% between 378.15 K and 813.15 K, which is basically consistent with the theoretical loss of water from MgB2O4·3H2O to MgB2O4 (32.96%) [13], and the deviation is within 0.05%. From the thermal analysis curve of inderite, it was found that the sample had a continuous weightlessness section between 373.15 K and 673.15 K, and the total weight loss rate was 48.31%, which was basically consistent with the theoretical water loss rate of 48.29% of Mg2B6O11·15H2O from hot loss of crystalline water to Mg2B6O11. The concentration of borate expressed as B2O3 was analyzed by the gravimetric methods of mannitol with an uncertainty of ±0.0005 in mass fraction [14]. The content of magnesium expressed as MgO in the sample was determined by EDTA complexometry with an uncertainty of ±0.0051 in mass fraction, and the content of H2O can be calculated by subtraction. The analytical results of MgB2O4·3H2O and Mg2B6O11·15H2O were compared with the theoretical values and are shown in Table 1, and it was shown that the purities of the synthesized pinnoite and inderite were higher than 99.9%.Figure 1
The X-ray diffraction patterns of pinnoite (a) and inderite (b).
(a)
(b)Figure 2
The TG-DSC curves of pinnoite (a) and inderite (b).
(a)
(b)Table 1
Chemical analytical results of pinnoite (MgB2O4·3H2O) and inderite (Mg2B6O11·15H2O)a.
Component content
Purity
w (MgO)
w (B2O3)
w (H2O)
n (MgO: B2O3: H2O)
Pinnoite (MgB
2
O
4
·3H
2
O)
Theoretical
1.0000
0.2459
0.4247
0.3274
1.00: 1.00: 3.00
Experimental
0.9920
0.2447
0.4243
0.3300
1.00: 1.00: 3.01
Inderite (Mg
2
B
6
O
11
·15H
2
O)
Theoretical
1.0000
0.1440
0.3732
0.4828
2.00:3.00:15.00
Experimental
0.9990
0.1439
0.3734
0.4827
2.00:3.00:15.02
aStandard uncertainties u are u(MgO) = 0.0051, u(B2O3) = 0.0005, and u(H2O) = 0.0079 in mass fraction.


### 2.2. Experimental Method

The high-precision calorimeter (Labsys, Setaram, France) was used for heat capacity experiment, which requires three groups of minerals, namely, blank, reference, and sample experiments, and alumina as a 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 is in accordance with 0.6879 J·g−1·K−1 reported in the literature [15], and the deviation is 0.0028. The heat capacities of the samples were carried out in the range of 306.15 K to 355.15 K with a heating rate of 2 K/min, putting about 15 mg of samples in the crucible weighted with an accuracy of 0.00001 g, and the flow rate of N2 is 20 mL/min.


## 2.1. Recrystallizations or Synthesizations and Characterizations for Pinnoite and Inderite

For pinnoite purification, 30.00 g of the MgB2O4·H2O purchased products was taken and dissolved in 100.00 g of fresh CO2-free deionized distilled water (DDW), and the pH was adjusted to 8 with 50% (v/v) hydrochloric acid, and then, the solution was stirred at 200 rpm for about one week at room temperature until the solution reaches equilibrium. Next, the precipitates were filtered and washed with DDW three times as well as once with anhydrous ethanol and then dried at 25°C in a vacuum drying box and characterized before use. The synthesis of inderite was done as described previously [11, 12]. Briefly, 40.00 g borax was dissolved in 400.00 g of fresh CO2-free deionized distilled water (DDW) under the condition of stirring at 343.15 K. After the borax dissolved completely, the temperature was decreased to 323.15 K to add 40.00 g of MgSO4·7H2O, and then the solution was stirred at 200 rpm for 12 hours. The precipitate was filtered in attemperator and then recrystallized in a thermostat water bath at 303 K. Similarly, it was filtered in an attemperator and washed three times with DDW and once with anhydrous ethanol and then dried in a desiccator before use.The pinnoite and inderite were identified by X-ray diffraction analysis (MSAL XD-3, Beijing Purkinje General Instrument Co. Ltd., China), and the results are shown in Figure1, and it showed that the diffraction peaks on patterns correspond well with the standard Atlas database. Figure 2 shows the method for the identification of pinnoite and inderite by TG-DSC (Labsys, Setaram, France), respectively. The thermal analysis curve results of pinnoite showed that the total weight loss rate of the sample is 33.21% between 378.15 K and 813.15 K, which is basically consistent with the theoretical loss of water from MgB2O4·3H2O to MgB2O4 (32.96%) [13], and the deviation is within 0.05%. From the thermal analysis curve of inderite, it was found that the sample had a continuous weightlessness section between 373.15 K and 673.15 K, and the total weight loss rate was 48.31%, which was basically consistent with the theoretical water loss rate of 48.29% of Mg2B6O11·15H2O from hot loss of crystalline water to Mg2B6O11. The concentration of borate expressed as B2O3 was analyzed by the gravimetric methods of mannitol with an uncertainty of ±0.0005 in mass fraction [14]. The content of magnesium expressed as MgO in the sample was determined by EDTA complexometry with an uncertainty of ±0.0051 in mass fraction, and the content of H2O can be calculated by subtraction. The analytical results of MgB2O4·3H2O and Mg2B6O11·15H2O were compared with the theoretical values and are shown in Table 1, and it was shown that the purities of the synthesized pinnoite and inderite were higher than 99.9%.Figure 1
The X-ray diffraction patterns of pinnoite (a) and inderite (b).
(a)
(b)Figure 2
The TG-DSC curves of pinnoite (a) and inderite (b).
(a)
(b)Table 1
Chemical analytical results of pinnoite (MgB2O4·3H2O) and inderite (Mg2B6O11·15H2O)a.
Component content
Purity
w (MgO)
w (B2O3)
w (H2O)
n (MgO: B2O3: H2O)
Pinnoite (MgB
2
O
4
·3H
2
O)
Theoretical
1.0000
0.2459
0.4247
0.3274
1.00: 1.00: 3.00
Experimental
0.9920
0.2447
0.4243
0.3300
1.00: 1.00: 3.01
Inderite (Mg
2
B
6
O
11
·15H
2
O)
Theoretical
1.0000
0.1440
0.3732
0.4828
2.00:3.00:15.00
Experimental
0.9990
0.1439
0.3734
0.4827
2.00:3.00:15.02
aStandard uncertainties u are u(MgO) = 0.0051, u(B2O3) = 0.0005, and u(H2O) = 0.0079 in mass fraction.


## 2.2. Experimental Method

The high-precision calorimeter (Labsys, Setaram, France) was used for heat capacity experiment, which requires three groups of minerals, namely, blank, reference, and sample experiments, and alumina as a 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 is in accordance with 0.6879 J·g−1·K−1 reported in the literature [15], and the deviation is 0.0028. The heat capacities of the samples were carried out in the range of 306.15 K to 355.15 K with a heating rate of 2 K/min, putting about 15 mg of samples in the crucible weighted with an accuracy of 0.00001 g, and the flow rate of N2 is 20 mL/min.


## 3. Results and Discussion

### 3.1. Measurement of the Heat Capacity

The values for the molar heat capacities of pinnoite and inderite were measured by the calorimeter at temperature from 306.15 to 355.15 K with the standard uncertainty of 0.05 J·mol−1·K−1 are listed in Table 2 and plotted in Figure 3 [16]. As shown in Figure 3, the heat capacities of pinnoite and inderite are all increased with the rise of temperature from 306.15 to 355.15 K, which shows that the structures of pinnoite and inderite are stable in these temperature regions, that is, neither phase transition nor other thermal anomalies take place within the temperature range of the experiment.Table 2
The molar heat capacities of pinnoite and inderite at 306.15∼355.15 Ka.
T (K)
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)
Pinnoite, MgB
2
O
4
·3H
2
O
306.15
154.85
323.15
169.84
340.15
181.16
307.15
155.94
324.15
170.55
341.15
181.66
308.15
157.45
325.15
171.22
342.15
182.19
309.15
158.71
326.15
171.93
343.15
182.68
310.15
159.85
327.15
172.60
344.15
183.16
311.15
160.76
328.15
173.30
345.15
183.63
312.15
161.68
329.15
173.96
346.15
184.09
313.15
162.60
330.15
174.65
347.15
184.53
314.15
163.39
331.15
175.37
348.15
184.96
315.15
164.14
332.15
176.07
349.15
185.40
316.15
164.88
333.15
176.80
350.15
185.86
317.15
165.52
334.15
177.57
351.15
186.34
318.15
166.17
335.15
178.27
352.15
186.86
319.15
166.84
336.15
178.91
353.15
187.43
320.15
167.57
337.15
179.53
354.15
188.04
321.15
168.32
338.15
180.09
355.15
188.70
322.15
169.07
339.15
180.63
Inderite, Mg
2
B
6
O
11
·15H
2
O
306.15
474.94
323.15
521.82
340.15
560.43
307.15
479.69
324.15
524.12
341.15
562.89
308.15
484.73
325.15
526.36
342.15
565.29
309.15
488.20
326.15
528.59
343.15
567.98
310.15
490.94
327.15
530.77
344.15
570.78
311.15
493.51
328.15
533.01
345.15
573.30
312.15
495.98
329.15
535.19
346.15
576.09
313.15
498.44
330.15
537.38
347.15
578.95
314.15
500.45
331.15
539.50
348.15
581.91
315.15
502.52
332.15
541.57
349.15
584.65
316.15
504.70
333.15
543.75
350.15
587.56
317.15
506.89
334.15
545.82
351.15
590.97
318.15
509.24
335.15
548.06
352.15
595.06
319.15
511.70
336.15
550.52
353.15
600.09
320.15
514.21
337.15
552.93
354.15
605.63
321.15
516.73
338.15
555.50
355.15
611.12
322.15
519.25
339.15
557.97
aThe sample weights for pinnoite and inderite were 15.92 and 15.27 mg, respectively. The temperature heating rate was 2 K·min−1. The standard uncertainty u is u (Cp,m) = 0.05 J·mol−1·K−1.Figure 3
Molar heat capacities versus temperature in the range of 306.15 K to 355.15 K for pinnoite (a) and inderite (b).
(a)
(b)In order to obtain the heat capacity quickly at a certain temperature, the molar heat capacities of pinnoite and inderite determined in this work have been fitted as equation (1) by means of a least-squares method with the correlation coefficients r = 0.99905 for pinnoite and 0.99924 for inderite listed in Table 3. On the basis of polynomial equations, the molar heat capacities of pinnoite and inderite at 298.15 K can be calculated as 147.49 and 446.59 J·mol−1·K−1, and the standard deviations between experimental values Cp,exp and fitted values Cp,fit through the polynomial equation are within 0.02:(1)Cp,mJ·mol−1·K−1=A0+A1T+A2T2+A3T3.Table 3
Polynomial coefficients of equation (1) for minerals of pinnoite and inderite at 306.15∼355.15 K.
Minerals
Polynomial coefficient
r
A
0
A
1
A
2
A
3
MgB2O4·3H2O
−2029.47058
16.94666
−0.04396
3.89409 × 10−5
0.99905
Mg2B6O11·15H2O
−30814.43795
282.68108
−0.85605
8.70708 × 10−4
0.99924


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

The thermodynamic functions of the relative standard states of pinnoite and inderite at 298.15 K can be derived from 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.Using the formula above, the thermodynamic functions (HT − H298.15), (ST − S298.15), and (GT − G298.15) of pinnoite and inderite are calculated on the basis of the obtained heat capacity values and are listed in Table 4 with a temperature of 1 K interval.Table 4
Molar heat capacities and thermodynamic functions (HT − H298.15), (ST − S298.15), and (GT − G298.15) of pinnoite and inderite.
T (K)
C
p,m
a (J·mol−1·K−1)
H
T − H298.15a (kJ·mol−1)
S
T − S298.15a (J·mol−·K−1)
G
T − G298.15a (kJ·mol−1)
Pinnoite, MgB
2
O
4
·3H
2
O
298.15
147.49
0.0000
0.0000
0.0000
306.15
154.85
1.2142
4.0183
−0.0160
307.15
155.94
1.3706
4.5282
−0.0203
308.15
157.45
1.5279
5.0396
−0.0251
309.15
158.71
1.6862
5.5524
−0.0303
310.15
159.85
1.8454
6.0665
−0.0362
311.15
160.76
2.0055
6.5820
−0.0425
312.15
161.68
2.1665
7.0986
−0.0493
313.15
162.60
2.3284
7.6165
−0.0567
314.15
163.39
2.4912
8.1355
−0.0646
315.15
164.14
2.6548
8.6555
−0.0730
316.15
164.88
2.8193
9.1766
−0.0819
317.15
165.52
2.9846
9.6986
−0.0913
318.15
166.17
3.1507
10.2215
−0.1013
319.15
166.84
3.3176
10.7453
−0.1117
320.15
167.57
3.4853
11.2700
−0.1228
321.15
168.32
3.6538
11.7954
−0.1343
322.15
169.07
3.8230
12.3215
−0.1463
323.15
169.84
3.9930
12.8483
−0.1589
324.15
170.55
4.1637
13.3758
−0.1720
325.15
171.22
4.3352
13.9039
−0.1857
326.15
171.93
4.5073
14.4325
−0.1999
327.15
172.60
4.6802
14.9616
−0.2145
328.15
173.30
4.8537
15.4913
−0.2298
329.15
173.96
5.0279
16.0213
−0.2455
330.15
174.65
5.2028
16.5518
−0.2618
331.15
175.37
5.3783
17.0827
−0.2786
332.15
176.07
5.5545
17.6139
−0.2960
333.15
176.80
5.7313
18.1453
−0.3139
334.15
177.57
5.9087
18.6771
−0.3323
335.15
178.27
6.0867
19.2091
−0.3512
336.15
178.91
6.2654
19.7413
−0.3707
337.15
179.53
6.4446
20.2737
−0.3907
338.15
180.09
6.6244
20.8063
−0.4112
339.15
180.63
6.8048
21.3389
−0.4323
340.15
181.16
6.9857
21.8717
−0.4539
341.15
181.66
7.1673
22.4045
−0.4761
342.15
182.19
7.3493
22.9374
−0.4987
343.15
182.68
7.5319
23.4703
−0.5219
344.15
183.16
7.7151
24.0033
−0.5457
345.15
183.63
7.8987
24.5361
−0.5699
346.15
184.09
8.0829
25.0690
−0.5947
347.15
184.53
8.2676
25.6018
−0.6201
348.15
184.96
8.4528
26.1345
−0.6459
349.15
185.40
8.6385
26.6671
−0.6723
350.15
185.86
8.8246
27.1995
−0.6993
351.15
186.34
9.0113
27.7319
−0.7267
352.15
186.86
9.1985
28.2641
−0.7547
353.15
187.43
9.3861
28.7961
−0.7833
354.15
188.04
9.5742
29.3279
−0.8123
355.15
188.70
9.7627
29.8596
−0.8419
Inderite, Mg
2
B
6
O
11
·15H
2
O
298.15
446.59
0.0000
0.0000
0.0000
306.15
474.94
3.7018
12.2505
−0.0487
307.15
479.69
4.1809
13.8128
−0.0617
308.15
484.73
4.6632
15.3806
−0.0763
309.15
488.20
5.1487
16.9535
−0.0925
310.15
490.94
5.6372
18.5311
−0.1102
311.15
493.51
6.1287
20.1131
−0.1295
312.15
495.98
6.6230
21.6992
−0.1504
313.15
498.44
7.1201
23.2891
−0.1729
314.15
500.45
7.6198
24.8825
−0.1970
315.15
502.52
8.1222
26.4791
−0.2227
316.15
504.70
8.6271
28.0788
−0.2500
317.15
506.89
9.1345
29.6812
−0.2789
318.15
509.24
9.6444
31.2862
−0.3093
319.15
511.70
10.1566
32.8937
−0.3414
320.15
514.21
10.6711
34.5034
−0.3751
321.15
516.73
11.1880
36.1152
−0.4104
322.15
519.25
11.7070
37.7290
−0.4474
323.15
521.82
12.2283
39.3446
−0.4859
324.15
524.12
12.7518
40.9621
−0.5260
325.15
526.36
13.2775
42.5812
−0.5678
326.15
528.59
13.8053
44.2019
−0.6112
327.15
530.77
14.3352
45.8243
−0.6562
328.15
533.01
14.8673
47.4482
−0.7029
329.15
535.19
15.4015
49.0737
−0.7511
330.15
537.38
15.9378
50.7008
−0.8010
331.15
539.50
16.4764
52.3294
−0.8525
332.15
541.57
17.0170
53.9596
−0.9057
333.15
543.75
17.5599
55.5916
−0.9604
334.15
545.82
18.1050
57.2252
−1.0169
335.15
548.06
18.6523
58.8607
−1.0749
336.15
550.52
19.2019
60.4981
−1.1346
337.15
552.93
19.7538
62.1375
−1.1959
338.15
555.50
20.3081
63.7791
−1.2588
339.15
557.97
20.8648
65.4230
−1.3235
340.15
560.43
21.4239
67.0693
−1.3897
341.15
562.89
21.9857
68.7183
−1.4576
342.15
565.29
22.5500
70.3701
−1.5271
343.15
567.98
23.1170
72.0248
−1.5983
344.15
570.78
23.6867
73.6828
−1.6712
345.15
573.30
24.2593
75.3442
−1.7457
346.15
576.09
24.8349
77.0092
−1.8219
347.15
578.95
25.4134
78.6782
−1.8997
348.15
581.91
25.9951
80.3514
−1.9792
349.15
584.65
26.5800
82.0290
−2.0604
350.15
587.56
27.1682
83.7113
−2.1433
351.15
590.97
27.7599
85.3987
−2.2278
352.15
595.06
28.3552
87.0914
−2.3141
353.15
600.09
28.9541
88.7898
−2.4020
354.15
605.63
29.5569
90.4942
−2.4917
355.15
611.12
30.1636
92.2050
−2.5830
aThe standard uncertainties u are u (Cp,m) = 0.05 J·mol−1·K−1, u(HT − H298.15) = 0.0056, u(ST − S298.15) = 0.0080, and u(GT − G298.15) = 0.0010.From the thermodynamic function data listed in Table4, it is shown that with the increase of temperature from 298.15 K to 355.15 K, the molar heat capacity, enthalpy (HT − H298.15), and entropy (ST − S298.15) increase with the increase of temperature, while the change of free energy (GT − G298.15) is just the opposite. The variations of (HT − H298.15), (ST − S298.15), and (GT − G298.15) with T are plotted in Figure 4.Figure 4
Variations of (a) (HT − H298.15), (b) (ST − S298.15), and (c) (GT − G298.15) with T for pinnoite and inderite.
(a)
(b)
(c)


## 3.1. Measurement of the Heat Capacity

The values for the molar heat capacities of pinnoite and inderite were measured by the calorimeter at temperature from 306.15 to 355.15 K with the standard uncertainty of 0.05 J·mol−1·K−1 are listed in Table 2 and plotted in Figure 3 [16]. As shown in Figure 3, the heat capacities of pinnoite and inderite are all increased with the rise of temperature from 306.15 to 355.15 K, which shows that the structures of pinnoite and inderite are stable in these temperature regions, that is, neither phase transition nor other thermal anomalies take place within the temperature range of the experiment.Table 2
The molar heat capacities of pinnoite and inderite at 306.15∼355.15 Ka.
T (K)
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)
Pinnoite, MgB
2
O
4
·3H
2
O
306.15
154.85
323.15
169.84
340.15
181.16
307.15
155.94
324.15
170.55
341.15
181.66
308.15
157.45
325.15
171.22
342.15
182.19
309.15
158.71
326.15
171.93
343.15
182.68
310.15
159.85
327.15
172.60
344.15
183.16
311.15
160.76
328.15
173.30
345.15
183.63
312.15
161.68
329.15
173.96
346.15
184.09
313.15
162.60
330.15
174.65
347.15
184.53
314.15
163.39
331.15
175.37
348.15
184.96
315.15
164.14
332.15
176.07
349.15
185.40
316.15
164.88
333.15
176.80
350.15
185.86
317.15
165.52
334.15
177.57
351.15
186.34
318.15
166.17
335.15
178.27
352.15
186.86
319.15
166.84
336.15
178.91
353.15
187.43
320.15
167.57
337.15
179.53
354.15
188.04
321.15
168.32
338.15
180.09
355.15
188.70
322.15
169.07
339.15
180.63
Inderite, Mg
2
B
6
O
11
·15H
2
O
306.15
474.94
323.15
521.82
340.15
560.43
307.15
479.69
324.15
524.12
341.15
562.89
308.15
484.73
325.15
526.36
342.15
565.29
309.15
488.20
326.15
528.59
343.15
567.98
310.15
490.94
327.15
530.77
344.15
570.78
311.15
493.51
328.15
533.01
345.15
573.30
312.15
495.98
329.15
535.19
346.15
576.09
313.15
498.44
330.15
537.38
347.15
578.95
314.15
500.45
331.15
539.50
348.15
581.91
315.15
502.52
332.15
541.57
349.15
584.65
316.15
504.70
333.15
543.75
350.15
587.56
317.15
506.89
334.15
545.82
351.15
590.97
318.15
509.24
335.15
548.06
352.15
595.06
319.15
511.70
336.15
550.52
353.15
600.09
320.15
514.21
337.15
552.93
354.15
605.63
321.15
516.73
338.15
555.50
355.15
611.12
322.15
519.25
339.15
557.97
aThe sample weights for pinnoite and inderite were 15.92 and 15.27 mg, respectively. The temperature heating rate was 2 K·min−1. The standard uncertainty u is u (Cp,m) = 0.05 J·mol−1·K−1.Figure 3
Molar heat capacities versus temperature in the range of 306.15 K to 355.15 K for pinnoite (a) and inderite (b).
(a)
(b)In order to obtain the heat capacity quickly at a certain temperature, the molar heat capacities of pinnoite and inderite determined in this work have been fitted as equation (1) by means of a least-squares method with the correlation coefficients r = 0.99905 for pinnoite and 0.99924 for inderite listed in Table 3. On the basis of polynomial equations, the molar heat capacities of pinnoite and inderite at 298.15 K can be calculated as 147.49 and 446.59 J·mol−1·K−1, and the standard deviations between experimental values Cp,exp and fitted values Cp,fit through the polynomial equation are within 0.02:(1)Cp,mJ·mol−1·K−1=A0+A1T+A2T2+A3T3.Table 3
Polynomial coefficients of equation (1) for minerals of pinnoite and inderite at 306.15∼355.15 K.
Minerals
Polynomial coefficient
r
A
0
A
1
A
2
A
3
MgB2O4·3H2O
−2029.47058
16.94666
−0.04396
3.89409 × 10−5
0.99905
Mg2B6O11·15H2O
−30814.43795
282.68108
−0.85605
8.70708 × 10−4
0.99924


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

The thermodynamic functions of the relative standard states of pinnoite and inderite at 298.15 K can be derived from 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.Using the formula above, the thermodynamic functions (HT − H298.15), (ST − S298.15), and (GT − G298.15) of pinnoite and inderite are calculated on the basis of the obtained heat capacity values and are listed in Table 4 with a temperature of 1 K interval.Table 4
Molar heat capacities and thermodynamic functions (HT − H298.15), (ST − S298.15), and (GT − G298.15) of pinnoite and inderite.
T (K)
C
p,m
a (J·mol−1·K−1)
H
T − H298.15a (kJ·mol−1)
S
T − S298.15a (J·mol−·K−1)
G
T − G298.15a (kJ·mol−1)
Pinnoite, MgB
2
O
4
·3H
2
O
298.15
147.49
0.0000
0.0000
0.0000
306.15
154.85
1.2142
4.0183
−0.0160
307.15
155.94
1.3706
4.5282
−0.0203
308.15
157.45
1.5279
5.0396
−0.0251
309.15
158.71
1.6862
5.5524
−0.0303
310.15
159.85
1.8454
6.0665
−0.0362
311.15
160.76
2.0055
6.5820
−0.0425
312.15
161.68
2.1665
7.0986
−0.0493
313.15
162.60
2.3284
7.6165
−0.0567
314.15
163.39
2.4912
8.1355
−0.0646
315.15
164.14
2.6548
8.6555
−0.0730
316.15
164.88
2.8193
9.1766
−0.0819
317.15
165.52
2.9846
9.6986
−0.0913
318.15
166.17
3.1507
10.2215
−0.1013
319.15
166.84
3.3176
10.7453
−0.1117
320.15
167.57
3.4853
11.2700
−0.1228
321.15
168.32
3.6538
11.7954
−0.1343
322.15
169.07
3.8230
12.3215
−0.1463
323.15
169.84
3.9930
12.8483
−0.1589
324.15
170.55
4.1637
13.3758
−0.1720
325.15
171.22
4.3352
13.9039
−0.1857
326.15
171.93
4.5073
14.4325
−0.1999
327.15
172.60
4.6802
14.9616
−0.2145
328.15
173.30
4.8537
15.4913
−0.2298
329.15
173.96
5.0279
16.0213
−0.2455
330.15
174.65
5.2028
16.5518
−0.2618
331.15
175.37
5.3783
17.0827
−0.2786
332.15
176.07
5.5545
17.6139
−0.2960
333.15
176.80
5.7313
18.1453
−0.3139
334.15
177.57
5.9087
18.6771
−0.3323
335.15
178.27
6.0867
19.2091
−0.3512
336.15
178.91
6.2654
19.7413
−0.3707
337.15
179.53
6.4446
20.2737
−0.3907
338.15
180.09
6.6244
20.8063
−0.4112
339.15
180.63
6.8048
21.3389
−0.4323
340.15
181.16
6.9857
21.8717
−0.4539
341.15
181.66
7.1673
22.4045
−0.4761
342.15
182.19
7.3493
22.9374
−0.4987
343.15
182.68
7.5319
23.4703
−0.5219
344.15
183.16
7.7151
24.0033
−0.5457
345.15
183.63
7.8987
24.5361
−0.5699
346.15
184.09
8.0829
25.0690
−0.5947
347.15
184.53
8.2676
25.6018
−0.6201
348.15
184.96
8.4528
26.1345
−0.6459
349.15
185.40
8.6385
26.6671
−0.6723
350.15
185.86
8.8246
27.1995
−0.6993
351.15
186.34
9.0113
27.7319
−0.7267
352.15
186.86
9.1985
28.2641
−0.7547
353.15
187.43
9.3861
28.7961
−0.7833
354.15
188.04
9.5742
29.3279
−0.8123
355.15
188.70
9.7627
29.8596
−0.8419
Inderite, Mg
2
B
6
O
11
·15H
2
O
298.15
446.59
0.0000
0.0000
0.0000
306.15
474.94
3.7018
12.2505
−0.0487
307.15
479.69
4.1809
13.8128
−0.0617
308.15
484.73
4.6632
15.3806
−0.0763
309.15
488.20
5.1487
16.9535
−0.0925
310.15
490.94
5.6372
18.5311
−0.1102
311.15
493.51
6.1287
20.1131
−0.1295
312.15
495.98
6.6230
21.6992
−0.1504
313.15
498.44
7.1201
23.2891
−0.1729
314.15
500.45
7.6198
24.8825
−0.1970
315.15
502.52
8.1222
26.4791
−0.2227
316.15
504.70
8.6271
28.0788
−0.2500
317.15
506.89
9.1345
29.6812
−0.2789
318.15
509.24
9.6444
31.2862
−0.3093
319.15
511.70
10.1566
32.8937
−0.3414
320.15
514.21
10.6711
34.5034
−0.3751
321.15
516.73
11.1880
36.1152
−0.4104
322.15
519.25
11.7070
37.7290
−0.4474
323.15
521.82
12.2283
39.3446
−0.4859
324.15
524.12
12.7518
40.9621
−0.5260
325.15
526.36
13.2775
42.5812
−0.5678
326.15
528.59
13.8053
44.2019
−0.6112
327.15
530.77
14.3352
45.8243
−0.6562
328.15
533.01
14.8673
47.4482
−0.7029
329.15
535.19
15.4015
49.0737
−0.7511
330.15
537.38
15.9378
50.7008
−0.8010
331.15
539.50
16.4764
52.3294
−0.8525
332.15
541.57
17.0170
53.9596
−0.9057
333.15
543.75
17.5599
55.5916
−0.9604
334.15
545.82
18.1050
57.2252
−1.0169
335.15
548.06
18.6523
58.8607
−1.0749
336.15
550.52
19.2019
60.4981
−1.1346
337.15
552.93
19.7538
62.1375
−1.1959
338.15
555.50
20.3081
63.7791
−1.2588
339.15
557.97
20.8648
65.4230
−1.3235
340.15
560.43
21.4239
67.0693
−1.3897
341.15
562.89
21.9857
68.7183
−1.4576
342.15
565.29
22.5500
70.3701
−1.5271
343.15
567.98
23.1170
72.0248
−1.5983
344.15
570.78
23.6867
73.6828
−1.6712
345.15
573.30
24.2593
75.3442
−1.7457
346.15
576.09
24.8349
77.0092
−1.8219
347.15
578.95
25.4134
78.6782
−1.8997
348.15
581.91
25.9951
80.3514
−1.9792
349.15
584.65
26.5800
82.0290
−2.0604
350.15
587.56
27.1682
83.7113
−2.1433
351.15
590.97
27.7599
85.3987
−2.2278
352.15
595.06
28.3552
87.0914
−2.3141
353.15
600.09
28.9541
88.7898
−2.4020
354.15
605.63
29.5569
90.4942
−2.4917
355.15
611.12
30.1636
92.2050
−2.5830
aThe standard uncertainties u are u (Cp,m) = 0.05 J·mol−1·K−1, u(HT − H298.15) = 0.0056, u(ST − S298.15) = 0.0080, and u(GT − G298.15) = 0.0010.From the thermodynamic function data listed in Table4, it is shown that with the increase of temperature from 298.15 K to 355.15 K, the molar heat capacity, enthalpy (HT − H298.15), and entropy (ST − S298.15) increase with the increase of temperature, while the change of free energy (GT − G298.15) is just the opposite. The variations of (HT − H298.15), (ST − S298.15), and (GT − G298.15) with T are plotted in Figure 4.Figure 4
Variations of (a) (HT − H298.15), (b) (ST − S298.15), and (c) (GT − G298.15) with T for pinnoite and inderite.
(a)
(b)
(c)


## 4. Conclusions

In the work, pinnoite and inderite have been successfully synthesized and characterized, and then the solid molar heat capacities of MgB2O4·3H2O and Mg2B6O11·15H2O were measured by differential scanning calorimetry. The experimental results showed that the molar heat capacities of the two magnesium borates are increased with the increase of temperature. No phase transitions or other thermal anomalies occurred. At the same time, heat capacity at various temperatures was fitted by the least-square method, and the polynomial equation of the change of the molar heat capacity with the temperature is obtained. The fitting results are in good agreement with the experimental data and can be used for the exploitation and utilization of magnesium and boron resources in salt lakes.



---

*Source: 6181356-2020-03-10.xml*