Measurements and predictions of thermodynamic activity coefficients and phase equilibria in ternary system KCl-K2B4O7-H2O at 318.15 K

doi:10.11949/0438-1157.20230506

Abstract

Abstract:

The potassium-boron rich underground brines in Sichuan Basin are important liquid mineral resources. To reveal the enrichment law of boron and potassium in the underground brines and the exploitation of brine resources, the studies on thermodynamic properties and phase equilibria of the underground brines are essential foundation. The ternary system KCl-K₂B₄O₇-H₂O containing boron and potassium is the most important subsystem in this brine. In this work, ion selective electrode is used to measure the cell potential of the cell without liquid junction K-ISE | KCl (m₁), K₂B₄O₇ (m₂) | Cl-ISE. The total ionic strength of the mixed solution is 0.01—1.00 mol·kg^-1, and the ionic strength ratio of K₂B₄O₇y_b is 0.8, 0.6, 0.4, 0.2 and 0, respectively. The mean activity coefficients of KCl in mixed solutions KCl-K₂B₄O₇-H₂O were calculated by using the measured cell potentials and Nernst equation at 318.15 K. Then, multiple linear regression and nonlinear programming were used to determine the single salt parameters $β (0), β (1) a n d C Φ$ of K₂B₄O₇, and the mixed ion interaction parameters $θ C l, B 4 O 5 (O H) 4$ and $ψ K, C l, B 4 O 5 (O H) 4$ in Pitzer model. The fitted parameters of Pitzer model can be used to further calculate the mean activity coefficient of K₂B₄O₇, osmotic coefficient, water activity, and excess Gibbs free energy of the mixed solutions. Furthermore, the phase equilibria of ternary system KCl-K₂B₄O₇-H₂O at 318.15 K are determined experimentally in this work. The results show that the phase diagram of the system contains one invariant point, two solid crystallization regions (KCl and K₂B₄O₇·4H₂O), and two isothermal solubility curves. Using the ion interaction parameters and Pitzer model fitted in this work, the phase equilibrium of the ternary system was theoretically predicted. The predicted results show that the calculated values are in good agreement with the experimental data. The research results provide an important theoretical basis for the development and utilization of boron-potassium resources in the underground brines.

Key words: activity coefficient, Pitzer model, cell potential method, phase equilibrium, potassium tetraborate

摘要：

四川盆地地下卤水含有丰富的液态钾硼资源，针对该卤水体系开展相应热力学性质和相平衡的研究，是揭示地下卤水中硼钾富集规律和资源开发所必需的关键性基础工作。含硼钾的KCl-K₂B₄O₇-H₂O三元体系是该卤水重要的子体系。应用离子选择性电极测量无液接电池K-ISE | KCl（m₁），K₂B₄O₇（m₂）| Cl-ISE的电动势，体系中混合溶液总离子强度为0.01~1.00 mol·kg^-1，K₂B₄O₇离子强度分数y_b分别为0.8、0.6、0.4、0.2和0。利用测定的电动势值和Nernst方程计算出混合溶液KCl-K₂B₄O₇-H₂O中KCl的平均活度系数，然后应用多元线性回归和非线性规划求解拟合出318.15 K下K₂B₄O₇的Pitzer模型单盐参数 $β (0) 、 β (1) 、 C Φ$ 以及混合离子作用参数 $θ C l, B 4 O 5 (O H) 4$ 和 $ψ K, C l, B 4 O 5 (O H) 4$ 。并利用拟合的Pitzer模型参数计算出混合溶液中K₂B₄O₇的平均活度系数、渗透系数、水活度和超额Gibbs自由能。采用等温溶解平衡法开展了318.15 K下三元体系KCl-K₂B₄O₇-H₂O相平衡的实验研究，结果表明该体系相图由一个共饱点，两个固相结晶区（KCl和K₂B₄O₇·4H₂O），两条等温溶解度曲线组成。应用拟合的离子作用参数和Pitzer模型，对该三元体系相平衡进行了理论预测，预测值和实验值较为吻合。研究结果可为该地下卤水中硼钾资源的开发利用提供理论依据。

关键词: 活度系数, Pitzer模型, 电动势法, 相平衡, 四硼酸钾

CLC Number:

O 642.5⁺42

Shihua SANG, Jia LIU, Xiaojun YANG, Zhenhua FENG, Xiaotian TAN, Yuqiu CEN, Binbin TANG. Measurements and predictions of thermodynamic activity coefficients and phase equilibria in ternary system KCl-K₂B₄O₇-H₂O at 318.15 K[J]. CIESC Journal, 2023, 74(10): 4051-4062.

桑世华, 刘佳, 杨晓军, 冯振华, 谭啸天, 岑雨秋, 唐彬彬. 三元体系KCl-K₂B₄O₇-H₂O在318.15 K下热力学活度系数及相平衡实验和预测[J]. 化工学报, 2023, 74(10): 4051-4062.

Figures/Tables 15

Table 1 Main experimental reagents

试剂名称	化学式	规格	CAS	生产公司
氯化钾	KCl	≥99.8% (GR)	7447-40-7	成都科隆化学品有限公司
四水四硼酸钾	K₂B₄O₇·4H₂O	≥99.5% (AR)	12045-78-2	成都科隆化学品有限公司

Table 2 Experiment facilities and instruments

设备	型号	生产公司
电鼓风干燥箱	101-0AB	北京中兴伟业仪器有限公司(±1℃)
搅拌器	JB-1	上海雷磁精密科学仪器有限公司
电子天平	AL104	梅特勒-托利多集团(0.0001 g)
超纯水机	UPT-II-20T	四川优普超纯科技有限公司
恒温循环水浴	Bilon-HX-08	上海比朗有限公司(±0.01℃)
离子计	Pxsj-226	上海雷磁精密科学仪器有限公司(±0.01 mV)
钾离子选择电极	PK-1-01	上海雷磁精密科学仪器有限公司
氯离子选择电极	PCl-1-01	上海雷磁精密科学仪器有限公司
钾离子参比电极	217-01	上海雷磁精密科学仪器有限公司
氯离子参比电极	C(K₂SO₄)-1	上海雷磁精密科学仪器有限公司

Table 3 Pitzer parameters of single salt KCl［33］

T/K	β⁽⁰⁾	β⁽¹⁾	$C Φ$	$A Φ$	lnK_sp
318.15	0.05754	0.24388	-0.00181	0.4601	2.50892

Table 3 Pitzer parameters of single salt KCl［33］

T/K	β⁽⁰⁾	β⁽¹⁾	$C Φ$	$A Φ$	lnK_sp
318.15	0.05754	0.24388	-0.00181	0.4601	2.50892

Table 4 Potentials of cell a and activity coefficients of KCl in solutions

m₀/(mol·kg^-1)	$γ 0 ± K C l$	2ln $a 0 ± K C l$	E_a/mV
0.0101	0.8976	-9.4095	379.48
0.0501	0.8106	-6.4093	461.64
0.1000	0.7632	-5.1461	496.36
0.2001	0.7127	-3.8956	530.63
0.2999	0.6832	-3.1701	550.66
0.3999	0.6629	-2.6554	564.54
0.5001	0.6477	-2.2547	575.4
0.6000	0.6358	-1.9275	584.74
0.6998	0.6262	-1.6500	591.94
0.7998	0.6183	-1.4083	598.38
0.8998	0.6117	-1.1941	604.67
0.9997	0.6062	-1.0017	610.25

Table 4 Potentials of cell a and activity coefficients of KCl in solutions

m₀/(mol·kg^-1)	$γ 0 ± K C l$	2ln $a 0 ± K C l$	E_a/mV
0.0101	0.8976	-9.4095	379.48
0.0501	0.8106	-6.4093	461.64
0.1000	0.7632	-5.1461	496.36
0.2001	0.7127	-3.8956	530.63
0.2999	0.6832	-3.1701	550.66
0.3999	0.6629	-2.6554	564.54
0.5001	0.6477	-2.2547	575.4
0.6000	0.6358	-1.9275	584.74
0.6998	0.6262	-1.6500	591.94
0.7998	0.6183	-1.4083	598.38
0.8998	0.6117	-1.1941	604.67
0.9997	0.6062	-1.0017	610.25

Fig.1 Relationship between 2lna0±KCl and Ea at 318.15 K

Table 5 Standard cell potential， electrode response slope and linear correlation coefficient

T/K	E⁰/mV	κ/mV	κ'/mV	R²
318.15	637.36	27.407	27.41	1

Table 6 The mean activity coefficients of KCl in the KCl-K2B4O7-H2O solutions at 318.15 K

I/(mol·kg^-1)	y_b	m₁/(mol·kg^-1)	m₂/(mol·kg^-1)	E_b/mV	$γ ± K C l$	$γ' ± K C l$
0.0101	0.0000	0.0101	0.0000	379.48	0.8975	0.8975
0.0100	0.1998	0.0080	0.0007	371.08	0.8965	0.8966
0.0100	0.3989	0.0060	0.0013	361.24	0.8953	0.8953
0.0099	0.5998	0.0040	0.0020	347.17	0.8944	0.8945
0.0099	0.8003	0.0020	0.0027	325.74	0.8929	0.8929
0.0501	0.0000	0.0501	0.0000	461.71	0.8106	0.8106
0.0500	0.2004	0.0400	0.0033	453.37	0.8070	0.8071
0.0501	0.4000	0.0300	0.0067	443.29	0.8030	0.8030
0.0500	0.6002	0.0200	0.0100	429.60	0.7990	0.7989
0.0501	0.7992	0.0101	0.0133	408.16	0.7944	0.7943
0.1000	0.0000	0.1000	0.0000	496.33	0.7632	0.7632
0.1000	0.1993	0.0801	0.0066	487.96	0.7575	0.7575
0.1001	0.4002	0.0600	0.0134	477.60	0.7513	0.7513
0.1000	0.5996	0.0400	0.0200	463.80	0.7450	0.7449
0.1001	0.7994	0.0201	0.0267	442.06	0.7380	0.7378
0.2001	0.0000	0.2001	0.0000	530.61	0.7127	0.7127
0.2001	0.2002	0.1600	0.0134	521.93	0.7042	0.7041
0.2001	0.4000	0.1201	0.0267	511.32	0.6952	0.6950
0.2000	0.6000	0.0800	0.0400	497.23	0.6856	0.6852
0.2000	0.8001	0.0400	0.0533	475.00	0.6754	0.6749
0.3000	0.0000	0.3000	0.0000	550.48	0.6832	0.6833
0.3001	0.2001	0.2400	0.0200	541.65	0.6728	0.6726
0.2999	0.4000	0.1800	0.0400	530.79	0.6615	0.6612
0.3000	0.6001	0.1200	0.0600	516.49	0.6496	0.6491
0.3000	0.8000	0.0600	0.0800	494.03	0.6370	0.6363
0.4000	0.0000	0.4000	0.0000	564.60	0.6629	0.6629
0.4000	0.2000	0.3200	0.0267	555.59	0.6508	0.6506
0.4001	0.4000	0.2401	0.0533	544.59	0.6379	0.6375
0.4001	0.6000	0.1600	0.0800	530.08	0.6241	0.6235
0.4000	0.7999	0.0801	0.1067	507.42	0.6096	0.6087
0.5001	0.0000	0.5001	0.0000	575.57	0.6476	0.6477
0.5001	0.2000	0.4001	0.0333	566.42	0.6343	0.6341
0.5000	0.4000	0.3000	0.0667	555.24	0.6199	0.6194
0.5000	0.6000	0.2000	0.1000	540.57	0.6046	0.6038
0.5001	0.7999	0.1000	0.1333	517.72	0.5886	0.5874
0.6000	0.0000	0.6000	0.0000	584.54	0.6358	0.6358
0.6000	0.2000	0.4800	0.0400	575.27	0.6213	0.6210
0.6001	0.4000	0.3601	0.0800	563.97	0.6057	0.6050
0.6000	0.6000	0.2400	0.1200	549.13	0.5891	0.5881
0.6000	0.8000	0.1200	0.1600	526.08	0.5715	0.5702
0.7000	0.0000	0.7000	0.0000	592.16	0.6262	0.6263
0.7000	0.2001	0.5599	0.0467	582.78	0.6108	0.6104
0.7001	0.4000	0.4200	0.0933	571.34	0.5939	0.5932
0.7001	0.5999	0.2801	0.1400	556.37	0.5761	0.5751
0.7001	0.8000	0.1400	0.1867	533.17	0.5573	0.5559

Table 6 The mean activity coefficients of KCl in the KCl-K2B4O7-H2O solutions at 318.15 K

I/(mol·kg^-1)	y_b	m₁/(mol·kg^-1)	m₂/(mol·kg^-1)	E_b/mV	$γ ± K C l$	$γ' ± K C l$
0.0101	0.0000	0.0101	0.0000	379.48	0.8975	0.8975
0.0100	0.1998	0.0080	0.0007	371.08	0.8965	0.8966
0.0100	0.3989	0.0060	0.0013	361.24	0.8953	0.8953
0.0099	0.5998	0.0040	0.0020	347.17	0.8944	0.8945
0.0099	0.8003	0.0020	0.0027	325.74	0.8929	0.8929
0.0501	0.0000	0.0501	0.0000	461.71	0.8106	0.8106
0.0500	0.2004	0.0400	0.0033	453.37	0.8070	0.8071
0.0501	0.4000	0.0300	0.0067	443.29	0.8030	0.8030
0.0500	0.6002	0.0200	0.0100	429.60	0.7990	0.7989
0.0501	0.7992	0.0101	0.0133	408.16	0.7944	0.7943
0.1000	0.0000	0.1000	0.0000	496.33	0.7632	0.7632
0.1000	0.1993	0.0801	0.0066	487.96	0.7575	0.7575
0.1001	0.4002	0.0600	0.0134	477.60	0.7513	0.7513
0.1000	0.5996	0.0400	0.0200	463.80	0.7450	0.7449
0.1001	0.7994	0.0201	0.0267	442.06	0.7380	0.7378
0.2001	0.0000	0.2001	0.0000	530.61	0.7127	0.7127
0.2001	0.2002	0.1600	0.0134	521.93	0.7042	0.7041
0.2001	0.4000	0.1201	0.0267	511.32	0.6952	0.6950
0.2000	0.6000	0.0800	0.0400	497.23	0.6856	0.6852
0.2000	0.8001	0.0400	0.0533	475.00	0.6754	0.6749
0.3000	0.0000	0.3000	0.0000	550.48	0.6832	0.6833
0.3001	0.2001	0.2400	0.0200	541.65	0.6728	0.6726
0.2999	0.4000	0.1800	0.0400	530.79	0.6615	0.6612
0.3000	0.6001	0.1200	0.0600	516.49	0.6496	0.6491
0.3000	0.8000	0.0600	0.0800	494.03	0.6370	0.6363
0.4000	0.0000	0.4000	0.0000	564.60	0.6629	0.6629
0.4000	0.2000	0.3200	0.0267	555.59	0.6508	0.6506
0.4001	0.4000	0.2401	0.0533	544.59	0.6379	0.6375
0.4001	0.6000	0.1600	0.0800	530.08	0.6241	0.6235
0.4000	0.7999	0.0801	0.1067	507.42	0.6096	0.6087
0.5001	0.0000	0.5001	0.0000	575.57	0.6476	0.6477
0.5001	0.2000	0.4001	0.0333	566.42	0.6343	0.6341
0.5000	0.4000	0.3000	0.0667	555.24	0.6199	0.6194
0.5000	0.6000	0.2000	0.1000	540.57	0.6046	0.6038
0.5001	0.7999	0.1000	0.1333	517.72	0.5886	0.5874
0.6000	0.0000	0.6000	0.0000	584.54	0.6358	0.6358
0.6000	0.2000	0.4800	0.0400	575.27	0.6213	0.6210
0.6001	0.4000	0.3601	0.0800	563.97	0.6057	0.6050
0.6000	0.6000	0.2400	0.1200	549.13	0.5891	0.5881
0.6000	0.8000	0.1200	0.1600	526.08	0.5715	0.5702
0.7000	0.0000	0.7000	0.0000	592.16	0.6262	0.6263
0.7000	0.2001	0.5599	0.0467	582.78	0.6108	0.6104
0.7001	0.4000	0.4200	0.0933	571.34	0.5939	0.5932
0.7001	0.5999	0.2801	0.1400	556.37	0.5761	0.5751
0.7001	0.8000	0.1400	0.1867	533.17	0.5573	0.5559

Fig.2 Relationship between lnγ±KCl and yb at different values of I at 318.15 K

Table 7 Ion interaction parameters of K2B4O7 in the Pitzer model at 318.15 K

I/(mol·kg^–1)	β⁽⁰⁾	β⁽¹⁾	$C Φ$	$θ C l, B 4 O 5 (O H) 4$	$ψ K, C l, B 4 O 5 (O H) 4$	lnK_sp
0.0100~1.0000	-0.011026	-0.159011	-0.002363	0.00412	0.022113	-4.7125

Table 7 Ion interaction parameters of K2B4O7 in the Pitzer model at 318.15 K

I/(mol·kg^–1)	β⁽⁰⁾	β⁽¹⁾	$C Φ$	$θ C l, B 4 O 5 (O H) 4$	$ψ K, C l, B 4 O 5 (O H) 4$	lnK_sp
0.0100~1.0000	-0.011026	-0.159011	-0.002363	0.00412	0.022113	-4.7125

Table 8 Mean activity coefficients γ±K2B4O5(OH)4， osmotic coefficient Φ， water activity aw and excess Gibbs free energy GE in KCl-K2B4O7-H2O mixed solutions at 318.15 K

I/(mol·kg^-1)	y_b	$γ ± K 2 B 4 O 5 (O H) 4$	Φ	a_w	G^E/(kJ·mol^-1)
0.0101	0.0000	0.7007	0.9662	0.9996	-0.0040
0.0100	0.1998	0.7038	0.9613	0.9997	-0.0046
0.0100	0.3989	0.7058	0.9554	0.9997	-0.0053
0.0099	0.5998	0.7091	0.9484	0.9998	-0.0059
0.0099	0.8003	0.7106	0.9393	0.9998	-0.0065
0.0501	0.0000	0.4764	0.9391	0.9983	-0.0395
0.0500	0.2004	0.4812	0.9279	0.9985	-0.0475
0.0501	0.4000	0.4851	0.9149	0.9987	-0.0552
0.0500	0.6002	0.4889	0.8994	0.9989	-0.0619
0.0501	0.7992	0.4917	0.8799	0.9990	-0.0684
0.1000	0.0000	0.3675	0.9256	0.9967	-0.1036
0.1000	0.1993	0.3730	0.9101	0.9971	-0.1268
0.1001	0.4002	0.3779	0.8920	0.9974	-0.1482
0.1000	0.5996	0.3824	0.8707	0.9978	-0.1669
0.1001	0.7994	0.3858	0.8442	0.9982	-0.1844
0.2001	0.0000	0.2630	0.9132	0.9934	-0.2666
0.2001	0.2002	0.2694	0.8917	0.9942	-0.3328
0.2001	0.4000	0.2751	0.8672	0.9950	-0.3918
0.2000	0.6000	0.2801	0.8383	0.9958	-0.4441
0.2000	0.8001	0.2843	0.8028	0.9965	-0.4903
0.3000	0.0000	0.2080	0.9074	0.9902	-0.4574
0.3001	0.2001	0.2146	0.8817	0.9915	-0.5790
0.2999	0.4000	0.2207	0.8525	0.9927	-0.6861
0.3000	0.6001	0.2259	0.8183	0.9938	-0.7808
0.3000	0.8000	0.2303	0.7766	0.9950	-0.8630
0.4000	0.0000	0.1726	0.9042	0.9871	-0.6673
0.4000	0.2000	0.1794	0.8753	0.9887	-0.8537
0.4001	0.4000	0.1855	0.8425	0.9903	-1.0181
0.4001	0.6000	0.1909	0.8042	0.9919	-1.1613
0.4000	0.7999	0.1954	0.7576	0.9935	-1.2843
0.5001	0.0000	0.1476	0.9026	0.9839	-0.8914
0.5001	0.2000	0.1545	0.8710	0.9860	-1.1512
0.5000	0.4000	0.1607	0.8351	0.9880	-1.3784
0.5000	0.6000	0.1661	0.7934	0.9901	-1.5759
0.5001	0.7999	0.1706	0.7428	0.9920	-1.7444
0.6000	0.0000	0.1290	0.9019	0.9807	-1.1260
0.6000	0.2000	0.1358	0.8679	0.9833	-1.4664
0.6001	0.4000	0.1419	0.8295	0.9858	-1.7636
0.6000	0.6000	0.1473	0.7848	0.9882	-2.0196
0.6000	0.8000	0.1519	0.7307	0.9906	-2.2362
0.7000	0.0000	0.1144	0.9019	0.9775	-1.3697
0.7000	0.2001	0.1211	0.8658	0.9806	-1.7972
0.7001	0.4000	0.1272	0.8251	0.9835	-2.1694

Table 8 Mean activity coefficients γ±K2B4O5(OH)4， osmotic coefficient Φ， water activity aw and excess Gibbs free energy GE in KCl-K2B4O7-H2O mixed solutions at 318.15 K

I/(mol·kg^-1)	y_b	$γ ± K 2 B 4 O 5 (O H) 4$	Φ	a_w	G^E/(kJ·mol^-1)
0.0101	0.0000	0.7007	0.9662	0.9996	-0.0040
0.0100	0.1998	0.7038	0.9613	0.9997	-0.0046
0.0100	0.3989	0.7058	0.9554	0.9997	-0.0053
0.0099	0.5998	0.7091	0.9484	0.9998	-0.0059
0.0099	0.8003	0.7106	0.9393	0.9998	-0.0065
0.0501	0.0000	0.4764	0.9391	0.9983	-0.0395
0.0500	0.2004	0.4812	0.9279	0.9985	-0.0475
0.0501	0.4000	0.4851	0.9149	0.9987	-0.0552
0.0500	0.6002	0.4889	0.8994	0.9989	-0.0619
0.0501	0.7992	0.4917	0.8799	0.9990	-0.0684
0.1000	0.0000	0.3675	0.9256	0.9967	-0.1036
0.1000	0.1993	0.3730	0.9101	0.9971	-0.1268
0.1001	0.4002	0.3779	0.8920	0.9974	-0.1482
0.1000	0.5996	0.3824	0.8707	0.9978	-0.1669
0.1001	0.7994	0.3858	0.8442	0.9982	-0.1844
0.2001	0.0000	0.2630	0.9132	0.9934	-0.2666
0.2001	0.2002	0.2694	0.8917	0.9942	-0.3328
0.2001	0.4000	0.2751	0.8672	0.9950	-0.3918
0.2000	0.6000	0.2801	0.8383	0.9958	-0.4441
0.2000	0.8001	0.2843	0.8028	0.9965	-0.4903
0.3000	0.0000	0.2080	0.9074	0.9902	-0.4574
0.3001	0.2001	0.2146	0.8817	0.9915	-0.5790
0.2999	0.4000	0.2207	0.8525	0.9927	-0.6861
0.3000	0.6001	0.2259	0.8183	0.9938	-0.7808
0.3000	0.8000	0.2303	0.7766	0.9950	-0.8630
0.4000	0.0000	0.1726	0.9042	0.9871	-0.6673
0.4000	0.2000	0.1794	0.8753	0.9887	-0.8537
0.4001	0.4000	0.1855	0.8425	0.9903	-1.0181
0.4001	0.6000	0.1909	0.8042	0.9919	-1.1613
0.4000	0.7999	0.1954	0.7576	0.9935	-1.2843
0.5001	0.0000	0.1476	0.9026	0.9839	-0.8914
0.5001	0.2000	0.1545	0.8710	0.9860	-1.1512
0.5000	0.4000	0.1607	0.8351	0.9880	-1.3784
0.5000	0.6000	0.1661	0.7934	0.9901	-1.5759
0.5001	0.7999	0.1706	0.7428	0.9920	-1.7444
0.6000	0.0000	0.1290	0.9019	0.9807	-1.1260
0.6000	0.2000	0.1358	0.8679	0.9833	-1.4664
0.6001	0.4000	0.1419	0.8295	0.9858	-1.7636
0.6000	0.6000	0.1473	0.7848	0.9882	-2.0196
0.6000	0.8000	0.1519	0.7307	0.9906	-2.2362
0.7000	0.0000	0.1144	0.9019	0.9775	-1.3697
0.7000	0.2001	0.1211	0.8658	0.9806	-1.7972
0.7001	0.4000	0.1272	0.8251	0.9835	-2.1694

Fig.3 Relationship between thermodynamic properties and I of the KCl-K2B4O7-H2O solutions under different value of yb at 318.15 K

Fig.4 Equilibrium phase diagram of ternary system KCl-K2B4O7-H2O at 318.15 K

Table 9 Calculated and experimental solubilities of salts in the KCl-K2B4O7-H2O ternary system at 318.15 K

计算值			实验值
No.	液相组成w(B)/%		No.	液相组成w(B)/%		湿渣组成w(B)/%		平衡固相
No.	KCl	K₂B₄O₇	No.	KCl	K₂B₄O₇	KCl	K₂B₄O₇	平衡固相
1	0.00	21.33	1, A	0.00	21.30	0.00	65.06	K₂B₄O₇·4H₂O
2	5.93	14.51	2	11.72	10.49	4.20	55.88	K₂B₄O₇·4H₂O
3	11.56	10.89	3	20.32	7.33	7.23	55.29	K₂B₄O₇·4H₂O
4	16.68	8.76	4	26.87	5.65	11.99	52.12	K₂B₄O₇·4H₂O
5	21.31	7.24	5,G	27.13	5.29	33.78	31.98	KCl + K₂B₄O₇·4H₂O
6	25.52	6.00	6	27.19	5.19	24.82	40.40	KCl
7,G’	26.92	5.61	7	27.26	5.02	43.63	27.65	KCl
8	27.31	4.76	8	27.59	5.30	69.79	5.91	KCl
9	28.04	3.21	9	27.49	4.25	54.70	2.71	KCl
10	29.55	0.00	10, B	29.65	0.00	68.67	0.00	KCl

Fig.5 X-Ray diffraction patterns of the invariant point in ternary system KCl-K2B4O7-H2O at 318.15 K

Fig.6 Comparison of calculated and experimental solubilities in the KCl-K2B4O7-H2O ternary system at 318.15 K

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Measurements and predictions of thermodynamic activity coefficients and phase equilibria in ternary system KCl-K₂B₄O₇-H₂O at 318.15 K

三元体系KCl-K₂B₄O₇-H₂O在318.15 K下热力学活度系数及相平衡实验和预测

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