电解质溶液渗透系数理论在水分活度等物理化学特性量计量中的应用

王海峰; 李佳

doi:10.12338/j.issn.2096-9015.2024.0191

电解质溶液渗透系数理论在水分活度等物理化学特性量计量中的应用

doi: 10.12338/j.issn.2096-9015.2024.0191

王海峰,
李佳

中国计量科学研究院，北京 100029

基金项目: 中国计量科学研究院自筹基本业务经费（AKYZZ2331-23）。

详细信息

作者简介:
王海峰（1978-），中国计量科学研究院副研究员，研究方向：水分和有机元素计量技术，邮箱：wanghf@nim.ac.cn

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出版历程
- 收稿日期: 2024-06-15
- 录用日期: 2024-07-08
- 修回日期: 2024-07-15
- 网络出版日期: 2024-08-02

Application of Osmotic Coefficient Theory of Electrolyte in Metrology of Physical Chemistry Quantities Including Water Activity

National Institute of Metrology, Beijing 100029, China

摘要

摘要: 渗透系数（ϕ）反映了电解质溶液中溶剂偏离理想溶液的程度。渗透系数可采用蒸气压法和电动势法等多种方法测定。美国国家标准局统计了已发表的数据，以每种电解质溶液的多套科学数据的平均值，作为该电解质溶液的渗透系数的标准值，并给出了渗透系数的标准偏差。该渗透系数的标准数据以德拜-休克尔公式的形式表达，方便使用者代入电解质溶液的质量摩尔浓度计算对应的渗透系数。渗透系数可用于计算电解质溶液的水分活度、冰点和渗透压摩尔浓度，从而为相关特性量标准溶液定值，分别用于校准相关特性量的测量仪器。在众多的电解质中，最常用的是氯化钠。国际标准和国家标准规定的上述特性量的标准值，和根据渗透系数标准数据计算得到的结果一致性良好。根据渗透系数标准数据计算相关特性量的标准值，能够通过渗透系数标准数据间接地溯源至蒸气压和电动势等量值的SI单位。
- 计量学 /
- 渗透系数 /
- 水分活度 /
- 冰点 /
- 渗透压摩尔浓度 /
- 标准溶液
Abstract: Osmotic coefficient (ϕ) is a measure of the deviation of the solvent of electrolyte from the ideal solution. ϕ was usually determined by the manometric method and the electromotive force method. National bureau of standard of United States of America published the reference value of osmotic coefficient equal to the average of many scientific data and its standard deviation based on the statistics. This reference data was expressed as the Debye-Hückel equation. When the molality of the electrolyte was introduced in the equation, and thus the corresponding osmotic coefficient was deduced. ϕ can be used to calculate the water activity, freezing point depression and osmotic pressure concentration of the solution of electrolyte, and thus the reference solution of these quantities were determined and then used to calibrate the instrument of these quantities. Sodium chloride was the most commonly used electrolyte. The reference values specified by the related international or national standard were well consistent with the results calculated using the reference data of ϕ. The reference values of related physical chemistry quantities calculated using the reference data of ϕ were traceable to SI units of vapor pressure or potential of the electromotive force indirectly.
- metrology /
- osmotic coefficient /
- water activity /
- freezing point depression /
- osmolality /
- reference material

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表 1 NaCl渗透系数原始数据的来源

Table 1. Source of the data of osmotic coefficient of NaCl

编号	测量方法	作者	年代
1	电势法	Allmand, Polack^[2]	1919
2	电势法	Harned^[3]	1929
3	电势法	Harned, Nims^[4]	1932
4	电势法	Brown, MacInnes^[5]	1935
5	电势法	Sakong, Huang	1962
6	电势法	Lebed, Aleksandrov	1964
7	电势法	Wilke, Schrӓnkler	1932
8	电势法	Janz, Gordon^[6]	1943
9	电势法	Caramazza	1960
10	电势法	Getman^[7]	1920
11	电势法	Haas, Jellinek	1932
12	双温法	Stokes^[8]	1947
13	扩散法	Harned^[9]	1959
14	蒸气压法	Negus	1922
15	蒸气压法	Pearce, Nelson^[10]	1932
16	蒸气压法	Olynyk, Gordon^[11]	1943
17	蒸气压法	Petit^[12]	1965
18	露点法	Hepburn^[13]	1928
19	等压法	Robinson, Sinclair^[14]	1934
20	等压法	Scatchard, Hamer^[15]	1938
21	等压法	Robinson^[16]	1939
22	等压法	Janis, Ferguson^[17]	1939
23	等压法	Robinson^[18]	1945

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表 2 NaCl溶液水分活度的计算值

Table 2. Calculated value of water activity of NaCl aqueous solution

质量摩尔浓度（mol/kg）	质量百分数	ISO 21807推荐的水分活度^[19]	ϕ标准数据	根据ϕ标准数据计算得到的水分活度
0.1	0.58%	0.9966	0.933	0.9966
0.2	1.15%	0.9934	0.924	0.9934
0.3	1.72%	0.9900	0.921	0.9901
0.4	2.28%	0.9868	0.921	0.9868
0.5	2.84%	0.9835	0.922	0.9835
0.6	3.39%	0.9802	0.923	0.9802
0.7	3.93%	0.9769	0.926	0.9769
0.8	4.47%	0.9736	0.929	0.9736
0.9	5.00%	0.9702	0.932	0.9702
1.0	5.52%	0.9669	0.936	0.9668
1.2	6.55%	0.9601	0.944	0.9600
1.4	7.56%	0.9532	0.953	0.9531
1.6	8.55%	0.9461	0.963	0.9460
1.8	9.52%	0.9389	0.973	0.9388
2.0	10.46%	0.9316	0.984	0.9315
2.2	11.39%	0.9242	0.995	0.9241
2.4	12.30%	0.9166	1.007	0.9166
2.6	13.19%	0.9089	1.020	0.9089
2.8	14.06%	0.9011	1.032	0.9011
3.0	14.92%	0.8932	1.046	0.8931
3.2	15.75%	0.8851	1.059	0.8851
3.4	16.58%	0.8769	1.073	0.8768
3.6	17.38%	0.8686	1.087	0.8685
3.8	18.17%	0.8600	1.101	0.8600
4.0	18.95%	0.8515	1.116	0.8514
5.0	22.61%	0.8068	1.192	0.8068
6.0	25.97%	0.7598	1.270	0.7599

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表 3 不饱和盐溶液的溶质、浓度、渗透系数和水分活度

Table 3. Solute, concentration, osmotic coefficient and water activity of unsaturated solution of salts

溶质	质量摩尔浓度（mol/kg）	渗透系数	水分活度
LiCl	13.481	2.851	0.250
LiCl	8.533	2.251	0.500
NaCl	5.953	1.266	0.762
NaCl	5.209	1.208	0.797
NaCl	4.029	1.118	0.850
NaCl	2.825	1.034	0.900
NaCl	1.487	0.957	0.950

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表 4 NaCl溶液的质量分数、质量摩尔浓度和冰点下降值

Table 4. Mass fraction, molality and freezing point depression of NaCl solution

质量摩尔浓度（mol/kg）	质量百分数	GB5413.38 规定的冰点^[22] （mK）	ϕ标准数据	根据ϕ标准数据计算得到的冰点（mK）
0.1165	0.676%	400	0.9305	403
0.1189	0.690%	408	0.9302	411
0.1315	0.763%	450	0.9288	454
0.1465	0.849%	500	0.9274	505
0.1495	0.866%	510	0.9271	515
0.1501	0.870%	512	0.9270	517
0.1525	0.884%	520	0.9268	525
0.1555	0.901%	530	0.9266	536
0.1585	0.918%	540	0.9264	546
0.1616	0.935%	550	0.9261	556
0.1637	0.948%	557	0.9260	563
0.1767	1.022%	600	0.9251	607

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表 5 NaCl溶液的质量摩尔浓度、质量分数和渗透压摩尔浓度

Table 5. Molality, mass fraction and Osmolality of NaCl solution

1kg溶剂所含的NaCl 质量（g/kg）	质量摩尔浓度（mol/kg）	质量百分数	药典规定的渗透压摩尔浓度（mOsmol/kg）^[22]	ϕ标准数据	根据ϕ标准数据计算的渗透压摩尔浓度（mOsmol/kg）
3.087	0.0528	0.3077%	100	0.9431	99.6
6.260	0.1071	0.6221%	200	0.9318	199.6
9.463	0.1619	0.9374%	300	0.9261	299.9
12.684	0.2170	1.2525%	400	0.9229	400.6
15.916	0.2723	1.5667%	500	0.9212	501.8
19.147	0.3276	1.8787%	600	0.9204	603.1
22.380	0.3829	2.1890%	700	0.9202	704.8

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参考文献(22)

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