{"title":"高 T 和 P 条件下 1-1 电解质的部分摩尔体积:相关性和预测","authors":"Andrey V. Plyasunov, Elena V. Cherkasova","doi":"10.1016/j.gca.2024.10.024","DOIUrl":null,"url":null,"abstract":"Knowledge of the partial molar volumes of aqueous ions allows accurate calculation of the pressure dependence of equilibrium constants, solubility of minerals, etc., thus being useful for thermodynamic modeling of hydrothermal processes. This study analyzed methods to correlate and predict the values of the partial molar volumes at infinite dilution, <mml:math altimg=\"si6.svg\"><mml:mrow><mml:msubsup><mml:mi>V</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow><mml:mi mathvariant=\"normal\">o</mml:mi></mml:msubsup></mml:mrow></mml:math>, for 1–1 electrolytes and singly charged ions at elevated T and P. Since the precise experimental values of the dielectric constant of water are measured only up to 873 K, we were interested only in non-electrostatic ways to correlate <mml:math altimg=\"si6.svg\"><mml:mrow><mml:msubsup><mml:mi>V</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow><mml:mi mathvariant=\"normal\">o</mml:mi></mml:msubsup></mml:mrow></mml:math> data. First of all, we compiled the <mml:math altimg=\"si6.svg\"><mml:mrow><mml:msubsup><mml:mi>V</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow><mml:mi mathvariant=\"normal\">o</mml:mi></mml:msubsup></mml:mrow></mml:math> values at T > 373 K for the following 1–1 electrolytes: HCl, LiCl, LiI, LiNO<ce:inf loc=\"post\">3</ce:inf>, LiOH, NaF, NaCl, NaBr, NaI, NaNO<ce:inf loc=\"post\">3</ce:inf>, NaOH, NaHCO<ce:inf loc=\"post\">3</ce:inf>, NaClO<ce:inf loc=\"post\">4</ce:inf>, NaH<ce:inf loc=\"post\">2</ce:inf>PO<ce:inf loc=\"post\">4</ce:inf>, NaTr (Tr stands for triflate), KF, KCl, KBr, KI, KNO<ce:inf loc=\"post\">3</ce:inf>, KOH, CsBr, and NH<ce:inf loc=\"post\">4</ce:inf>Cl. Relations, following from the “density” model and from the Fluctuation Solution Theory (FST) were employed to analyze data. It was concluded that at the current state of knowledge of <mml:math altimg=\"si6.svg\"><mml:mrow><mml:msubsup><mml:mi>V</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow><mml:mi mathvariant=\"normal\">o</mml:mi></mml:msubsup></mml:mrow></mml:math> the FST-relations for electrolytes are recommended mainly to reject strongly deviating experimental outliers. However, the “density” model provides a simple and fairly accurate way to describe the compiled set of data with only two parameters for each ion, <mml:math altimg=\"si4.svg\"><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:math> and <mml:math altimg=\"si5.svg\"><mml:mrow><mml:msub><mml:mi>V</mml:mi><mml:mtext>hc</mml:mtext></mml:msub></mml:mrow></mml:math>, values of which were evaluated for the following singly-charged ions: H<ce:sup loc=\"post\">+</ce:sup>, Li<ce:sup loc=\"post\">+</ce:sup>, Na<ce:sup loc=\"post\">+</ce:sup>, K<ce:sup loc=\"post\">+</ce:sup>, Cs<ce:sup loc=\"post\">+</ce:sup>, NH<ce:inf loc=\"post\">4</ce:inf><ce:sup loc=\"post\">+</ce:sup>, F<ce:sup loc=\"post\">-</ce:sup>, Cl<ce:sup loc=\"post\">-</ce:sup>, Br<ce:sup loc=\"post\">-</ce:sup>, I<ce:sup loc=\"post\">-</ce:sup>, OH<ce:sup loc=\"post\">–</ce:sup>, NO<ce:inf loc=\"post\">3</ce:inf><ce:sup loc=\"post\">–</ce:sup>, H<ce:inf loc=\"post\">2</ce:inf>PO<ce:inf loc=\"post\">4</ce:inf><ce:sup loc=\"post\">-</ce:sup>, HCO<ce:inf loc=\"post\">3</ce:inf><ce:sup loc=\"post\">–</ce:sup>, ClO<ce:inf loc=\"post\">4</ce:inf><ce:sup loc=\"post\">-</ce:sup>, Tr<ce:sup loc=\"post\">-</ce:sup> (Tr = triflate). Following <ce:cross-ref ref>Mesmer et al. (1988)</ce:cross-ref>, we consider the fitting parameters <mml:math altimg=\"si5.svg\"><mml:mrow><mml:msub><mml:mi>V</mml:mi><mml:mtext>hc</mml:mtext></mml:msub></mml:mrow></mml:math> and <mml:math altimg=\"si4.svg\"><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:math> to be related to the intrinsic volume of the ion and to the number of water molecules transferred from the bulk water to a hydration shell around the ion, respectively.","PeriodicalId":327,"journal":{"name":"Geochimica et Cosmochimica Acta","volume":"74 1","pages":""},"PeriodicalIF":4.5000,"publicationDate":"2024-10-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Partial molar volumes of 1–1 electrolytes at high T and P: correlations and predictions\",\"authors\":\"Andrey V. Plyasunov, Elena V. Cherkasova\",\"doi\":\"10.1016/j.gca.2024.10.024\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Knowledge of the partial molar volumes of aqueous ions allows accurate calculation of the pressure dependence of equilibrium constants, solubility of minerals, etc., thus being useful for thermodynamic modeling of hydrothermal processes. This study analyzed methods to correlate and predict the values of the partial molar volumes at infinite dilution, <mml:math altimg=\\\"si6.svg\\\"><mml:mrow><mml:msubsup><mml:mi>V</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow><mml:mi mathvariant=\\\"normal\\\">o</mml:mi></mml:msubsup></mml:mrow></mml:math>, for 1–1 electrolytes and singly charged ions at elevated T and P. Since the precise experimental values of the dielectric constant of water are measured only up to 873 K, we were interested only in non-electrostatic ways to correlate <mml:math altimg=\\\"si6.svg\\\"><mml:mrow><mml:msubsup><mml:mi>V</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow><mml:mi mathvariant=\\\"normal\\\">o</mml:mi></mml:msubsup></mml:mrow></mml:math> data. First of all, we compiled the <mml:math altimg=\\\"si6.svg\\\"><mml:mrow><mml:msubsup><mml:mi>V</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow><mml:mi mathvariant=\\\"normal\\\">o</mml:mi></mml:msubsup></mml:mrow></mml:math> values at T > 373 K for the following 1–1 electrolytes: HCl, LiCl, LiI, LiNO<ce:inf loc=\\\"post\\\">3</ce:inf>, LiOH, NaF, NaCl, NaBr, NaI, NaNO<ce:inf loc=\\\"post\\\">3</ce:inf>, NaOH, NaHCO<ce:inf loc=\\\"post\\\">3</ce:inf>, NaClO<ce:inf loc=\\\"post\\\">4</ce:inf>, NaH<ce:inf loc=\\\"post\\\">2</ce:inf>PO<ce:inf loc=\\\"post\\\">4</ce:inf>, NaTr (Tr stands for triflate), KF, KCl, KBr, KI, KNO<ce:inf loc=\\\"post\\\">3</ce:inf>, KOH, CsBr, and NH<ce:inf loc=\\\"post\\\">4</ce:inf>Cl. Relations, following from the “density” model and from the Fluctuation Solution Theory (FST) were employed to analyze data. It was concluded that at the current state of knowledge of <mml:math altimg=\\\"si6.svg\\\"><mml:mrow><mml:msubsup><mml:mi>V</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow><mml:mi mathvariant=\\\"normal\\\">o</mml:mi></mml:msubsup></mml:mrow></mml:math> the FST-relations for electrolytes are recommended mainly to reject strongly deviating experimental outliers. However, the “density” model provides a simple and fairly accurate way to describe the compiled set of data with only two parameters for each ion, <mml:math altimg=\\\"si4.svg\\\"><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:math> and <mml:math altimg=\\\"si5.svg\\\"><mml:mrow><mml:msub><mml:mi>V</mml:mi><mml:mtext>hc</mml:mtext></mml:msub></mml:mrow></mml:math>, values of which were evaluated for the following singly-charged ions: H<ce:sup loc=\\\"post\\\">+</ce:sup>, Li<ce:sup loc=\\\"post\\\">+</ce:sup>, Na<ce:sup loc=\\\"post\\\">+</ce:sup>, K<ce:sup loc=\\\"post\\\">+</ce:sup>, Cs<ce:sup loc=\\\"post\\\">+</ce:sup>, NH<ce:inf loc=\\\"post\\\">4</ce:inf><ce:sup loc=\\\"post\\\">+</ce:sup>, F<ce:sup loc=\\\"post\\\">-</ce:sup>, Cl<ce:sup loc=\\\"post\\\">-</ce:sup>, Br<ce:sup loc=\\\"post\\\">-</ce:sup>, I<ce:sup loc=\\\"post\\\">-</ce:sup>, OH<ce:sup loc=\\\"post\\\">–</ce:sup>, NO<ce:inf loc=\\\"post\\\">3</ce:inf><ce:sup loc=\\\"post\\\">–</ce:sup>, H<ce:inf loc=\\\"post\\\">2</ce:inf>PO<ce:inf loc=\\\"post\\\">4</ce:inf><ce:sup loc=\\\"post\\\">-</ce:sup>, HCO<ce:inf loc=\\\"post\\\">3</ce:inf><ce:sup loc=\\\"post\\\">–</ce:sup>, ClO<ce:inf loc=\\\"post\\\">4</ce:inf><ce:sup loc=\\\"post\\\">-</ce:sup>, Tr<ce:sup loc=\\\"post\\\">-</ce:sup> (Tr = triflate). Following <ce:cross-ref ref>Mesmer et al. (1988)</ce:cross-ref>, we consider the fitting parameters <mml:math altimg=\\\"si5.svg\\\"><mml:mrow><mml:msub><mml:mi>V</mml:mi><mml:mtext>hc</mml:mtext></mml:msub></mml:mrow></mml:math> and <mml:math altimg=\\\"si4.svg\\\"><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:math> to be related to the intrinsic volume of the ion and to the number of water molecules transferred from the bulk water to a hydration shell around the ion, respectively.\",\"PeriodicalId\":327,\"journal\":{\"name\":\"Geochimica et Cosmochimica Acta\",\"volume\":\"74 1\",\"pages\":\"\"},\"PeriodicalIF\":4.5000,\"publicationDate\":\"2024-10-26\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Geochimica et Cosmochimica Acta\",\"FirstCategoryId\":\"89\",\"ListUrlMain\":\"https://doi.org/10.1016/j.gca.2024.10.024\",\"RegionNum\":1,\"RegionCategory\":\"地球科学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"GEOCHEMISTRY & GEOPHYSICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Geochimica et Cosmochimica Acta","FirstCategoryId":"89","ListUrlMain":"https://doi.org/10.1016/j.gca.2024.10.024","RegionNum":1,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"GEOCHEMISTRY & GEOPHYSICS","Score":null,"Total":0}
引用次数: 0
摘要
了解了水溶液离子的部分摩尔体积,就可以准确计算平衡常数的压力依赖性、矿物的溶解度等,从而有助于热液过程的热力学建模。本研究分析了关联和预测 1-1 种电解质和单电荷离子在高温度和高压力下无限稀释时的部分摩尔体积(V2o)值的方法。由于水的介电常数的精确实验值只测到 873 K,我们只对关联 V2o 数据的非静电方法感兴趣。首先,我们汇编了以下 1-1 种电解质在 T > 373 K 时的 V2o 值:HCl、LiCl、LiI、LiNO3、LiOH、NaF、NaCl、NaBr、NaI、NaNO3、NaOH、NaHCO3、NaClO4、NaH2PO4、NaTr(Tr 代表三盐酸盐)、KF、KCl、KBr、KI、KNO3、KOH、CsBr 和 NH4Cl。数据分析采用了 "密度 "模型和波动解理论(FST)的关系。得出的结论是,根据目前对 V2o 的了解,建议使用电解质的 FST 关系,主要是为了剔除偏差较大的实验异常值。然而,"密度 "模型提供了一种简单而相当准确的方法来描述所汇编的数据集,每种离子只有两个参数,即 n 和 Vhc:H+、Li+、Na+、K+、Cs+、NH4+、F-、Cl-、Br-、I-、OH-、NO3-、H2PO4-、HCO3-、ClO4-、Tr-(Tr = 三酸盐)。根据 Mesmer 等人(1988 年)的研究,我们认为拟合参数 Vhc 和 n 分别与离子的固有体积和从体水转移到离子周围水合壳的水分子数有关。
Partial molar volumes of 1–1 electrolytes at high T and P: correlations and predictions
Knowledge of the partial molar volumes of aqueous ions allows accurate calculation of the pressure dependence of equilibrium constants, solubility of minerals, etc., thus being useful for thermodynamic modeling of hydrothermal processes. This study analyzed methods to correlate and predict the values of the partial molar volumes at infinite dilution, V2o, for 1–1 electrolytes and singly charged ions at elevated T and P. Since the precise experimental values of the dielectric constant of water are measured only up to 873 K, we were interested only in non-electrostatic ways to correlate V2o data. First of all, we compiled the V2o values at T > 373 K for the following 1–1 electrolytes: HCl, LiCl, LiI, LiNO3, LiOH, NaF, NaCl, NaBr, NaI, NaNO3, NaOH, NaHCO3, NaClO4, NaH2PO4, NaTr (Tr stands for triflate), KF, KCl, KBr, KI, KNO3, KOH, CsBr, and NH4Cl. Relations, following from the “density” model and from the Fluctuation Solution Theory (FST) were employed to analyze data. It was concluded that at the current state of knowledge of V2o the FST-relations for electrolytes are recommended mainly to reject strongly deviating experimental outliers. However, the “density” model provides a simple and fairly accurate way to describe the compiled set of data with only two parameters for each ion, n and Vhc, values of which were evaluated for the following singly-charged ions: H+, Li+, Na+, K+, Cs+, NH4+, F-, Cl-, Br-, I-, OH–, NO3–, H2PO4-, HCO3–, ClO4-, Tr- (Tr = triflate). Following Mesmer et al. (1988), we consider the fitting parameters Vhc and n to be related to the intrinsic volume of the ion and to the number of water molecules transferred from the bulk water to a hydration shell around the ion, respectively.
期刊介绍:
Geochimica et Cosmochimica Acta publishes research papers in a wide range of subjects in terrestrial geochemistry, meteoritics, and planetary geochemistry. The scope of the journal includes:
1). Physical chemistry of gases, aqueous solutions, glasses, and crystalline solids
2). Igneous and metamorphic petrology
3). Chemical processes in the atmosphere, hydrosphere, biosphere, and lithosphere of the Earth
4). Organic geochemistry
5). Isotope geochemistry
6). Meteoritics and meteorite impacts
7). Lunar science; and
8). Planetary geochemistry.