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The Partition of Salts (I) Between Two Immiscible Solution Phases and (Ii) Between the Solid Salt Phase and Its Saturated Salt Solution

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The Partition of Salts (I) Between Two Immiscible Solution Phases and (Ii) Between the Solid Salt Phase and Its Saturated Salt Solution ChemTexts (2020) 6:17 https://doi.org/10.1007/s40828-020-0109-0 (0123456789().,-volV)(0123456789().,-volV) LECTURE TEXT The partition of salts (i) between two immiscible solution phases and (ii) between the solid salt phase and its saturated salt solution Fritz Scholz1 · Heike Kahlert1 · Richard Thede1 Received: 17 December 2019 / Accepted: 2 March 2020 / Published online: 24 April 2020 © The Author(s) 2020 Abstract The partition of salts between two polar immiscible solvents results from the partition of the cations and anions. Because electroneutrality rules in both phases, the partition of cations is affected by that of anions, and vice versa. Thus, the partition of a salt is determined by the chemical potentials of cations and anions in both phases, and it is limited by the boundary condition of electroneutrality. Whereas the partition of neutral molecules does not produce a Galvani potential difference at the interface, the partition of salts does. Here, the equations to calculate this Galvani potential difference are derived for salts of the general composition CatðzCatÞþAnðzAnÞÀ and for uni-univalent salts CatþAnÀ. The activity of a mCat mAn specific ion in a particular phase can thus be purposefully tuned by the choice of a suitable counterion. Finally, the distribution of a salt between its solid phase and its saturated solution is also presented, together with a discussion of the Galvani potential difference across the interface of the two phases. Graphical abstract Dear Plus, but I do Come over, beloved not like your Minus, we need your phase! charge! Phase α Phase β Keywords Partition · Partition constant · Ion · Salt · Electrolyte · Galvani potential difference · Ion adsorption · Fajans · Precipitation · Titration List of symbols Latin symbols a Activity Fritz Scholz and Heike Kahlert equally contributed as authors. A Neutral compound A & Fritz Scholz AnðzAnÞÀ Anion An with z negative charges [email protected] B, C,... Compounds B, C, etc. & Heike Kahlert c Molar concentration [email protected] c* Standard concentration (1 mol L−1) ðzCatÞþ Cation Cat with z positive charges 1 Institut fu¨r Biochemie, Universita¨t Greifswald, Felix- Cat Hausdorff-Str. 4, 17489 Greifswald, Germany DCM Dichloromethane 123 17 Page 2 of 12 ChemTexts (2020) 6:17 − e Electron Da;b/ Difference of inner electric potentials of the E Electrolyte phases phase a and b, i.e. the Galvani potential E Electric potential difference between these two phases. It is f Activity coefficient defined as Da;b/ ¼ /b À /a F Faraday constant (9.64853383(83)9 ÀÀ 0 Formal potential of ion transfer Ds;sol/ ; 104 C mol−1) c i g Free energy (Gibbs energy) Other symbols G Molar free energy (molar Gibbs energy) ÀÀ Plimsoll symbol, as superscript indicating standard D ÀÀ Standard Gibbs energy of transfer of A from a!bGA quantities phase a to phase b KIP Formation constant of ion pairs (association Introduction constant) K ; ; Partition constant of species A pðAÞ T p The partition of neutral compounds between immiscible Ksp Solubility product solvents is very well covered in textbooks of general, i Chemical species i physical and analytical chemistry; however, the partition of IP Ion pair salts can be found only in special monographs, where it is ln Natural logarithm (logarithm to the base e, with often presented in a form which is not easily understand- e being the Euler constant) able for students. Here, we provide an introductory text log Decadic logarithm (logarithm to the base 10) discussing salt partition on the basis of the thermodynamics M Metal phase as taught in Bachelor courses. n Amount of substance (unit: mol) of atoms, The partition of salts is of high importance in many molecules, ions or electrons fields of science: ion transfer (e.g. of drugs) through nb Nitrobenzene membranes, ion transfer catalysis in organic synthesis, and Ox Oxidized form of a redox pair extraction of metal ions in analytical chemistry are just the p Partition most common examples. p Pressure When the partition of compounds between liquid phases À pic Picrate (2,4,6-trinitrophenolate) is treated, usually the phrase ‘partition between two R Universal gas constant −1 −1 immiscible liquid phases’ is used. However, completely (8.31446261815324 J K mol ) immiscible liquids do not exist. That phrase just points to Red Reduced form of a redox pair those systems where the mutual miscibility is so small that s Indicates a solid phase (here a salt phase) the phases can be considered as pure phases, at least for a sol Indicates a solution phase simplified treatment. T Absolute temperature TBA? Tetrabutylammonium ion TEA? Tetraethylammonium ion ? Partition of neutral compounds TMA Tetramethylammonium ion between two immiscible solution phases TPA? Tetraphenylarsonium ion − TPB Tetraphenylborate ion The Nernst distribution law describes the partition of a w Water neutral compound A between two immiscible liquid phases z Charge of an ion, number of exchanged a and b electrons Aa Ab: ðEquilibrium IÞ Greek symbols An example is the distribution of iodine between water a Phase alpha (Greek letter alpha) and tetrachloromethane. Walter Nernst published the b Phase beta (Greek letter beta) respective equation in 1891 [1]. In modern terms, it states l Chemical potential (Greek letter mu in italics) that the ratio of activities [2] of the compound in the two l Electrochemical potential phases is constant at constant temperature (T) and pressure m Stoichiometric number (Greek letter nu in (p): italics) / Inner electric potential (Greek letter phi in KpðAÞ;T;p ¼ aA; b aA; a ð1Þ italics) KpðAÞ;T;p is called the partition constant of A, and the upright p in the subscript stands for partition. In 123 ChemTexts (2020) 6:17 Page 3 of 12 17 É l l Da bG equilibrium, the chemical potentials A; a and A; b of the aA; b ! i À 2:303RT : KpðAÞ;T;p ¼ ¼ 10 ð10Þ distributed compound A must be the same in both phases: aA; a l l : A; a ¼ A; b ð2Þ Remember, the chemical potential is the partial deriva- z )+ z )- tive of the Gibbs energy over the amount (unit: mol) of Partition of a salt Catð Cat Anð An mCat mAn substance (atoms, molecules or ions) (here of A), at con- between two immiscible solution phases stant temperature, pressure and constant amounts (unit: mol) of all other compounds (e.g. B, C, etc.): For a very simple reason, the partition of a salt between o immiscible solvents is more complex than that of neutral l g : A ¼ o ð3Þ compounds: the two constituents of a salt, i.e. cations and nA T;p;n ;n ;... B C anions, are on one side free in solution, but on the other This means that the chemical potential is a measure of side, their transfer to the other phase is restricted by the the ability to produce or consume work. Since a system condition of electroneutrality in both bulk phases. The does not produce or consume work when it is in equilib- electroneutrality is the boundary condition for the partition. rium, the chemical potentials of A in the phases a and b Only in the interfacial region (double layer region), where must be equal at equilibrium, as otherwise a flux of A from the two phases meet, is the condition of electroneutrality one phase to the other would occur. Since the chemical violated. This causes the occurrence of an interfacial lÀÀ potential difference called Galvani potential difference. A potential of A can be split into a standard term A (the salt CatðzCatÞþAnðzAnÞÀ partitions between two polar immis- chemical standard potential) and an activity-dependent mCat mAn term: cible solvent phases a and b according to ÀÀ z z l l m ðzCatÞþ m ðzAnÞÀ m ð CatÞþ m ð AnÞÀ: A ¼ A þ RT ln aA ð4Þ Cat;aCata þ An;aAna Cat;bCatb þ An;bAnb it follows from the condition (2) that ðEquilibrium IIÞ lÀÀ lÀÀ ; A; a þ RT ln aA; a ¼ A; b þ RT ln aA; b ð5Þ Since the stoichiometry of the salt is the same in both lÀÀ lÀÀ : m m m m m m A; a À A; b ¼ RT ln aA; b À RT ln aA; a ð6Þ phases, i.e. Cat;a ¼ Cat;b ¼ Cat and An;a ¼ An;b ¼ An, one can write The difference of chemical standard potentials is a m m a Cat a An constant: ÀÁCatðzCatÞþ;b AnðzAnÞÀ;b : K ðzCatÞþ ðzAnÞÀ ¼ m m ð11Þ p Catm Anm ; T;p Cat An a ; b a ; b Cat An a z a z lÀÀ lÀÀ A : A : Catð CatÞþ;a Anð AnÞÀ;a A; a À A; b ¼ RT ln ¼ 2 303RT log ð7Þ aA; a aA; a Equilibrium II indicates that the salt is assumed to be Since the partition constant has been defined as completely dissociated in both phases, i.e. no ion pairs þ À KpðAÞ;T;p ¼ aA; b aA; a (1), the following equation results exist in the two phases. Ion pairs, e.g.½ Cat An ionpair of a from (7) and (1): uni-univalent salt, form when the electrostatic attraction ÀÀ ÀÀ ÀÀ ÀÀ l Àl l Àl between the opposite charged ions is not overcome by the aA; b A; a A; b A; a A; b RT 2:303RT : KpðAÞ;T;p ¼ ¼ e ¼ 10 ð8Þ free energy of solvation of the single ions (see the example a ; a A of ½TBAþpicÀ at the end of this paper). This happens Equation (8) nicely shows that KpðAÞ;T;p is larger than 1 especially in solvents which have a low dielectric constant, ÀÀ ÀÀ ÀÀ ÀÀ i.e. which are rather nonpolar.
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