Chapter-3- Ionic Interaction

1. Chapter-3- Ionic Interaction Dr/ El Hassane ANOUAR Chemistry Department, College of Sciences and Humanities, Prince Sattam bin Abdulaziz University, P.O. Box 83, Al-Kharij 11942, Saudi Arabia. (The slides are summarized from: Principles and applications of Electrochemistry (D. R. Crow) College Of Science and humanities, PSAU

2. 3.1 The nature of electrolytes • When electrolytes dissolved in a solvent: • The ions become free to move • The highly ordered lattice structure characteristic of crystals is almost entirely destroyed. • Crystal structures have high lattice energies Dissolution In solvent (e.g., water) College Of Science and humanities, PSAU

3. 3.1 The nature of electrolytes • Lattice energy (Elattice): The energy required to completely separate one mole of a solid ionic compound into gaseous ions. It is always endothermic. • Hess’ Law (Born-Haber cycles) is used to calculate lattice energy (Elattice) Lattice energy increases as Q increases ΔH = -Elattice= ΔHf− ΔHsub − ½ ΔHBE − IE − EA College Of Science and humanities, PSAU

4. 3.1 The nature of electrolytes • In a crystal: • Energies of a large number of component ion-pairs contribute to the total lattice energy which is effectively the energy evolved when the lattice is built up from free ions. • A large amount of energy is required to break down the ordered structure and liberate free ions. College Of Science and humanities, PSAU

5. 3.1 The nature of electrolytes • Explanation of easy dissolution of lattice structure => Occurrenceof another process (Exothermic reactions of individual ions with the solvent), which produces sufficient energy (Heat of solvation) to compensate for that lost in the rupture of the lattice bonds. College Of Science and humanities, PSAU

6. 3.1 The nature of electrolytes • From the First Law of Thermodynamics: • The algebraic sum of the lattice • and solvation energies is the heat of solution. Heat of solution = Elattice + Solvation energy • This explains both: • Why the heats of solution are usually fairly small • Why they may be endothermic or exothermic - depending upon whether the lattice energy or solvation energy is the greater quantity. College Of Science and humanities, PSAU

7. 3.1 The nature of electrolytes • Interionic and ion-solvent interactions are so numerous and important in solution that, no ion may be regarded as behaving independently of others. • In the most dilute cases, ion may be regarded as behaving independently of others/ • Certain dynamic properties such as ion conductances, mobilities and transportnumbers may be determined, although values for such properties are not absolute but vary with ion environment. College Of Science and humanities, PSAU

8. 3.2 Ion activity • In electrolytic solution, the properties of one ion species are affected by the presence of other ions with which they interact electrostatically. • Thus, the concentration of a species is an unsatisfactory parameter to use in attempting to predict its contribution to the bulk properties of a solution. • We use the activity (a): = mole fraction molar concentration molal concentration rational activity coefficient , are practical activity coefficients College Of Science and humanities, PSAU

9. 3.2 Ion activity Example The chemical potential of a species i may be expressed in the forms = • To determine properties of an electrolyte: • Mean ion activities (a±) and mean ion activity coefficients ( ) and Number of cations deriving from each 'molecule' of the electrolyte Number of anions deriving from each 'molecule' of the electrolyte Note: Both forms takes account of both types of ions characteristic of an electrolyte College Of Science and humanities, PSAU

10. 3.3 Ion-ion and ion-solvent interactions • In strong electrolytes, ions are not entirely free to move independently of one another through in solution. Ions will move randomly with respect to one another due to fairly violent thermal motion. Coulombic forces will exert their influence to some extent with the result that each cation and anion is surrounded on a time average by an 'ion atmosphere' containing a relatively higher proportion of ions carrying charge of an opposite sign to that on the central ion. College Of Science and humanities, PSAU

11. 3.3 Ion-ion and ion-solvent interactions • Application of an electric field: • Movement of ions will be very slow and subject to disruption by the thermal motion. • Movement of the atmosphere occurs in a direction opposite to that of the central ion => Breakdown symmetric ion atmosphere • As the ion moves in one direction through the solution => re-formation of the ion atmosphere College Of Science and humanities, PSAU

12. 3.3 Ion-ion and ion-solvent interactions • The time-lag between the restructuring of the atmosphere and the movement of the central ion causes the atmosphere to be asymmetrically distributed around the central ion causing some attraction of the latter in a direction opposite to that of its motion. This is known as the asymmetry, or relaxation effect. central ions experience increased viscoushindrance to their motion on account of solvated atmosphere ions which, on account of the latter's movement in the opposite direction to the central ion, produce movement of solvent in this opposing direction as well. This is known as the electrophoretic effect. College Of Science and humanities, PSAU

13. 3.3 Ion-ion and ion-solvent interactions • The central ions experience increased viscoushindrance to their motion on account of solvated atmosphere ions which, on account of the latter's movement in the opposite direction to the central ion, produce movement of solvent in this opposing direction as well. This is known as the electrophoretic effect. • These interactions increase in significance with increasing concentration of the electrolyte. College Of Science and humanities, PSAU

14. 2.4 The electrical potential in the vicinity of an ion • The electrical potential, , at some point is the work done in bringing a unit positive charge from infinity (where ) to that point. College Of Science and humanities, PSAU

15. 2.4 The electrical potential in the vicinity of an ion • The concentration of positive and negative ions (N+,N-) at the point P, where the potential is ψ may be found from the Boltzmann distribution law, thus. where k = Boltzmann constan Ni = Number of ions of either kind per unit volume in the bulk College Of Science and humanities, PSAU

16. 2.4 The electrical potential in the vicinity of an ion • The electrical density () at the point P where the potential is is the excess positive or negative electricity per unit volume at that point. Where Thus, College Of Science and humanities, PSAU

17. 2.4 The electrical potential in the vicinity of an ion Example 1: 1 electrolyte => and Thus, Assume that => and = 1+ = • For electrolytes, , College Of Science and humanities, PSAU

18. 2.4 The electrical potential in the vicinity of an ion • Poisson equation: Electrostatic potential and charge density relation • where D is the dielectric constant of the solvent medium • x, y, z are the coordinates of the point at which the potential is . • In terms of polar coordinates, Poisson equation becomes • Thus, College Of Science and humanities, PSAU

19. 2.4 The electrical potential in the vicinity of an ion where Thus, A general solution of Equation is in which A, A' are integration constants. Since as , (A' = 0) Therefore, by substitution of into expression, we obtain: College Of Science and humanities, PSAU

20. 2.4 The electrical potential in the vicinity of an ion • For electro-neutrality: • The total negative charge of the atmosphere about a given positively charged central ion = • The total charge of the atmosphere is determined by considering the charge carried by a spherical shell of thickness dr and distance r from the central ion and integrating from the closest distance that atmosphere and central ions may approach out to infinity. Spherical shell of thickness dr Integration by parts Hence, Central ion College Of Science and humanities, PSAU

21. 3.4 The electrical potential in the vicinity of an ion • When r approaches a, the distance of closest approach: • In general is composed of two contributions: Spherical shell of thickness dr The effective radius- that of the ion atmosphere Central ion College Of Science and humanities, PSAU

22. 3.5 Electrical potential and thermodynamic functions: The Debye-Hückel equation • For an ideal solution, the chemical potential of an ion i in is given by xi : Mole fraction of ion i • For non-ideal solutions Equation • By definition is the change in free energy of the system which would occur if 1 g-ion of species i were added to a large quantity of it • may be regarded as the contribution that the ion atmosphere makes to the total energy of the ion. College Of Science and humanities, PSAU

23. 3.5 Electrical potential and thermodynamic functions: The Debye-Hückel equation • The contribution per ion is and may be equated to the work which must be performed to give an ion of potential (due to its atmosphere) its charge ). • The work done, , in charging the ion by an increment of charge, , is so that the work,, required to give the ion its charge is Therefore, College Of Science and humanities, PSAU

24. 3.5 Electrical potential and thermodynamic functions: The Debye-Hückel equation • In terms of the mean ion activity coefficient for the electrolyte the becomes College Of Science and humanities, PSAU

25. 3.5 Electrical potential and thermodynamic functions: The Debye-Hückel equation Hence Debye-Hückel equation For water at 298 K, A = 511 and B = 3.29 × 107 College Of Science and humanities, PSAU

26. 2.6 Limiting and extended forms of the Debye-Hückel equation • For very dilute solutions, the so-called 'Limiting Law' holds, viz. • The equation • In practice, activity coefficients show a turning point at some value of , after which they progressively increase. • It is thus seen to be necessary to modify Equation by the addition of a further term which is an increasing function of , i.e Hückel equation College Of Science and humanities, PSAU

27. 2.7 Applications of the Debye-Hückel equation College Of Science and humanities, PSAU

28. College Of Science and humanities, PSAU

29. College Of Science and humanities, PSAU

30. College Of Science and humanities, PSAU