1. Interactions in an electrolyte Sähkökemian peruseet KE-31.4100 Tanja Kallio tanja.kallio@aalto.fi C213 CH 2.4-2.5

2. Solvent – ion interactions

3. ion neutral 1 2 3 vacuum solvent W 2 = cavity formation + surface tension W 2 ~ negligible W 1 = discharging an ion W 3 = charging a molecule total

4. Experimental values for hydration energy

5. Ion – ion interactions

6. Debye length (1/2) Spatial distribution of ions around the central ion obeys Boltzmann distribution (2.32) r r counterion 273 K

7. Debye length (2/2) Charge density around the central ion is obtained by summarizing charge densities of all the ions first term of Taylor series electroneutrality (2.33) (2.34)  -1 = Debye length = thickness of the double layer Dependence of potential on charge density is given by Poisson equation r r

8. Electrostatic potential falloff (2.36) General solution for the previous equation in spherical coordinates is (  (r) = 0 when r →  ) Integration constant is determined taking into account that the total charge density around the central ion is equal but opposite that of the central ion After calculus we obtain distance of closest approach

9. Debye-Hückel limiting law (1/3) Electrostatic work done to move the central ion inside the ion cloud potential distribution around the central ion (2.36) potential field created by the central ion at distance a (2.37) Consequently (2.39)

10. Debye-Hückel limiting law (2/3) Comparison of (2.39) and (2.40) gives us  2 = 1 (infinite dilution) (2.41) activity coefficients origins from electrostatic interactions between ions (2.40) When diluting the solution from concentration c 1 to c 2 (infinite dilute) work is done

11. Debye-Hückel limiting law (3/3) ion strength Sifting to log system Utilizing definition of mean activity: (2.42) (2.43) experimental D-H law D-H limiting law

12. Ionpairs  ± = 1 → K d =  2 c/(1   ) Equilibrium constants for ion assosiation/dissosiataion Bjerrumin theory Ions around the central ion obey Maxwell-Bolzman distribution Potential profile immediately around the central ion obeys (2.37) Hypothesis: ions form ion pair when distance is smaller than q Fouss theory Ions must be in contact to form an ionpair Probability of forming an ion pair depends on number of ions, solvent volume, space occupied by the species and electrostatic energy on the surface of the ion

13. Super acids and Hammett acid function M.A. Paul and F.A. Long, Chem. Rev. 57 (1957) 1-45 Hammett acid function H 0 for 0.1 M HCl-solutions. Abscissa: content of the organic component in mol-% B + H +  BH + very acidic acids  extension to the conventional pH scale is needed a weak indicator base B is added into the acid solution equilibrium constant for the indicator acid measurable for super basis BH + OH − (H 2 O) n  B − + (n + 1)H 2 O unknown concentration depends on the pH of the super aid Hammet acid function is defined so that it becomes equal to pH in ideally diluted aqueous solutions

14. Summary

15. Interaction in electrolyte solutions solvent – ion interactions ion neutral 1 2 3 vacuum solvent ion – ion interactions Debye length Debye – Hückel law superacids