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 an molecule total

4. Experimental values for hydration energy

5. Ion – ion interactions

6. Debye lenght Spatial distribution of ions around the central ion obeys Boltzmann distribution Charge density around the central ion is obtained by summarizing charge densities of all the ions first term of Taylor series electroneutrality (2.32) (2.33) (2.34) Debye length = thickness of the double layer Dependence of potential on charge density is given by Poisson equation

7. Falloff in the electrostatic potential (2.36)

8. Debye-Hückel limiting law (1/2) Electrostatic work done to move the central ion inside the ion cloud potential distribution around the central ion (2.36) potential field crated by the central ion at distance a (2.37) (2.37) When diluting the solution from concentration c 1 to c 2 (infinite dilute) work is done activity coefficients origins from electrostatic interactions between ions (2.39) (2.40) By combining (2.39) and (2.40)  2 = 1 (infinite dilution) (2.41)

9. Debye-Hückel limiting law (2/2) ion strength Sifting to log system Utilizing definition of mean activity: (2.42) (2.43) experimental D-H law D-H limiting law

10. 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 the species and electrostatic energy on the surface of the ion

11. 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

12. Summary

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