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Interactions in an electrolyte

Interactions in an electrolyte. Sähkökemian peruseet KE-31.4100 Tanja Kallio tanja.kallio@aalto.fi C213. CH 2.4-2.5. Solvent – ion interactions. Solvent – ion interactions. ion. neutral. W 1 = discharging an ion. 1. vacuum. 2. total. 3.

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Interactions in an electrolyte

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

  2. Solvent – ion interactions

  3. Solvent – ion interactions ion neutral W1 = discharging an ion 1 vacuum 2 total 3 W2 = cavityformation + surface tension W2 ~ negligible solvent W3 = charginga molecule

  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 r r (2.32) counterion 273 K

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

  8. Electrostatic potential falloff General solution for the previous equation in spherical coordinates is (f(r) = 0 whenr→ ) 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 distance of closest approach After calculus we obtain (2.36)

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

  10. Debye-Hückel limiting law (2/3) When diluting the solution from concentration c1to c2 (infinite dilute) work is done (2.40) activity coefficients origins from electrostatic interactions between ions Comparison of (2.39) and (2.40) gives us (2.41) g2 = 1 (infinite dilution)

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

  12. Ionpairs Equilibrium constants for ion assosiation/dissosiataion g± = 1 → Kd = a2c/(1 a) 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. Hammett acid function H0 for 0.1 M HCl-solutions. Abscissa: content of the organic component in mol-% Super acids and Hammett acid function very acidic acids  extension to the conventional pH scale is needed a weak indicator base B is added into the acid solution B + H+  BH+ measurable 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 for super basis BH + OH−(H2O)nB−+ (n + 1)H2O equilibrium constant for the indicator acid measurable M.A. Paul and F.A. Long, Chem. Rev. 57 (1957) 1-45

  14. Summary

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

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