1. Diffusion-Reaction

2. Acid Base Reactions RCOOH RCOO - + H + k1k1 k -1

3. Naproxen

4. Naproxen Physical Properties Solubility of free acid [HA] o =1.37x10 -4 M Mw=230.36 [HA] o = 315.6 gm/L. =0.315 mg/ml pKa= 4.57 How long does it take a small particle ~ 0.1mm in radius to dissolve (in acid)?

6. Dissolution time (Large Particle)

7. What does ionization of the acid do? Let’s start with a film model CsCs h C=0 SS

8. At the interface the ionization increases the solubility and we have HA, A- and H+ diffusing species. CsCs h C=0 HA A-A- H+H+

9. Non Steady State Membrane Transport

10. Assumptions Stagnant fluid v i =0 Steady State dC/dt = 0 One dimensional

11. Transport Equation: One for each species

12. Acid Base Reaction Terms RCOOH RCOO - + H + k1k1 k -1

13. Add Equations HA tot H tot

14. Total HA + A -

15. Total H=H + + HA

16. Resulting Equations

17. Now add Boundary Conditions Solid Bulk: HA=0 A - = 0 H + =H + bulk Interface BC’s HA=HA 0 = solubility K A = H + A - /HA dH + /dx=dA - /dx=0 (can not penetrate boundary) 0 h x

18. Solve these equations: Key assumptions Equilibrium rate constants are fast relative to diffusion Equal diffusivities Equal film thickness

19. Resulting Equations

20. Conclusion Ionization at the interface accelerated dissolution…due to added species (A - ) The effect can be orders of magnitude. pH=pKa +2 ~ 10 2 increase in rate

21. Reversible Reaction: A B k1k1 k -1

22. Lovastatin: Lactone-Free Acid (A) (E) K=[E]/[A}

23. Reversible Reaction: (Not include ionization at this time) Aqueous phase k 1,a,k -1,a K a Membrane Phase; k1,m,k-1,m Km Equilibrium constant differs in two phases: K a >K m Partition Coefficients PC A PC E

24. Transport Equations: In each Phase

27. Let’s do one Phase (Olander reference) Material A diffuses into film m’ and can react to form E in film

28. Solution (Olander)