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Diffusion-Reaction

Diffusion-Reaction. Acid Base Reactions. k 1. RCOOH RCOO - + H +. k -1. Naproxen. 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

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Diffusion-Reaction

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  1. Diffusion-Reaction

  2. Acid Base Reactions k1 RCOOH RCOO- + H+ k-1

  3. Naproxen

  4. Naproxen Physical Properties • Solubility of free acid [HA]o=1.37x10-4M • 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)?

  5. Dissolution time (Large Particle)

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

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

  8. Non Steady State Membrane Transport

  9. Assumptions • Stagnant fluid vi=0 • Steady State dC/dt = 0 • One dimensional

  10. Transport Equation: One for each species

  11. Acid Base Reaction Terms k1 RCOOH RCOO- + H+ k-1

  12. Add Equations HAtot Htot

  13. Total HA + A-

  14. Total H=H+ + HA

  15. Resulting Equations

  16. Now add Boundary Conditions Interface BC’s HA=HA0= solubility KA = H+ A -/HA dH+ /dx=dA - /dx=0 (can not penetrate boundary) Solid Bulk: HA=0 A - = 0 H +=H + bulk x 0 h

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

  18. Resulting Equations

  19. Conclusion • Ionization at the interface accelerated dissolution…due to added species (A-) • The effect can be orders of magnitude. pH=pKa +2 ~ 102 increase in rate

  20. Reversible Reaction: k1 A B k-1

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

  22. Reversible Reaction: (Not include ionization at this time) Membrane Phase; k1,m ,k-1,m Km Aqueous phase k1,a ,k-1,a Ka Partition Coefficients PCA PCE Equilibrium constant differs in two phases: Ka>Km

  23. Transport Equations: In each Phase

  24. Transport Equations: In each Phase

  25. Transport Equations: In each Phase

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

  27. Solution (Olander)

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