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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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acid base reactions
Acid Base Reactions

k1

RCOOH RCOO- + H+

k-1

naproxen physical properties
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)?
at the interface the ionization increases the solubility and we have ha a and h diffusing species
At the interface the ionization increases the solubility and we have HA, A- and H+ diffusing species.

A-

Cs

H+

C=0

HA

h

assumptions
Assumptions
  • Stagnant fluid vi=0
  • Steady State dC/dt = 0
  • One dimensional
acid base reaction terms
Acid Base Reaction Terms

k1

RCOOH RCOO- + H+

k-1

add equations
Add Equations

HAtot

Htot

now add boundary conditions
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

solve these equations key assumptions
Solve these equations: Key assumptions
  • Equilibrium rate constants are fast relative to diffusion
  • Equal diffusivities
  • Equal film thickness
conclusion
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

reversible reaction not include ionization at this time
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

let s do one phase olander reference
Let’s do one Phase (Olander reference)

Material A diffuses into film m’ and can react to form E in film

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