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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)?



What does ionization of the acid do let s start with a film model
What does ionization of the acid do?Let’s start with a film model

Cs

SS

C=0

h


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


Non steady state membrane transport
Non Steady State Membrane Transport we have HA, A- and H+ diffusing species.


Assumptions
Assumptions we have HA, A- and H+ diffusing species.

  • Stagnant fluid vi=0

  • Steady State dC/dt = 0

  • One dimensional


Transport equation one for each species
Transport Equation: One for each species we have HA, A- and H+ diffusing species.


Acid base reaction terms
Acid Base Reaction Terms we have HA, A- and H+ diffusing species.

k1

RCOOH RCOO- + H+

k-1


Add equations
Add Equations we have HA, A- and H+ diffusing species.

HAtot

Htot


Total ha a
Total HA + A we have HA, A- and H+ diffusing species.-


Total h h ha
Total H=H we have HA, A- and H+ diffusing species.+ + HA


Resulting equations
Resulting Equations we have HA, A- and H+ diffusing species.


Now add boundary conditions
Now add Boundary Conditions we have HA, A- and H+ diffusing species.

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 we have HA, A- and H+ diffusing species.

  • Equilibrium rate constants are fast relative to diffusion

  • Equal diffusivities

  • Equal film thickness


Resulting equations1
Resulting Equations we have HA, A- and H+ diffusing species.


Conclusion
Conclusion we have HA, A- and H+ diffusing species.

  • 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
Reversible Reaction: we have HA, A- and H+ diffusing species.

k1

A

B

k-1


Lovastatin lactone free acid
Lovastatin: Lactone-Free Acid we have HA, A- and H+ diffusing species.

(A)

K=[E]/[A}

(E)


Reversible reaction not include ionization at this time
Reversible Reaction: (Not include ionization at this time) we have HA, A- and H+ diffusing species.

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


Transport equations in each phase
Transport Equations: In each Phase we have HA, A- and H+ diffusing species.


Transport equations in each phase1
Transport Equations: In each Phase we have HA, A- and H+ diffusing species.


Transport equations in each phase2
Transport Equations: In each Phase we have HA, A- and H+ diffusing species.


Let s do one phase olander reference
Let’s do one Phase (Olander reference) we have HA, A- and H+ diffusing species.

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


Solution olander
Solution (Olander) we have HA, A- and H+ diffusing species.


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