diffusion-reaction. acid base reactions rcooh rcoo - + h + k1k1 k -1
Post on 22-Dec-2015
216 views
TRANSCRIPT
Diffusion-Reaction
Acid Base Reactions
RCOOH RCOO- + H+
k1
k-1
1 1/ [ ) [ ][ ]dC dt k RCOOH k RCOO H
Naproxen
H3CO
COOH
CH3
Naproxen
Log P: 2.97CLogP: 2.816
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)?
Dissolution time (Large Particle)
hr
DChrt sodiss
3.6
sec22857
)315)(.000005/(.)003.0)(01.0)(1200(
)/(
What does ionization of the acid do?
Let’s start with a film model
Cs
h
C=0
SS
At the interface the ionization increases the solubility and we have HA, A- and H+ diffusing species.
Cs
h
C=0
HA
A-
H+
Non Steady State Membrane Transport
2 2 2 2 2 2
2 2
/ [ / / / ]
( / / / ) [ ]
Non Steady, stagnant
C/ t=D / [ ]
x y zC t v C x v C y v C z
D C x C y C z r
C x r
Assumptions
• Stagnant fluid vi=0
• Steady State dC/dt = 0
• One dimensional
Transport Equation: One for each species
HH
AA
HAHA
rdxHdD
rdxAdD
rdxHAdD
22
22
22
/0
/0
/0
Acid Base Reaction Terms
RCOOH RCOO- + H+
k1
k-1
1 1
1 1
1 1
[ ) [ ][ ]
[ ) [ ][ ]
[ ) [ ][ ]
HA
A
H
HA A H
r k RCOOH k RCOO H
r k RCOOH k RCOO H
r k RCOOH k RCOO H
r r r
Add Equations
HH
AA
HAHA
rdxHdD
rdxAdD
rdxHAdD
22
22
22
/0
/0
/0HAtot
Htot
Total HA + A-
A
tot
tot
AHA
AAHAHA
D
AHAHA
dxHADd
dxAdDdxHAdD
rdxAdDrdxHAdD
HA
22
2222
2222
D Assume
][
0/][
]//[
]/[/
Total H=H+ + HA
H
tot
tot
HHA
HHHHA
D
HHAH
dxHDd
dxHdDdxHAdD
rdxHdDrdxHAdD
HA
22
2222
2222
D Assume
][
/][
]//[
]/[/
Resulting Equations
dcxH
baxHA
HAAHK
dxHDd
dxHADd
tot
tot
A
tot
tot
][
][
Solution
]/[][
0/][
0/][22
22
Now add Boundary Conditions
Solid
Bulk:
HA=0
A - = 0
H +=H + bulk
Interface BC’s
HA=HA0= solubility
KA = H+ A -/HA
dH+ /dx=dA - /dx=0 (can not penetrate boundary)
0 hx
Solve these equations: Key assumptions
• Equilibrium rate constants are fast relative to diffusion
• Equal diffusivities
• Equal film thickness
Resulting Equations
dcxH
baxHA
tot
tot
][
][
Condition mEquilibriu and sBC' with Solve
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:
A B
k1
k-1
Lovastatin: Lactone-Free Acid
H3C
CH3
O
O
HO
H
CH3
H H
H3C
O
O
H3C
CH3
O
OH
HO
H
CH3
H H
H3C
O
O
OH
H2O
(A)
(E)
K=[E]/[A}
Reversible Reaction: (Not include ionization at this time)
Aqueous phase
k1,a
,k-1,a
Ka
Membrane Phase;k1,m,k-1,mKm
Equilibrium constant differs in two phases: Ka>Km
Partition Coefficients
PCA
PCE
Transport Equations: In each Phase
AEK
axaEDAD
dxEdDdxAdD
rr
EA
EA
EA
/
][][
0//
ma, Phase;Each In
21
2222
Transport Equations: In each Phase
AEK
axaEDAD
dxEdDdxAdD
rr
EA
EA
EA
/
][][
0//
ma, Phase;Each In
21
2222
Transport Equations: In each Phase
AEK
axaEDAD
dxEdDdxAdD
rr
EA
EA
EA
/
][][
0//
ma, Phase;Each In
21
2222
Let’s do one Phase (Olander reference)
1
A
film E)in the(A
componentA totalofflux J SS),(at Film intoA ofFlux
,
,0
:'
adE/dxDdA/dx-DJ
AAxx
AAx
sBC
EA
LL
l
Material A diffuses into film m’ and can react to form E in film
Solution (Olander)
membrane theintoflux the
increases membrane in theReaction
t.CoeffieienTransfer Mass
})/(1{
)]()/(1)[/(0
A
AEAA
LlAELA
k
KDDkk
AAKDDxDJ