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Diffusion-Reaction

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Diffusion-Reaction

k1

RCOOH RCOO- + H+

k-1

- 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)?

Cs

SS

C=0

h

A-

Cs

H+

C=0

HA

h

- Stagnant fluid vi=0
- Steady State dC/dt = 0
- One dimensional

k1

RCOOH RCOO- + H+

k-1

HAtot

Htot

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

- Equilibrium rate constants are fast relative to diffusion
- Equal diffusivities
- Equal film thickness

- 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

k1

A

B

k-1

(A)

K=[E]/[A}

(E)

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

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