Is that pvc (poly vinyl chloride) is used as a coating for gas diffusion layer? If yes means which is the solvent that pvc is soluble?
At the steady state; The flux of gas molecules going through a thin membrane regardless its chemical composition may be defined by the following connection using Fick's first law:
J = - D [ Cin - C out]/ delta x for diatomic gas such as hydrogen or nitrogen one can used Sievert’s Law: C= s SQR(p) where p is the partial pressure , s is a proportionality constant, equal to the solubility of gas molecules in membrane at unit pressure. P= Ds is known as permeability. D is the diffusion coefficient of the gas molecule in the membrane, which is temperature dependent quantity.
J = - Ds [ SQRpin - SQRpout]/ delta x
Sievert Law can be easily derived for the dissociation reaction at the surface of the membrane in terms of chemical potential assoaciated with moleculer and atomis species; : H2 = 2 H ; 2 ChemPot H - ChemPot H2 = DELG EQL 0, Gibb free energy of reaction for the natural and equilibrium cases. One gets little mathematical manipulations:
pH =SQR( pH2) EXP[-DEL Go /2RT] WHERE s = EXP[-DEL Go /2RT] solubility
2 ChemPoto H - ChemPoto H2 = DELGo at the standard state (1 atm)
The amount of gas Q/t, which diffuses per area through a membrane with the thickness L after a definated time t, is described by the first Fick law:
Q/t = -D*delta c/L
D is the diffusion constant and delta c is the difference in concentration.
The difference in concentration delta c is given by the Henry law:
delta c =S.delta p.
delta p is the diffference in pressure and S is the solubility constant.
When you introduce the Henry law into the Fick law you get
Q/t = -D*S*delta p/L
D*S = P the constant of permeation
You can easily perform permeation measurements: you take a cup and put a solvent, like water, into it. Then you close the cup with your membrane.You watch the weight loss over the time.
Q= P*A(p1- p2)*t/L
A is the membrane area, p1 is the vapour pressure inside the cup, p2 is the vapour pressure outside the cup.
Dear Dr. Horacek, you haven't considered the reaction taking place at the interphase between film and its gaseous environment. This reaction takes place between the chemical species in the gas phase and the same species as an adsorb species at the surface of the bulk phase, which subsequently penetrates as a solute species in the bulk. Dissociation of multi-atomic molecules at the surface very important step, which are mostly very fast reactions and doesn’t influence the kinetics directly but energetically are important. The driving force for the diffusion of the solute in the bulk is the gradient of chemical potential (concentration in simple cases) of species in the bulk not in the gaseous phase! Therefore you have to relate the fugacity of the gas state and the chemical potential in the bulk. That means you have to know the solubility.
If your chemical species is monatomic in the gas phase then of course it doesn't involve dissociation reaction. Then your formula is OK. Regards.
Before you apply Henry's Law you have to know the molecular state of your chemical species in the gaseous phase. Don't forget only the atoms are able to move in the solid environment not the molecules.
It seems to me that you are misusing the Henry's law (See: Darken&Gurry, p.250). That law gives the linear connection between the activity of the solute and its atomic fraction in dilute solid solutions. It is nothing to with the partial pressure in the gaseous environment directly.
as = gamma Ns, where gamma, what you call solubility as also known as the activity coefficient of solute, which is temperature dependent (also it is concentration dependent out side of the Henry's law range).
Happy New Year Regards
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