Charged Membrane

[podpod]

Hi!
I have troubles with the solution of this problem:
Consider a cation transfer membrane with a fixed concentration Cx of sulfonate (SO3-) groups. The membrane is in equilibrium with a solution of a 2-1 salt (CaCl2).
Calculate the Donnan potential between the cation transfer membrane and a 0.02 M CaCl2 solution. The charge density of the membrane is 2.5 meq per g dry membrane. The water sorption of the membrane in 0.01 M CaCl2 is 0.25 g per g dry membrane and the density of the wet membrane is 1.15 g/cm3.

I use (s) and (m) for concentration in solution and in membrane respectively. In order to find the Donnan potential I need C(m)Cl-.

Having C(s)Ca2+ = 0.02M and C(m)Cl- = 0.04M because of 0.02M of CaCl2, I thought to apply a two-equations system to find C(m) of the ions:
{ C(m)Ca * C(m)Cl^2 = C(s)Ca * C(s)Cl^2 ;
2*C(m)Ca = C(m)Cl + Cx }

to do this I need Cx referred to liter, but it is expressed in 2.5 meq/g of dry m. That's my problem: I don't know how I can use the other parameters to have Cx[mol/L].

​thank you very much!!

[studiot]

I note several research articles for analysis of the Donnan Equation with divalent ions, some using numerical methods to solve the equations.

 

Presumabably you need to go back to first principles to derive the relationships.