A negatively charged membrane having a concentration of charge of 10 mol/L (ZX=1) is used to retain salt. The concentration in co-ions in the solution is 1 mol/L.
a) Calculate the partition coefficient for MgCl2, Na2SO4 and NaCl.
To calculate the concentration inside a membrane during Donnan exlusion, it is necessary to solve the equation :
$$\frac{c_B^{m}}{c_B}=(\frac{|z_B| c_B}{|z_B| c_B^{m}+|z_X| c_X^{m}})^{\frac{|z_B|}{|z_A|}}$$
cb=1. #concentration of co-ion in mol/L
zb=1. #valency of co-ion the membrane in mol/L
za=2. #valency of counter-ion in the membrane in mol/L
cxm=10. #concentration of charge in the membrane in mol/L
zx=1. #valency of charge in the membrane in mol/L
# Function that should be zero to satisfy the Donnan exclusion law
def f(cbm):
out=(cbm/cb)-((zb*cb/(zb*cbm+zx*cxm))**(zb/za))
return out
# Find cbm to satisfy Donnan exclusion
from scipy.optimize import newton
#For NaCl
zb=1.
za=1.
x=newton(f, x0=cb)
print ('For NaCl , the concentration in co-ion inside the membrane should be :', round(x,3), 'mol/L')
#For MgCl2
zb=1.
za=2.
x=newton(f, x0=cb)
print ('For MgCl2 , the concentration in co-ion inside the membrane should be :', round(x,3), 'mol/L')
#For Na2SO4
zb=2.
za=1.
x=newton(f, x0=cb)
print ('For Na2SO4, the concentration in co-ion inside the membrane should be :', round(x,3), 'mol/L')
For Nacl , the concentration in co-ion inside the membrane should be : 0.099 mol/L For Mgcl2 , the concentration in co-ion inside the membrane should be : 0.311 mol/L For Na2SO4, the concentration in co-ion inside the membrane should be : 0.039 mol/L
b) Sort these electrolytes from the more excluded to the less excluded by the membrane.
The exclusion is higher :
This sorting rule will be satisfied in NanoFiltration or Reverse Osmosis processes even if the operating conditions (permeate flux ...) are modifying the values.