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