Question

A system contains a 0.1 molar solution of NaCl and a 0.01 M solution of NaCl separated by an oherise impermeable membrane hat contains a special sodium-conducting pore called an ionophore. The 0.1M solution is inside the membane and the 0.01 Molar solution is outsie the membrane. This ionophore allows free diffusion of the Na+ ions, but not Cl- ions. T=300K, R= 8.31 J/K/mol, F= 96500 J/mol/volt...

a) what is the total chemical potential difference, that includes concentration dependent potential and electrical potential, in Joules/mol (outside minus inside) for the sodium ions?

b) considering that chemical potential can have both a concentration dependent component and an electrical component, what is the electrical potential, in volts, of the inside of the memebrane with respect to the outside?

c) what is the chemical potential difference in Joule/mol (inside minus outside) for the chloride ions.

Answer 1

a) The chemical potential difference would depend on osmotic pressures of the solution inside and outside the membrane . The osmotic pressures (pi ) can be calculated separately using equation pi = cST. The difference in osmotic pessures would represent chemical potential difference.

where c = concentration in moles /litre or, molarity of solution , S is solution constant = R ( ie .8.31 J/K/mol ) ,

T = temperature in Kelvin ( given as 300 K )

Hence , pi ( inside membrane ) = 0.1 x 8.31 x300 --------------- pi (outside membrane ) = 0.01 x 8.31 x 300

---------------------------------------------- = 249.3 ---------------------------------------------------------------- = 24.93 ----------------

chemical potential difference (outside - inside= 24.3 - 249.3 = -225 J / mol

b) Apply Nernst equation to calculate electrical potentials on both the sides of the membrane separately & find out the difference in potentials on both the sides to get electrical potential.

Thus Nernst equation -------- E = Eo  - 0,0591 / n log [ Mn+ ]

E (inside membrane ) = E^o  - 0.0591 / 1 log 0.1 , and E (outside membrane ) = E^o  - .0591 log 0.01

Electrical potential = E^o + 0.0591 - E^o   - 0.1182

-------------------------- = - 0.059 V

c) chemical potential difference for the chloride ions (inside - outside ) = 249.3 - 24.3 = 225 J / mol

  

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