In an experiment, a 0.001 (mole fraction) solution of polysaccharide in water is made and is placed in the compartment A
In an experiment, a 0.001 (mole fraction) solution of polysaccharide in water is made and is placed in the compartment A (see Figure below). Compartment B is filled with pure water. The two compartments are separated by a porous semi-permeable membrane that allows the exchange of water molecules between the two compartments, but not that of the larger polysaccharide molecules
- a) Show that the chemical potential of water in compartment A is lower than that in compartment B by 2.48 J/mol.
- b) As a result of this chemical potential difference, water molecules will move from compartment B to compartment A. This causes the pressure in compartment A, relative to that in B, to increase. How would this affect the chemical potential of water in compartment B? When would the diffusion of water from B to A cease (i.e. equilibrium is achieved)?
- c) Using your answer to part (b), work out the difference between the pressure in compartment A and B when equilibrium is achieved.
You may assume that the chemical potential of molecules in a liquid at pressure P2 relative to that, for the same liquid, at pressure P1 is given by the formula: Vm (P2 - P1), where Vm is the molar volume of the liquid. For water take Vm =18 cm3/mol and assume the temperature of the apparatus is 298 K.
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