vapor and osmotic pressure

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A solution of the sugar mannitol ( molar mass 182.2 g/mol ) is prepared by adding 54.66 g of mannitol to 1.000 kg of water. The vapor pressure of pure liquid water is 17.54 torr at 20o C. Mannitol is nonvolatile and does not ionize in aqueous solution.

a.) Assuming that aqueous mannitol solutions behave ideally, calculate the vapor-pressure lowering for the above solution at 20o C.

b.) The observed vapor-pressure lowering of the mannitol solution above is 0.0930 torr. Calculate the activity coefficient ( based on mole fraction ) of water in this solution.

c.) Calculate the osmotic pressure of the mannitol solution of part ( b ) when it is measured against pure water, and compare it with the osmotic pressure of the ideal solution.

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