1) van't Hoff presented data published by a scientist named Pfeffer on the behavior of osmotic pressure Π as a function of concentration c in aqueous sugar solutions.
Find an equation for Π as a function of c by fitting these data. Hint: if you know a theoretical relationship between osmotic pressure and concentration, try to fit these data to that relationship. Otherwise, try simple fits first (i.e., linear, semi-log, log-log).
c (%) Π (mm) 1 535 2 1016 2.74 1518 4 2082 6 3075
2) van't Hoff derived an analogue of Gay-Lussac's law for the dependence of the osmotic pressure on absolute temperature, namely Π/T = constant for a given concentration. He then went on to test this relationship using experimental data. In each of the following cases, he quoted the osmotic pressure Π_{1} (in mm Hg) of a solution at a temperature T_{1}, and computed the expected osmotic pressure Π_{2} at another temperature T_{2}. Compute Π_{2} for the following aqueous solutions.
a) cane-sugar: Π_{1} = 544 mm Hg at T_{1} = 32°C; what is Π_{2} at 14.15°C?
b) sodium tartrate: Π_{1} = 1564 mm Hg at T_{1} = 36.6°C; what is Π_{2} at 13.3°C?
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