van't Hoff osmotic pressure

Jacobus van't Hoff analyzed the phenomenon of osmotic pressure both empirically and theoretically, establishing an analogy between solutions and gases.

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.

c (%) Π (mm)
1 535
2 1016
2.74 1518
4 2082
6 3075

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).

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 Π₁ (in mm Hg) of a solution at a temperature T₁, and computed the expected osmotic pressure Π₂ at another temperature T₂. Compute Π₂ for the following aqueous solutions.
a) cane-sugar: Π₁ = 544 mm Hg at T₁ = 32°C; what is Π₂ at 14.15°C?
b) sodium tartrate: Π₁ = 1564 mm Hg at T₁ = 36.6°C; what is Π₂ at 13.3°C?

Reference

J. H. van't Hoff, "The Role of Osmotic Pressure in the Analogy Between Solutions and Gases," Zeitschrift für physikalische Chemie 1, 481-508 (1887)

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