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)
Copyright 2003 by Carmen Giunta. Permission is granted to reproduce for non-commercial educational purposes.