Question

Derive van’t Hoff general solution equation.

Answer 1

Hint : The van’t Hoff theory explains that substance in dilute solution obey the ideal gas law, which derive the osmotic pressure formula
$\pi =CRT$
Where C is molar concentration of solute
R is gas constant
T is absolute temperature

Complete step by step solution :
Suppose a dilute solution of a volume V containing W grams of a substance having molecular weight M at an absolute temperature T. then, concentration of the solution, $C=\cfrac { n }{ V }$ and no. of moles of the substance, $n=\cfrac { W }{ M }$
Van’t Hoff used gas laws on solution and derived a solution equation which is as follows:
Van’t Hoff Boyle's law: The osmotic pressure of a solution is directly proportional to its concentration (c) at a particular temperature.
$\ \pi \alpha C$

$\because Concentration=\cfrac { 1 }{ Dilution(V) } \\\ \therefore \ \pi \alpha \cfrac { 1 }{ V }$

Van’t Hoff Pressure-Temperature law: The osmotic pressure of solution is directly proportional to its absolute temperature at a particular concentration and dilution.
$\pi \alpha T$
On combination of above two laws
$\pi \alpha \cfrac { T }{ V } \\\ \pi =\cfrac { RT }{ V } \\\ \pi V=nRT$

This is the van’t Hoff general solution equation.

Note : Osmotic pressure is the tendency of solvent molecules to move in the direction of lower solvent activity and Osmosis refers to the movement of fluid across a membrane in response to different concentrations of solutes on the two sides of the membrane.The movement of fluid takes place from its region of high concentration to the region of its low concentration.