Question

How is osmotic pressure dependent upon the number of moles of a solute?

Answer 1

According to Boyle-van’t Hoff law

`pi prop 1/V` (at constant temperature)    ...(i)

and according to Charles’-van't Hoff law

π ∝ T (at constant concentration)    ...(ii)

Combining equation (i) and (ii), we have

`pi prop T/V`

or `pi = S T/V`

or πV = ST   ...(iii)

In this equation, S is a constant known as the solution constant. van’t Hoff showed that the value of solution constant (S) is equal to that of the gas constant, R, i.e.,

S = R

Hence, equation (iii) can be written as 

πV = RT   ...(iv)

This equation is similar to the gas equation (PV = RT) and is known as the van’t Hoff equation.

For n moles of the solute dissolved in V litres of the solution, van’t Hoff equation can be written as

πV = nRT    ...(v)

∴ `pi = n/V RT`

If temperature is kept constant,

`pi prop n/V`

Thus, osmotic pressure of a solution depends upon the number of moles of solute dissolved in a definite volume of solution.