# Relation between dilution and osmotic pressure

The following question is taken from IAT 2024, an entrance test for research institutes in India at the high school level:

Which one of the following plots correctly describes the variation of osmotic pressure $$(\Pi)$$ of a fixed amount of a solute against the volume $$(V)$$ of the solution at a fixed temperature?

Neither of the graphs make sense to me. I know that for ideal solutions the osmotic pressure is equal to the product of the concentration, temperature and gas constant, and hence it should be inversely proportional to the dilution.

But physically speaking won't the solute start to precipitate out above a certain concentration? Graph (a) seems to suggest that the pressure would increase without bound as volume decreases.

Graph (b) does consider this possibility, but it makes the volume equal to zero, which also seems wrong.

So what's the solution? Are either of these graphs correct?

Osmotic pressure is directly proportional to molar concentration. Molar concentration is inversely proportional to volume. Hence osmotic pressure is inversely proportional to volume.

Volume can never go to zero, hence (b) is wrong. Overall, (a) is correct.

• That's what I thought in the exam too...both seemed a bit dodgy to me..I know that simple mathematics would imply that (a) is correct, but just out of curiosity : above a certain concentration, wouldn't the solute start to precipitate out? 'Fixed' amount of solute doesn't really make sense in that case... Commented Jun 14 at 6:15
• (1) Those are out of scope of the Equation & the graph , @AadhaarMurty , It is assumed that the quantities make sense Mathematically & Physically , when we are working within the suitable range. (2) Considering that the Solute has finite volume , the Solution can not go less than that. More-over , nobody has made the graph beyond a certain volume , hence very large volume is itself unknown & infinite volume is unknowable. (3) Over-all , that graph is APPROXIMATING reality.
– Prem
Commented Jun 14 at 12:18