Q.Derive van’t Hoff general solution equation.
🔒You're viewing a preview — the full solution, concept, methods & PYQ mapping are locked.
🔒 Start your 14-day free trial to unlock the full solution →Concept understanding — Osmotic Pressure
Osmotic Pressure: The Push of Pure Solvent
Imagine you have a U-shaped tube with a special membrane at the bottom that only lets water molecules pass through — not sugar molecules. On one side you put pure water, on the other side you put a sugar solution. What happens?
Water moves from the pure side into the solution side. The solution level rises. This is osmosis — the spontaneous net movement of solvent across a semipermeable membrane from a region of lower solute concentration to higher solute concentration.
But here's the key question: what if you don't want that level to rise? What if you want to keep the solution side exactly where it is?
You would have to push down on the solution side with extra pressure — just enough to stop the water from coming in. That extra pressure is osmotic pressure.
Osmotic pressure is not a pressure the solution "has" inside it. It is the external pressure you must apply to prevent osmosis. Think of it as the "resistance pressure" that exactly balances the tendency of solvent to dilute the solution.
The Precise Definition
Osmotic pressure (Π) is the minimum excess pressure that must be applied to a solution to prevent the inward flow of solvent across a semipermeable membrane.
The membrane must be permeable only to solvent molecules, not to solute particles. This is the defining condition — if the membrane leaks solute, you don't get true osmotic pressure.
The van't Hoff Equation
For dilute solutions, osmotic pressure follows a beautifully simple law:
Π=CRT
Where:
- Π = osmotic pressure (in atm or Pa)
- C = molar concentration of solute (mol/L or mol/m³)
- R = universal gas constant
- T = absolute temperature (K)
This is van't Hoff's law of osmotic pressure. It looks exactly like the ideal gas law (PV=nRT rearranged as P=(n/V)RT), and that's no coincidence — van't Hoff noticed that solute particles in dilute solution behave like gas molecules bouncing around, creating a "pressure" against the membrane.
This equation works only for non-electrolyte solutions at low concentrations. For electrolytes, you must include the van't Hoff factor i: Π=iCRT. A 0.1 M NaCl solution gives nearly twice the osmotic pressure of a 0.1 M glucose solution because NaCl dissociates into two ions.
Why It Matters for Macromolecules
Here's where osmotic pressure becomes a powerful tool. Suppose you have a protein — say, hemoglobin — and you want to know its molar mass. You can't easily measure its concentration in mol/L because you don't know the molar mass yet. But you can measure:
- The mass of protein dissolved (say, w grams in V liters)
- The osmotic pressure Π of that solution
Since C=n/V=(w/M)/V, where M is the molar mass:
Π=MVwRT
Rearrange:
M=ΠVwRT
| Property | Why osmotic pressure wins |
|----------|---------------------------|
| Boiling point elevation | Very small for macromolecules — hard to measure |
| Freezing point depression | Very small — same problem | …
Van't Hoff's general solution equation is derived by recognising that dilute solutions obey gas-law-like relations for osmotic pressure, combining the Boyle-, Gay-Lussac-, and Avogadro-law analogues. …
Osmotic pressure obeys a gas-law-like relation, πV=nRT, derived from its dependence on concentration, temperature, and Avogadro's law.
Van't Hoff observed that dilute solutions behave analogously to ideal gases with respect to osmotic pressure (π), obeying three laws:
- Boyle–van't Hoff law: at constant temperature, osmotic pressure is inversely proportional to volume, π∝V1 (i.e. πV= constant).
- Gay-Lussac–van't Hoff (Charles') law: at constant volume, osmotic pressure is directly proportional to absolute temperature, π∝T.
Combining these two: πV∝T, or πV=kT for a fixed amount of solute.
…
Showing the 12 most recent of 36 on this concept.
- CBSE 2026Set DZ1 markMCQQ.Which formula is used to calculate osmotic pressure?(a) π=CRT(b) π=VRT(c) π=PVT(d) π=nRT
›Reveal solutionSolution
Osmotic pressure is a colligative property given by π=CRT, so option (a) is correct.
Osmotic pressure (π) is the extra pressure that must be applied on the solution side of a semipermeable membrane to just stop the net flow of solvent into the solution. For a dilute solution it depends only on the number of solute particles per unit volume, i.e. the molar concentration C=n/V.
The van't Hoff equation for osmotic pressure is:
π=CRT=VnRT …
- CBSE 2026Set ANNUAL1 markMCQQ.Isotonic solutions have the same:(a) Normality(b) Molarity(c) Osmotic pressure(d) Formality
›Reveal solutionSolution
Isotonic solutions have equal osmotic pressure, which is why cells neither swell nor shrink when placed in an isotonic medium.
Osmotic pressure (π) of a solution is given by π = CRT, where C is the molar concentration of solute particles. Two solutions are said to be isotonic with respect to each other when they exhibit the SAME osmotic pressure at the same temperature. When such solutions are separated by a semipermeable membrane, there is no net flow of solvent from one to the other — this is why isotonic saline (0.9% NaCl) is used for intravenous drips, since it matches the osmotic pressure of blood plasma and doesn't cause red blood cells to swell (hypotonic) or shrink (hypertonic).
…
- CBSE 2026Set ANNUAL1 markMCQQ.A plant cell shrinks when it is kept in a(a) Hypotonic solution(b) Hypertonic solution(c) Isotonic solution(d) Pure water
›Reveal solutionSolution
A plant cell placed in a hypertonic solution loses water to its surroundings by osmosis and shrinks; this is called plasmolysis.
A solution is hypertonic relative to the cell sap if it has a higher solute concentration (higher osmotic pressure) than the cell's interior. Water always moves from a region of lower solute concentration (higher water potential) to higher solute concentration (lower water potential) across the semi-permeable cell membrane.
…
- CBSE 2026Set ANNUAL1 markMCQQ.Sea water is converted into fresh water based upon the phenomenon of:(a) Diffusion(b) Osmosis(c) Plasmolysis(d) Reverse Osmosis
›Reveal solutionSolution
Desalination of sea water to get fresh water uses reverse osmosis.
In normal osmosis, solvent flows from a dilute solution to a concentrated solution through a semipermeable membrane. If a pressure greater than the osmotic pressure of the sea water is applied on the sea-water side, the flow of solvent is reversed — pure water is forced from the concentrated (saline) side through the membrane to the dilute side, leav …
- CBSE 2026Set ANNUAL1 markMCQQ.The pressure of solution that just prevents the flow of solvent is called:(a) Vapour Pressure(b) Osmotic Pressure(c) Partial Pressure(d) Gas pressure
›Reveal solutionSolution
The pressure that just stops solvent flow (osmosis) is the osmotic pressure.
When a solution is separated from pure solvent by a semipermeable membrane, solvent flows into the solution (osmosis). The excess pressure that must be applied on the solution side to just prevent this net inflow of solvent is …
- CBSE 2025Set D1 markMCQQ.Isotonic solutions have equal(a) osmotic pressure(b) vapour pressure(c) relative lowering of vapour pressure(d) elevation of boiling point
›Reveal solutionSolution
Isotonic solutions have equal osmotic pressure.
By definition, two solutions are isotonic if they exert the same osmotic pressure at the same temperature. Because osmotic pressure pi = C R T, isotonic solutions must have the same molar concentration of particles.
…
- CBSE 2025Set ANNUAL1 markMCQQ.The porous membrane used in reverse osmosis plant is made up by:(a) Cellulose acetone(b) Potassium nitrate(c) Mercuric iodide(d) Starch
›Reveal solutionSolution
The semi-permeable membrane used in reverse osmosis water purification plants is made of cellulose acetate.
In reverse osmosis, a pressure greater than the osmotic pressure of the solution (e.g. seawater) is applied on the solution side, forcing pure solvent (water) to flow through a semi-permeable membrane from the concentrated to the dilute side — the reverse of normal osmosis. The membrane commonly used for this purpose in desalination/purification plants is made of cellulose acetate — a synthetic semi-permeable …
- CBSE 2025Set ANNUAL1 markMCQQ.Which of the following colligative properties is used to determine molar masses of proteins, polymers or other macromolecules?(a) Depression in freezing point(b) Relative lowering of vapour pressure(c) Osmotic pressure(d) Elevation in boiling point
›Reveal solutionSolution
Colligative properties are inversely proportional to molar mass, so for very large molecules (proteins, polymers) most of them become too small to measure precisely — except osmotic pressure, which stays measurable even in very dilute solutions.
Why the other options fail
- (a) Depression in freezing point ΔTf=Kfm and (d) Elevation in boiling point ΔTb=Kbm: for a macromolecule of large M, the molality m=M×w1w2×1000 is tiny, so ΔTf/ΔTb become too small (often a few thousandths of a kelvin) to measure accurately with an ordinary thermometer.
- (b) Relative lowering of vapour pressure p1∘p1∘−p1=x2 also becomes vanishingly small and is experimentally hard to measure with the needed precision for dilute macromolecular solutions. …
- CBSE 2025Set ANNUAL1 markQ.What are hypertonic solutions?
›Reveal solutionSolution
A hypertonic solution has a greater osmotic pressure (higher effective solute concentration) than a reference solution, so it draws water out of a cell placed in it.
Definition
When two solutions are compared, the one with the higher osmotic pressure (i.e. higher concentration of osmotically active solute particles) is called the hypertonic solution relative to the other (which is then called hypotonic).
…
- CBSE 2024Set D1 markMCQQ.Isotonic solutions have the same(a) Density(b) Normality(c) Strength(d) Molar concentration
›Reveal solutionSolution
Isotonic solutions have the same osmotic pressure. Since osmotic pressure pi = CRT, equal pi at the same temperature means equal molar concentration C.
Osmotic pressure of a dilute solution: pi = CRT, where C is molar concentration, R the gas constant and T the temperature.
…
- CBSE 2024Set D1 markMCQQ.The osmotic pressure of a solution is represented by which of the following equations?(a) pi = CR/T(b) pi/C = RT(c) pi = CT/R(d) pi = RT/C
›Reveal solutionSolution
Osmotic pressure: pi = CRT, i.e. pi/C = RT.
For a dilute solution the osmotic pressure (pi) is given by the van't Hoff equation:
pi = CRT
…
- CBSE 2024Set ANNUAL1 markQ.The two solutions with equal osmotic pressure are called ______.
›Reveal solutionSolution
Two solutions having equal osmotic pressure at a given temperature are called isotonic solutions.
Osmotic pressure (pi) is the colligative property that measures the pressure needed to stop the net flow of solvent across a semipermeable membrane. If two solutions have exactly the same osmotic pressure at the same temperature, no net osmosis occurs when they are separated by a semipermeable membrane and placed in contact - such solutions are called isotonic solutions.
…
🎓Unlock everything free for 14 days
- ✓Full step-by-step solutions
- ✓Concept-first explanations
- ✓Methods, shortcuts & mistakes
- ✓PYQ mapping + timed mock tests
Full access for 14 days. No credit card required.