Osmotic Pressure Problems
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Direct answer
Osmotic pressure (pi) is the minimum pressure needed to stop the inward flow of solvent across a semipermeable membrane, and for dilute solutions it obeys the van't Hoff relation pi = CRT, with C in moles per litre, R = 0.083 L bar K^-1 mol^-1 and T in kelvin. Because pi counts solute particles, an electrolyte such as NaCl shows nearly double the calculated value, handled through the van't Hoff factor i, so the working equation becomes pi = iCRT. Molar mass follows from M = wRT/(pi × V), which is why osmometry is the standard method for proteins and polymers: tiny sample masses still give measurable pressures at room temperature. Applying a pressure larger than pi reverses the solvent flow — reverse osmosis.
What you must remember
- Master equation: pi = (n/V)RT; match R to the pressure unit — 0.083 L bar K^-1 mol^-1 for bar, 0.0821 L atm K^-1 mol^-1 for atm. Mixing the two is the single commonest numerical slip.
- Molar mass: M = wRT/(pi × V); isotonic solutions exert equal pi at the same temperature — 0.9% saline (about 0.15 M NaCl) is isotonic with blood plasma at roughly 300 milliosmoles per litre.
- van't Hoff factor: i = pi(observed)/pi(calculated); for K4[Fe(CN)6] the ideal i = 5 (four K+ plus one complex ion), so pi = 5CRT, while benzoic acid in benzene dimerises and i drops to about 0.5.
- Why osmometry for biomolecules: pi is measured at ordinary temperature, so thermolabile proteins need no boiling-point or freezing-point experiment; NCERT's classic worked example lands near 61,000 g/mol at 300 K.
- Direction of flow: solvent crosses from the dilute side to the concentrated side until the built-up pi annuls the chemical-potential difference; the membrane passes solvent and blocks solute.
- Reverse osmosis: external pressure greater than pi drives water out of brine; the membrane rejects dissolved salts — the working principle of desalination plants.
- Biology linkage: red cells swell and lyse in hypotonic media and crenate in hypertonic media — vocabulary JEE Main occasionally borrows for assertion-reason items.
A worked protein numerical
Take the NCERT-style classic: 200 mL of an aqueous protein solution contains 1.26 g of protein and shows pi = 2.57 × 10^-3 bar at 300 K. Convert the volume first: 200 mL = 0.200 L. Moles of protein = piV/RT = (2.57 × 10^-3 × 0.200)/(0.083 × 300) = 2.06 × 10^-5 mol. Molar mass = 1.26 g ÷ 2.06 × 10^-5 mol = about 61,000 g/mol, which is exactly how the NCERT example reports it. Notice the strategy: nothing was boiled or frozen, and a fraction of a gram gave a clean answer.
Now watch the electrolyte twist. If 0.1 M Na2SO4 dissociated ideally into 2 Na+ and 1 SO4^2-, i = 3 and pi = 3 × 0.1 × RT; measured i is slightly below 3 because of inter-ionic attraction. For a JEE integer-answer question, the ideal value is what you compute first, and the direction of the deviation is what you state second.
How the exam frames it
JEE Main keeps this to one clean numerical: find M, find i, or find the pressure needed for reverse osmosis — always given "at temperature T K", and the kelvin conversion is the trap they hope you miss. The second recurring trap is molarity versus molality: pi uses molarity because it is a pressure of a solution at a stated temperature, whereas elevation of boiling point uses molality; if a question warms the solution, pi changes but molality does not. JEE Advanced adds the two-compartment framing — solutions A and B separated by a membrane, asking which way water flows and what back-pressure stops it. The decision rule is one line: water flows toward the higher pi (higher effective particle concentration), and the stopping pressure equals pi(hypertonic) − pi(hypotonic).
Frequently asked questions
Why is osmotic pressure preferred for polymer molar masses?
Measurement happens at room temperature, needs no phase change, and even dilute macromolecular solutions develop a readable pressure, so tiny, heat-sensitive samples give reliable molar masses.
What is the ideal van't Hoff factor for K4[Fe(CN)6]?
Five — the salt gives four K+ ions and one [Fe(CN)6]^4- ion, so pi = 5CRT assuming complete dissociation.
Why does 0.1 M NaCl show nearly twice the osmotic pressure of 0.1 M glucose?
NaCl dissociates into Na+ and Cl-, roughly doubling the particle count (i near 2), while glucose remains molecular (i = 1).
What pressure makes reverse osmosis happen?
Any applied pressure greater than the solution's osmotic pi reverses solvent flow through the membrane; at exactly pi the net flow is zero.
Does osmotic pressure change on dilution?
Yes — pi = CRT falls in direct proportion to concentration at fixed temperature, unlike molality-based colligative properties of a weighed sample.