# Osmotic Pressure Problems > Osmotic pressure problems in JEE Chemistry: pi = CRT, molar mass of proteins, van't Hoff factor, reverse osmosis and fully worked numericals. - Canonical URL: https://prepelephant.com/topics/jee/chemistry/osmotic-pressure-problems - Exam / course: JEE · Subject: Chemistry - Publisher: PrepElephant (https://prepelephant.com) — Prepared and reviewed by the PrepElephant Academic Review Team - First published: 2026-10-02 - Last updated: 2026-10-02 - How to cite: "Osmotic Pressure Problems", PrepElephant, https://prepelephant.com/topics/jee/chemistry/osmotic-pressure-problems ## 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.