Osmotic Pressure
Osmotic pressure is a colligative property — a property that depends on the number of solute particles dissolved in a solution, not on the chemical identity of those particles. When two solutions of different concentrations are separated by a semipermeable membrane (one that allows solvent molecules to pass but blocks most solute particles), solvent molecules spontaneously move from the region of lower solute concentration (higher solvent concentration) to the region of higher solute concentration (lower solvent concentration). This net movement of solvent is called osmosis. The osmotic pressure (π) of a solution is the minimum external pressure that must be applied to the more concentrated solution to prevent the net flow of solvent across the membrane. It is a measurable, quantitative property directly linked to the molar concentration of dissolved particles. Because osmotic pressure can be very large even in dilute solutions, it is one of the most sensitive colligative properties and has enormous practical importance in biology, medicine, and food preservation. Understanding osmotic pressure helps explain why red blood cells swell or shrink in different saline concentrations, why plants wilt without water, how kidneys filter blood, and how reverse osmosis systems purify drinking water. The three key solution classifications — isotonic, hypertonic, and hypotonic — describe the relationship between a solution's osmotic pressure and a reference solution (typically the fluid inside a living cell).
- The Semipermeable Membrane
- Why Solvent Moves: Thermodynamic Driving Force
- Defining Osmotic Pressure
- The van't Hoff Factor (i)
- Isotonic, Hypertonic, and Hypotonic Solutions
- Reverse Osmosis
The Semipermeable Membrane
A semipermeable membrane has pores small enough to allow water molecules (or other small solvent molecules) to pass freely, but large enough to block larger solute molecules or ions. Biological cell membranes are semipermeable due to their phospholipid bilayer structure with selective protein channels. Dialysis tubing and cellophane used in laboratory demonstrations are synthetic examples.
Why Solvent Moves: Thermodynamic Driving Force
Water moves from the side with lower solute concentration to the side with higher solute concentration because dissolving solute particles lowers the chemical potential (a measure of free energy per mole) of the solvent. Water spontaneously flows toward lower chemical potential, i.e., toward the solution with more dissolved particles. This continues until equilibrium is reached or an opposing pressure stops the flow.
Defining Osmotic Pressure
Osmotic pressure (π) is the hydrostatic pressure that builds up on the more concentrated side as solvent flows in, measured in atmospheres (atm) or pascals (Pa). Alternatively, it is the external pressure you must apply to the concentrated solution to completely halt osmosis. For a dilute solution at temperature T with molar concentration c of dissolved particles: π = cRT, known as the van't Hoff equation for osmotic pressure.
The van't Hoff Factor (i)
For electrolytes (compounds that dissociate into ions), the total concentration of particles is greater than the formula-unit concentration. The van't Hoff factor i accounts for this: π = icRT. For example, NaCl dissociates into Na⁺ and Cl⁻, so i ≈ 2. For glucose (a non-electrolyte), i = 1. For \ce{CaCl2}, i ≈ 3 (one \ce{Ca^{2+}} and two \ce{Cl^-} ions). In reality, inter-ionic attractions in concentrated solutions make i slightly less than the theoretical integer value.
Isotonic, Hypertonic, and Hypotonic Solutions
When comparing a solution to a reference (such as blood plasma at ~0.9% NaCl by mass, π ≈ 7.7 atm at 37 °C): An ISOTONIC solution has the same osmotic pressure as the reference — no net osmosis occurs, and cells maintain normal volume. A HYPERTONIC solution has higher osmotic pressure than the reference — water flows OUT of cells, causing them to shrink (crenation in animal cells, plasmolysis in plant cells). A HYPOTONIC solution has lower osmotic pressure — water flows INTO cells, causing them to swell and potentially burst (lysis in animal cells, turgor pressure buildup in plant cells).
Reverse Osmosis
If an external pressure greater than the osmotic pressure is applied to the concentrated solution side, solvent is forced to flow in the reverse direction — from the concentrated side to the dilute side. This is reverse osmosis (RO), used in water desalination plants and home water purifiers. Seawater has π ≈ 27 atm, so RO membranes must withstand pressures exceeding this value to produce fresh water.
The Key Equation
- \pi — Osmotic pressure (atm (or Pa)): The pressure required to stop net solvent flow across a semipermeable membrane; 1 atm = 101,325 Pa
- i — Van't Hoff factor (dimensionless): The number of particles one formula unit produces in solution; i = 1 for non-electrolytes, i ≈ 2 for NaCl, i ≈ 3 for CaCl₂
- c — Molar concentration (molarity) (mol L⁻¹ (M)): Moles of solute dissolved per litre of solution; must be the total formula-unit concentration before accounting for dissociation
- R — Ideal gas constant (L·atm mol⁻¹ K⁻¹): R = 0.08206 L·atm mol⁻¹ K⁻¹ when pressure is in atm; use R = 8.314 J mol⁻¹ K⁻¹ when pressure is in Pa
- T — Absolute temperature (K (Kelvin)): Temperature in Kelvin; T(K) = T(°C) + 273.15. Always convert Celsius to Kelvin before calculating.
Worked Example
Problem. A glucose (\ce{C6H12O6}, molar mass = 180.16 g mol⁻¹) solution is prepared by dissolving 18.0 g of glucose in enough water to make 500.0 mL of solution. Calculate the osmotic pressure of this solution at 25 °C. Is this solution isotonic, hypertonic, or hypotonic relative to blood plasma (π_blood ≈ 7.7 atm at 37 °C, but compare at 25 °C where π_blood ≈ 7.4 atm)?
Answer. The osmotic pressure is approximately 4.89 atm. The solution is hypotonic relative to blood plasma.
Origins · 1 minJacobus Henricus van 't Hoff and how this was discovered
Van 't Hoff derived the equation π = cRT for osmotic pressure in 1885, drawing an elegant analogy with the ideal gas law (PV = nRT). He recognized that dissolved particles exert pressure on a semipermeable membrane in a manner mathematically equivalent to the pressure exerted by gas molecules on the walls of a container. This insight unified the behaviour of dilute solutions and ideal gases under one theoretical framework and laid the quantitative foundation for the study of colligative properties. For this work and his contributions to chemical kinetics and stereochemistry (including the tetrahedral carbon atom model), he was awarded the very first Nobel Prize in Chemistry in 1901. Van 't Hoff published his revolutionary paper on the three-dimensional arrangement of atoms in carbon compounds when he was just 22 years old — before he even completed his PhD. His ideas were initially ridiculed by some senior chemists, but were soon experimentally confirmed and became the cornerstone of modern organic stereochemistry.
Related Concepts
- Boiling Point Elevation — Like osmotic pressure, boiling point elevation is a colligative property that depends on the concentration of solute particles. Both are described by equations involving the van't Hoff factor and molar concentration.
- Freezing Point Depression — Freezing point depression is another colligative property. Understanding how solute particles lower the chemical potential of a solvent directly connects to how they also generate osmotic pressure across membranes.
- Molarity and Solution Concentration — The van't Hoff equation π = icRT requires molar concentration (c) in mol L⁻¹. Mastery of molarity calculations is essential for solving osmotic pressure problems accurately.
- Vapour Pressure Lowering and Raoult's Law — Raoult's Law describes how solute particles lower the vapour pressure of a solvent, which is the thermodynamic origin of all colligative properties including osmotic pressure. Both phenomena stem from the reduction in solvent chemical potential.
- Electrolytes and Ionic Dissociation — The van't Hoff factor i depends on how many ions an electrolyte produces. Understanding strong vs. weak electrolyte dissociation is critical for correctly predicting the osmotic pressure of salt solutions like NaCl or CaCl₂.