Osmotic Pressure Calculator

Find a solution's osmotic pressure.

How it is calculated

The van't Hoff equation gives osmotic pressure for a dilute solution: Π = i × M × R × T. i is the van't Hoff factor (roughly the number of particles one formula unit gives, such as 2 for NaCl, 1 for glucose; blank or invalid values are treated as 1), M is molarity in mol/L, R = 0.0820573 L·atm/(mol·K) and T is the absolute temperature, calculated as °C + 273.15. The result is in atmospheres and also converted to kilopascals (× 101.325). Molarity cannot be negative. The equation is ideal-solution behaviour, so it is least accurate at high concentrations or for strongly interacting ions, where the effective i is below the ideal value.

Worked example

Saline of 0.154 mol/L NaCl (i = 2) at body temperature 37 °C. Absolute temperature: 37 + 273.15 = 310.15 K. Π = 2 × 0.154 × 0.0820573 × 310.15 = 7.84 atm. In kilopascals: 7.84 × 101.325 = 794.25 kPa. This is why physiological saline is considered isotonic with blood.

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Common mistakes

  • Typing the temperature in kelvin when the field expects °C; the tool adds 273.15 itself.
  • Using molality or percent concentration instead of molarity (mol/L).
  • Forgetting the van't Hoff factor for salts, which makes the pressure half or a third of the real value.
  • Assuming the ideal i for concentrated solutions where ions pair up.
  • Mixing units by reading the answer in atmospheres when you need kPa, or vice versa.

About this calculator

This calculator finds a solution's osmotic pressure using the van't Hoff equation: Π = i·M·R·T, where i is the van't Hoff factor (number of particles a solute dissociates into), M is molarity, R is the gas constant, and T is absolute temperature. This is the pressure that must be applied to a solution to stop osmotic flow across a semipermeable membrane.

Chemistry and biology students, pharmacists, and lab scientists use it to predict how a solution will behave across a cell membrane or dialysis membrane, to formulate isotonic IV fluids and eye drops, and to solve colligative-properties problems. Enter the concentration, temperature, and van't Hoff factor to get the osmotic pressure.

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