Osmotic pressure calculator

How do you calculate osmotic pressure?

Π = MRT, where M is the molar concentration of dissolved particles, R = 0.08206 L·atm/(mol·K) and T the temperature in kelvins (OpenStax Chemistry 2e). For ionic solutes multiply by the van ’t Hoff factor i: Π = iMRT.

Example

A 0.30 M glucose solution at 37 °C (310 K): Π = 0.30 × 0.08206 × 310 = 7.6 atm.

What value of i should I use?

The number of particles each formula unit makes: 1 for glucose or sucrose, 2 for NaCl, 3 for MgCl₂ in theory. Measured values are a little lower — OpenStax lists 1.9 for 0.050 m NaCl and 2.7 for MgCl₂.

What units does the result use?

Atmospheres, with conversions to mm Hg (torr), kPa and psi. 1 atm = 760 mm Hg = 101.325 kPa.

Why does osmotic pressure matter?

It drives water across membranes from a dilute solution to a concentrated one. It is why IV fluids are matched to blood’s concentration.

What is reverse osmosis?

If you apply a pressure greater than the solution’s osmotic pressure to the solution side of a semipermeable membrane, solvent is forced out of the solution instead of in (OpenStax Chemistry 2e, section 11.4). The method is used to desalinate seawater and to make high-purity drinking water. The calculator’s result is the pressure that the applied pressure has to exceed.

Can osmotic pressure give the molar mass of a large molecule?

Yes; it suits large molecules such as proteins. Rearrange to M = Π ÷ (RT), multiply by the volume to get moles, and divide the mass by the moles. OpenStax Example 11.12: 10.0 g of hemoglobin in 0.500 L gives Π = 5.9 torr at 22 °C, so M = 3.2 × 10⁻⁴ mol/L, 1.6 × 10⁻⁴ mol, and a molar mass of 62,000 g/mol.

The formula and its terms

Osmosis is the transfer of solvent through a semipermeable membrane, which passes solvent but not certain solutes, from the purer side toward the more concentrated solution. The pressure that stops the net transfer is the osmotic pressure, Π (OpenStax Chemistry 2e, section 11.4). For a dilute solution, Π = MRT, with M the molarity, R = 0.08206 L·atm/(mol·K) and T in kelvin. Because osmotic pressure depends on the number of dissolved particles, an electrolyte needs the van ’t Hoff factor i, the particles in solution per formula unit dissolved: Π = iMRT. The calculator reports atm and converts to mm Hg, kPa, psi and bar.

Worked example

The glucose example above has i = 1. An ionic solute needs i. Physiological saline is 0.9% sodium chloride (m/v), which is 9 g/L, or 9 ÷ 58.44 = 0.154 M. Sodium chloride splits into two ions, so the ideal i is 2, and at body temperature (310.15 K) Π = 2 × 0.154 × 0.08206 × 310.15 = 7.8 atm. With the measured i = 1.9 that OpenStax lists for 0.050 m NaCl the result is 7.4 atm, so a real ionic solution lands a little below the ideal figure. For comparison, the 0.30 M glucose solution of OpenStax Example 11.10 gives 7.6 atm, in the same range. The molar-mass case is in the FAQ above.

Common mistakes

Leaving out i is the most frequent slip: for the saline above, i = 1 would give 3.9 atm, half the correct value. Second, entering Celsius as kelvin: 37 °C typed as 37 K gives 0.91 atm for the glucose example, about eight times too small, so set the temperature unit. Third, using molality or grams per liter where the formula wants molarity; the formula is for dilute solutions, so for concentrated ones the answer is only an estimate. Fourth, the units of the answer: 1 atm is 760 mm Hg, so 7.6 atm is about 5,800 mm Hg, while the hemoglobin pressure of 5.9 torr is only 0.0078 atm.

Sources: OpenStax Chemistry 2e, section 11.4 “Colligative Properties” (osmosis, Π = MRT, Table 11.3 of van ’t Hoff factors, reverse osmosis, Examples 11.10 and 11.12) and section 3.4 (0.9% m/v saline). Related: freezing point depression calculator, molality calculator, molarity calculator and percent to molarity calculator.