Chemistry / Unit 8 Chem 1576 worked example, 60 to 90 seconds
Calculating Osmotic Pressure
The idea
Calculating a solution's osmotic pressure means substituting its molarity and kelvin temperature into the same gas-constant relationship used for the ideal gas law, osmotic pressure equals molarity times the gas constant times temperature.
In practice
A 0.30 M glucose solution has molarity M = 0.30 mol/L at body temperature, T = 37 °C (310 K), with gas constant R = 0.08206 L·atm/(mol·K). Substituting these named values into Π = MRT gives Π = (0.30 mol/L)(0.08206 L·atm/(mol·K))(310 K); the liters and kelvin cancel between the molarity and gas-constant terms, leaving units of atmospheres, for an osmotic pressure of about 7.6 atm — comfortably positive and of the modest size expected for a dilute solution.
Where people slip
Using Celsius temperature directly in this calculation, rather than converting to kelvin first, produces an osmotic pressure with no physical meaning, the same unit error this unit has already flagged for the ideal gas law.
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