Periodic Table of Elements

Osmotic Pressure

Osmotic pressure is the pressure applied by a solution to prevent the inward flow of water across a semipermeable membrane.

The osmotic pressure is expressed by the formula:
Π = iMRT
where:
Π is the osmotic pressure in atm
i = van 't Hoff factor of the solute.
M = molar concentration in mol/L
R = universal gas constant = 0.082057 L atm mol-1 K-1
T is the temperature of the gas (measured in Kelvin).

The universal, gas constant (R) is a numerical value made up of the combination of atandard pressure (1 atmosphere or 760 torr), stanard temperature (273 K), and the fact that 1 mole of a gas occupies a volume of 22.4 liters at STP.

Values of R
0.082057 L atm mol-1 K-1
62.364 L Torr mol-1 K-1
8.3145 m3 Pa mol-1 K-1
8.3145 J mol-1 K-1

Example 1:
10 grams of glucose is dissolved in 200 ml of water. What is the osmotic pressure at 30 °C?
i = van 't Hoff factor for glucose i = 1
molar mass of glucose (C6H12O6) = 6(12) + 12(1) + 6(16) = 180 g/mol
n = Moles for glucose = 10 g x 1 mol/180 g = 0.0555 mol
M = molar concentration in mol/L = mol/Volume = 0.0555/(200 ml x 1 L/1000 ml) = 0.0555/0.2L = 0.2775 mol/L
R = universal gas constant = 0.082057 L atm mol-1 K-1
T is the temperature of the gas (measured in Kelvin) = 30 + 273 = 303 K
Π = iMRT

Osmotic pressure Π = 1x0.2775 mol/Lx0.082057 L atm mol-1 K-1x303 K = 6.899 atm

Osmotic Pressure is based upon absolute temperature. The absolute temperature is calculated by adding 273 to the temperature in Celsius scale. 10°C is equiavalent to 283 K.

T = 10°C + 273 = 283K