# Osmotic Pressure Formula

Osmosis is the phenomenon of the route of solvent but not solute through a semipermeable membrane from solvent to the solution or from weak to concentrated solution. The natural phenomenon like pure water from the sea, industrial extraction and purification are based on the osmosis process. Osmosis can be described as a selective separation aspect.

**What is osmotic pressure?**

Osmotic pressure is the excess pressure required to be applied to a solution to prevent osmosis when the solution is separated from a solvent via semipermeable membrane, usually denoted by ‘π.’

According to Van’t Hoff’s law, Osmotic Pressure formula is given by

**Osmotic Pressure = iRTc**

Where,

i = number of ions created by dissociation of solute molecules

R = ideal gas constant

T = absolute temperature in K

C = molar or molal concentration

The formula which relates osmotic pressure to temperature and concentration is similar to ideal gas equation.

Where,

‘π’ is the osmotic pressure in mmHg

n = number of solute particles

R = universal gas constant

V = volume of the solution in litres

**Example 1**

Determine the osmotic pressure of the aqueous solution which contains 14g of urea in 300cm3 of the solution at 250C.

**Solution**

The given entities are

i = 14g

T = 25oC = 298K

c = 300 cm3

R = 8.314 JK-1mol^{-1}

We have an equation

Osmotic pressure = iRTc

Substituting the above values, we get

Osmotic pressure = 14g x 8.314 JK^{-1}mol^{-1} x 298K x 300cm^{3}

Osmotic pressure = 104.05 x 105 Nm^{-2}

**Example 2**

Determine the osmotic pressure of a solution made by adding 13.65g of sucrose(C12H22O11) in water to make 250 mL of solution at 25^{o}C.

**Solution**

Calculate the concentration of sucrose

Molar mass of sucrose = 12(2) + 22(1) + 11(16)

Molar mass = 342

nsucrose = 13.65 x 1 mol / 342

nsucrose = 0.04 mol

msucrose = nsucrose / volumesolution

= 0.04mol/0.25L

= 0.16mol/L

T = 25oC + 273

= 298 K

Osmotic Pressure, ‘π’ = iMRT

= 1 x 0.16 mol / L x 0.08206 x 298 K

= 3.9atm

Hence, the osmotic pressure of sucrose = 3.9atm