Osmotic Pressure Formula

Osmosis is the movement of solvent molecules through a partially permeable membrane from a low-solute-concentration region to a high-solute-concentration region. Both sides of the selectively permeable membrane finally achieve equilibrium (identical solute concentration on both sides).

The lowest force per unit of area, i.e. pressure that must be given to a solution to stop the passage of solvent molecules across a semipermeable barrier is known as osmotic pressure (osmosis). It is a colligative feature that is influenced by the solute particle concentration in the solution.

Formula

π = i × C × R × T

where,

• i denotes the Van’t Hoff factor
• C denotes the molar concentration of the solute in the solution
• R = 0.0821
• T denotes the temperature in Kelvins

Sample Problems

Problem 1. Find the osmotic pressure of a solution formed when 1 m of salt is dissolved in 1 L of water at 20°C.

Solution:

C = 1m/1L = 1 M

i = 2

T = 20°C = 293.15 K

Since, π = i × C × R × T

= 2 × 1 × 0.0821 × 293.15

= 48.135 atm

Problem 2. Find the osmotic pressure of a solution formed when 2 m of salt is dissolved in 1 L of water at 30°C.

Solution:

C = 2m/1L = 2 M

i = 2

T = 30°C = 300 K

Since, π = i × C × R × T

= 2 × 2 × 0.0821 × 303.15

= 99.55 atm

Problem 3. Find the osmotic pressure of KCl at 300 K given its molar concentration is 1.9 M.

Solution:

C = 1.9 M

i = 2

T = 300 K

Since, π = i × C × R × T

= 2 × 1.9 × 0.0821 × 300

= 93.59 atm

Problem 4. The osmotic pressure of HCl at 300 K is 90 atm. Calculate its molar concentration.

Solution:

π = 90 atm

T = 300 K

i = 2

Since, π = i × C × R × T

⇒ C = π/(iRT) 

= 90/(2 × 0.0821 × 300)

= 1.827 M

Problem 5. Find the osmotic pressure of KCl at 290 K given its molar concentration is 1.89 M.

Solution:

C = 1.8 M

i = 2

T = 290 K

Since, π = i × C × R × T

= 2 × 1.8 × 0.0821 × 290

= 85.71 atm