How to Calculate Osmotic Pressure

The osmotic pressure of a solution is the minimum amount of pressure needed to prevent water from flowing into it across a semipermeable membrane. Osmotic pressure also reflects how readily water can enter the solution via osmosis, as across a cell membrane. For a dilute solution, osmotic pressure obeys a form of the ideal gas law and can be calculated provided you know the concentration of the solution and the temperature.

Osmotic Pressure Problem

What is the osmotic pressure of a solution prepared by adding 13.65 g of sucrose (C₁₂H₂₂O₁₁) to enough water to make 250 mL of solution at 25 °C?

Solution:

Osmosis and osmotic pressure are related. Osmosis is the flow of a solvent into a solution through a semipermeable membrane. Osmotic pressure is the pressure that stops the process of osmosis. Osmotic pressure is a colligative property of a substance since it depends on the concentration of the solute and not its chemical nature.

Osmotic pressure is expressed by the formula:

Π = iMRT (note how it resembles the PV = nRT form of the Ideal Gas Law)

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 = 0.08206 L·atm/mol·K
T = absolute temperature in K

Step 1, Find the Concentration of Sucrose

To do this, look up the atomic weights of the elements in the compound:

From the periodic table:
C = 12 g/mol
H = 1 g/mol
O = 16 g/mol

Use the atomic weights to find the molar mass of the compound. Multiply the subscripts in the formula times the atomic weight of the element. If there is no subscript, it means one atom is present.

molar mass of sucrose = 12(12) + 22(1) + 11(16)
molar mass of sucrose = 144 + 22 + 176
molar mass of sucrose = 342

n_sucrose = 13.65 g x 1 mol/342 g
n_sucrose = 0.04 mol

M_sucrose = n_sucrose/Volume_solution
M_sucrose = 0.04 mol/(250 mL x 1 L/1000 mL)
M_sucrose = 0.04 mol/0.25 L
M_sucrose = 0.16 mol/L

Step 2, Find absolute temperature

Remember, absolute temperature is always given in Kelvin. If the temperature is given in Celsius or Fahrenheit, convert it to Kelvin.

T = °C + 273
T = 25 + 273
T = 298 K

Step 3, Determine the van 't Hoff factor

Sucrose does not dissociate in water; therefore the van 't Hoff factor = 1.

Step 4, Find the Osmotic Pressure

To find the osmotic pressure, plug the values into the equation.

Π = iMRT
Π = 1 x 0.16 mol/L x 0.08206 L·atm/mol·K x 298 K
Π = 3.9 atm

Answer:

The osmotic pressure of the sucrose solution is 3.9 atm.

Tips for Solving Osmotic Pressure Problems

The biggest issue when solving the problem is knowing the van't Hoff factor and using the correct units for terms in the equation. If a solution dissolves in water (e.g., sodium chloride), it's necessary to either have the van't Hoff factor given or else look it up. Work in units of atmospheres for pressure, Kelvin for temperature, moles for mass, and liters for volume. Watch significant figures if unit conversions are required.