This example problem demonstrates how to calculate the osmotic pressure of a solution.**Problem:**

What is the osmotic pressure of a solution prepared by adding 13.65 g of sucrose (C_{12}H_{22}O_{11}) to enough water to make 250 mL of solution at 25 °C?**Solution:**

Osmosis is the flow of a solvent into a solution through a semipermiable 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

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 concentration of sucrose

From the periodic table:

C = 12 g/mol

H = 1 g/mol

O = 16 g/mol

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

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 osmotic pressure

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 a the sucrose solution is 3.9 atm.