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Osmotic Pressure Example

Calculating Osmotic Pressure Example Problem

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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 (C12H22O11) 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

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

Msucrose = nsucrose/Volumesolution
Msucrose = 0.04 mol/(250 mL x 1 L/1000 mL)
Msucrose = 0.04 mol/0.25 L
Msucrose = 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.

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