# Calculate Osmotic Pressure Example Problem

This example problem demonstrates how to calculate the amount of solute to add to create a specific osmotic pressure in a solution.

## Osmotic Pressure Example Problem

How much glucose (C6H12O6) per liter should be used for an intravenous solution to match the 7.65 atm at 37 degrees Celsius osmotic pressure of blood?
Solution:
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

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, and T = absolute temperature in Kelvin.
Step 1: Determine the van 't Hoff factor.
Since glucose does not dissociate into ions in solution, the van 't Hoff factor = 1.
Step 2: Find the absolute temperature.
T = Degrees Celsius + 273
T = 37 + 273
T = 310 Kelvin
Step 3: Find the concentration of glucose.
Π = iMRT
M = Π/iRT
M = 7.65 atm/(1)(0.08206 L·atm/mol·K)(310)
M = 0.301 mol/L
Step 4: Find the amount of sucrose per liter.
M = mol/Volume
Mol = M·Volume
Mol = 0.301 mol/L x 1 L
Mol = 0.301 mol
From the periodic table:
C = 12 g/mol
H = 1 g/mol
O = 16 g/mol
Molar mass of glucose = 6(12) + 12(1) + 6(16)
Molar mass of glucose = 72 + 12 + 96
Molar mass of glucose = 180 g/mol
Mass of glucose = 0.301 mol x 180 g/1 mol
Mass of glucose = 54.1 grams