This example problem demonstrates how to calculate the amount of solute to add to create a specific osmotic pressure in a solution.
How much glucose (C6H12O6) per liter should be used for an intravenous solution to match the 7.65 atm at 37 °C osmotic pressure of blood?
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
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: - Determine the van 't Hoff factor
Since glucose does not dissociate into ions in solution, the van 't Hoff factor = 1
Step 2: - Find absolute temperature
T = °C + 273
T = 37 + 273
T = 310 K
Step 3: - Find 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 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 g
54.1 grams per liter of glucose should be used for an intravenous solution to match the 7.65 atm at 37 °C osmotic pressure of blood.