Calculate Osmotic Pressure Example Problem

Worked Osmotic Pressure Example Problem

Red blood cells undergo crenation in a hypertonic solution and may swell and burst in a hypotonic solution. Osmotic pressure of the solution is important to protect the cells.
Red blood cells undergo crenation in a hypertonic solution and may swell and burst in a hypotonic solution. Osmotic pressure of the solution is important to protect the cells. PHOTO INSOLITE REALITE/SCIENCE PHOTO LIBRARY / Getty Images

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 °C osmotic pressure of blood?

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: - 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

Answer:

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.

What Happens If You Get the Answer Wrong

Osmotic pressure is critical when dealing with blood cells. If the solution is hypertonic to the cytoplasm of the red blood cells, they will shrink via a process called crenation. If the solution is hypotonic with respect to the osmotic pressure of the cytoplasm, water will rush into the cells to try to reach equilibrium.

The red blood cells may burst. In an isotonic solution, red and white blood cells maintain their normal structure and function.

It's important to remember there may be other solutes in the solution which affect osmotic pressure. If a solution is isotonic with respect to glucose but contains more or less of an ionic species (sodium ions, potassium ions, and so on), these species may migrate into or out of a cell to try to reach equilibrium.