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Calculate Osmotic Pressure Example Problem

Worked Osmotic Pressure Example Problem

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The effect of osmotic pressure on red blood cells in shown.

The effect of osmotic pressure on red blood cells in shown. From left to right, the effect is depicted of a hypertonic, isotonic and isotonic solution on red blood cells.

LadyofHats, Public Domain

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

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.

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