Question

How many grams of glucose (C6H12O6) should be used to make 1 Liter of an intravenous solution to match the osmotic pressure of blood (7.65 atm) at 37 °C?

Answer 1

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

van 't Hoff factor is 1 for glucose

Absolute temperature = 310K

Concentration of glucose =

Π = iMRT
M = Π/iRT
M = 7.65 atm/ 1 x 0.08206 L·atm/mol·K x 310
M = 0.301 mol/L

The amount of sucrose per liter

M = mol/Volume
mol = M·Volume
mol = 0.301 mol/L x 1 L
mol = 0.301 mol

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 to be used for an intravenous solution to match the 7.65 atm at 37 °C osmotic pressure of blood.