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QUESTION

# How do you calculate osmolarity from molarity?

You multiply the molarity by the number of osmoles that each produces.

An osmole (Osmol) is 1 mol of particles that contribute to the osmotic pressure of a solution.

For example, "NaCl" dissociates completely in water to form "Na"^+ ions and "Cl"^"-" ions.

Thus, each mole of "NaCl" becomes two osmoles in solution: one mole of "Na"^+ and one mole of "Cl"^"-".

A solution of 1 mol/L "NaCl" has an of 2 Osmol/L.

Also, a solution of 1 mol/L "CaCl"_2 has an osmolarity of 3 Osmol/L (1 mol "Ca"^(2+) and 2 mol "Cl"^"-").

EXAMPLE

Calculate the osmolarity of blood.

Solution

The concentrations of solutes are: "[Na"^+] = "0.140 mol/L"; ["glucose"] = "180 mg/100 mL"; "[BUN] (blood urea nitrogen)" = "20 mg/100 mL".

["Na"^+] = "0.140 mol/L".

But, each "Na"^+ ion pairs with a negative ion "X"^"-" such as "Cl"^"-" to give 2 Osmol of particles.

"NaX osmolarity" = (0.140 color(red)(cancel(color(black)("mol"))))/"1 L" × "2 Osmol"/(1 color(red)(cancel(color(black)("mol")))) = "0.280 Osmol/L"

"Glucose osmolarity" = (0.150 color(red)(cancel(color(black)("g"))))/(100 color(red)(cancel(color(black)("mL")))) × (1000 color(red)(cancel(color(black)("mL"))))/"1 L" × (1 color(red)(cancel(color(black)("mol"))))/(180.2 color(red)(cancel(color(black)("g")))) × "1 Osmol"/(1 color(red)(cancel(color(black)("mol")))) = "0.008 32 Osmol/L"

"BUN osmolarity" = (0.020 color(red)(cancel(color(black)("g"))))/(100 color(red)(cancel(color(black)("mL")))) × (1000 color(red)(cancel(color(black)("mL"))))/"1 L" × (1 color(red)(cancel(color(black)("mol"))))/(28.01 color(red)(cancel(color(black)("g")))) ×"1 Osmol"/(1 color(red)(cancel(color(black)("mol")))) = "0.0071 Osmol/L"

"Blood osmolarity" = "(0.280 + 0.008 32 + 0.0071) Osmol/L" = "0.295 Osmol/L" = "295 mOsmol/L"