How do you calculate osmolarity from molarity?

1 Answer
Mar 20, 2014

Answer:

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

Explanation:

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 osmolarity 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"#