An osmole 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: 1 mol of #"Na"⁺# and 1 mol of #"Cl"⁻#.
A solution of 1 mol/L #"NaCl"# has an osmolarity of 2 Osmol/L.
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.
The concentrations of solutes are: [#"Na"^+#] = 0.140 mol/L; [#"glucose"#] = 180 mg/100 mL;
[#"BUN"#] (blood urea nitrogen) = 20 mg/100 mL.
Solution
[#"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"))))/(1color(white)(l)"L") × (2color(white)(l)"Osmol")/(1color(red)(cancel(color(black)("mol")))) = "0.280 Osmol/L"#
#"Glucose osmolarity" =(0.150color(red)(cancel(color(black)("g"))))/(100color(red)(cancel(color(black)("mL")))) × (1000color(red)(cancel(color(black)("mL"))))/(1color(white)(l)"L") × (1color(red)(cancel(color(black)("mol"))))/(180.2color(red)(cancel(color(black)("g")))) × (1color(white)(l)"Osmol")/(1color(red)(cancel(color(black)("mol")))) = "0.008 32 Osmol/L"#
#"BUN osmolarity" = (0.020color(red)(cancel(color(black)("g"))))/(100color(red)(cancel(color(black)("mL")))) × (1000color(red)(cancel(color(black)("mL"))))/(1color(white)(l)"L") × (1color(red)(cancel(color(black)("mol"))))/(28.01color(red)(cancel(color(black)("g")))) ×(1color(white)(l)"Osmol")/(1color(red)(cancel(color(black)("mol")))) = "0.0071 mol/L"#
∴ #"Blood osmolarity" = "(0.280 + 0.008 32 + 0.0071) Osmol/L"#
#= "0.295 Osmol/L" = "295 mOsmol/L"#
Here's a video on calculating osmolarity.
