An osmole is 1 mol of particles that contribute to the osmotic pressure of a solution.
For example, "NaCl""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.