# What is osmolarity?

Jun 23, 2014

Osmolarity is the number of osmoles of solute per litre of solution.

#### Explanation:

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

For example, $\text{NaCl}$ dissociates completely in water to form "Na"⁺ ions and "Cl"⁻ ions.

Thus, each mole of $\text{NaCl}$ becomes two osmoles in solution: 1 mol of "Na"⁺ and 1 mol of "Cl"⁻.

A solution of 1 mol/L $\text{NaCl}$ has an osmolarity of 2 Osmol/L.

A solution of 1 mol/L ${\text{CaCl}}_{2}$ has an osmolarity of 3 Osmol/L
(1 mol $\text{Ca"^"2+}$ and 2 mol $\text{Cl"^"-}$).

EXAMPLE

Calculate the osmolarity of blood.

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

Solution

[${\text{Na}}^{+}$] = 0.140 mol/L.

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

$\text{NaX osmolarity" = (0.140 color(red)(cancel(color(black)("mol"))))/(1color(white)(l)"L") × (2color(white)(l)"Osmol")/(1color(red)(cancel(color(black)("mol")))) = "0.280 Osmol/L}$

$\text{Glucose osmolarity" =(0.150color(red)(cancel(color(black)("g"))))/(100color(red)(cancel(color(black)("mL")))) × (1000color(red)(cancel(color(black)("mL"))))/(1color(white)(l)"L") × (1color(red)(cancel(color(black)("mol"))))/(180.2color(red)(cancel(color(black)("g")))) × (1color(white)(l)"Osmol")/(1color(red)(cancel(color(black)("mol")))) = "0.008 32 Osmol/L}$

$\text{BUN osmolarity" = (0.020color(red)(cancel(color(black)("g"))))/(100color(red)(cancel(color(black)("mL")))) × (1000color(red)(cancel(color(black)("mL"))))/(1color(white)(l)"L") × (1color(red)(cancel(color(black)("mol"))))/(28.01color(red)(cancel(color(black)("g")))) ×(1color(white)(l)"Osmol")/(1color(red)(cancel(color(black)("mol")))) = "0.0071 mol/L}$

$\text{Blood osmolarity" = "(0.280 + 0.008 32 + 0.0071) Osmol/L}$

$= \text{0.295 Osmol/L" = "295 mOsmol/L}$

Here's a video on calculating osmolarity.