# Osmolarity

## Key Questions

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.

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, $\text{NaCl}$ dissociates completely in water to form ${\text{Na}}^{+}$ ions and ${\text{Cl}}^{-}$ ions.

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

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 1

Calculate the osmolarity of blood. The concentrations of solutes are:

["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.

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

$\text{Glucose osmolarity" = (0.180 cancel("g"))/(100 cancel("mL")) × (1000 cancel("mL"))/"1 L" × (1 cancel("mol"))/(180.2 cancel("g")) × "1 Osmol"/(1 cancel("mol")) = "0.009 99 Osmol/L}$

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

$\text{Blood osmolarity" = "(0.280 + 0.009 99 + 0.0071) Osmol/L"= "0.297 Osmol/L" = "297 mOsmol/L}$

EXAMPLE 2

Calculate the osmolarity of an IV admixture that contains 500 mL sterile water; 50 mL NaHCO₃ 8.4 %; 10 mL of 2 mmol/mL KCl; 0.5 mL heparin 5000 units; 1 mL pyridoxine; 1 mL thiamine.

Solution

Set up a table for easy calculation.

$\text{Osmolarity" = "141.96 mOsmol"/(562.5 cancel("mL")) × (1000 cancel("mL"))/"1 L" = "252 mOsmol/L}$

• Osmolarity is an old term for osmotic concentration. This can be used to measure the amount of solute (think sugar) dissolved in a solvent (water).

If the level of solute of a solution is higher than the concentration of solute inside of the cell, water will flow out of the cell during osmosis. See egg in syrup in the video below.

If the level of solute outside the cell is lower than the levels of solute inside of the cell, water will flow into the cell. See the egg when placed into distilled water in the video.

Here is a video of a lab conducted to test osmosis in eggs placed into different solutions.

Video from: Noel Pauller

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