molarity

Solution Concentration: Units
There are a number of common units that express the concentration of solute in a solution:
 * molarity (M), in moles of solute per liter of solution
 * molality (m), in moles of solute per kilogram of solvent
 * percent by mass (%m/m), in mass of solute per mass of solution
 * percent by mass/volume (%m/v), in mass of solute per milliliter of solution
 * percent by volume (%v/v), in mL of solute per mL of solution
 * mole fraction (X), in moles of solute per total moles of solution
 * parts per million (ppm), in mg solute per L of solution (or 1 unit per million units)
 * parts per billion (ppb), in micrograms of solute per L of solution (or 1 unit per billion units)

Here is a quick diagram to remind you how to make a 1 L solution correctly:


 * Molarity**

Molarity is a derived unit (M) defined as mole(s) of solute per liter of solution (mol/L).


 * M = mol solute/L solution**

Essentially, it is the concentration of a solute within a solution.

A solution made by dissolving 2.0 moles of NaCl in 4.0 liters of water has a concentration of 2.0 mol/4.0 L, or 0.50 M NaCl.

Try this online [|molarity calculator]!


 * Molality**

Molality is defined as the mole(s) of solute per kilogram of solvent (mol/kg).


 * m = mole solute/kg solvent**

This is an important distinction from molarity, where the denominator was the volume of the solution. In molality, only the mass of the solvent is important.

Why the difference? When temperature changes, so does the volume of a solution, but its mass remains the same. So if there is a temperature change occurring, the molality will not change (whereas molarity would).

Example: 2.0 moles of NaCl are dissolved in 500 g of water. The molality would therefore be 2.0 moles / 0.500 kg, which equals 4.0 molal.


 * Percent by Mass**

Percent by mass is defined as the mass of the solute divided by the mass of the solution, expressed as a percentage:


 * %w/w = (mass solute/mass solution) x 100**

Again, the mass of the solution doesn't change with temperature changes, so its percent by mass would remain constant during temperature changes.

Example: 2.0 moles of NaCl are dissolved in 500 g of water.

2.0 mol NaCl x 58.44 g/mol = 117 g NaCl;

117 g NaCl + 500 g water = 617 g of solution;

117 g NaCl / 617 g solution x 100 = 18.9% w/w NaCl


 * Percent by mass/volume**

This unit is defined as the mass of the solute in grams per milliliter of solution, and is closely related to the //**density**// of a solution.


 * %m/v = (g solute / mL solution) x 100**

Now that the unit relies on volume, it is sensitive to change with temperature changes.