2.3 Other Measures of Concentration

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Although we will almost exclusively use molarity to describe solution concentration, there are some other ways to express solution concentration. Here are some of the more common alternatives:

Molality. Molality is defined as the number of moles of solute dissolved in one kilogram of solvent. Notice the two key differences between molarity and molality.

Molality uses mass rather than volume, and
Molality uses solvent instead of solution.

Mass per unit volume. This unit is typically milligrams per milliliter (mg/mL) or milligrams per cubic centimeter (mg/cm³). A useful note is that 1 mL = 1 cm³ and that cm³ is sometimes referred to as a "cc" (cubic centimeter).

Mass per unit volume is handy when discussing how soluble a material is in water or a particular solvent. For example, "the solubility of Substance X is 3 grams per liter".

Percent by Mass. Also called weight percent or percent by weight, this is simply the mass of the solute divided by the total mass of the solution and multiplied by 100%:

percent by mass

mass of component

mass of solution

100

Parts per million (PPM). Parts per million works like percent by mass, but is more convenient when there is only a small amount of solute present. PPM is defined as the mass of the component in solution divided by the total mass of the solution multiplied by 10⁶ (one million):

A solution with a concentration of 1 ppm has 1 gram of substance for every million grams of solution. Because the density of water is 1 g per mL and we are adding such a tiny amount of solute, the density of a solution at such a low concentration is approximately 1 g per mL. Therefore, in general, one ppm implies one mg of solute per liter of solution.

Here's an example.

A sample of water contains 25 ppm of lead ions, Pb²⁺. Convert this concentration to molarity, mol·L^-1.

Solution:

There are a number of different ways to set up the answer to the conversion; this is just one method. Since the conversion involves mass, we will need to know the molar mass of Pb²⁺, which is 206.2 g·mol^-1

		change g to mL		change mL to L		change g to mol
										.
25 ppm	=	25 g Pb²⁺ 10⁶g H₂O	=	25 g Pb²⁺ 10⁶mL H₂O	=	25 g Pb²⁺ 10³L H₂O	×	1 mol 207.2 g	=	1.2 × 10^-4mol L

Parts per billion (PPB). This is like ppm, but is parts per billion (10⁹) instead of million (caution: the word billion has different meanings in different countries). A solution with 1 ppb of solute has 1 microgram (10^-6) of material per liter.