Chemistry: Determining the Concentration of a Solution

Determining the Concentration of a Solution

There are many ways to measure the amount of solute present in a solution. Each method is useful for a different purpose in chemistry, so we're unfortunately stuck with the task of learning all of them. Without further ado, here they are:

Qualitative Concentrations

The amount of solute present in a solution can be described without numbers by one of the following terms:

• Unsaturated: "Unsaturated" refers to any solution that is still capable of dissolving more of a solute. For example, a glass of iced tea is not saturated with sugar if you've placed one tablespoon of sugar in it because it's still capable of dissolving more sugar. This term isn't very good for determining the exact quantity of solute present—for example, both a glass of water and a filled swimming pool would be said to be unsaturated salt solutions if there were one gram of salt dissolved in each.
• Saturated: These solutions have dissolved the maximum possible amount of solute. For example, if you keep adding sugar to a glass of Kool-Aid, it will eventually stop dissolving and settle to the bottom (little kids, however, refuse to believe this). This solution is said to be saturated.
• Supersaturated: These solutions are those that have dissolved more than the normal maximum possible amount of solute. These solutions are unusual and aren't very stable. For example, the addition of a small mote of dust to such a solution causes enough of a disturbance that crystals spontaneously form until the solution reaches a saturated state.

It's easy to tell if a solution is unsaturated, saturated, or supersaturated by adding a very small amount of solute. If the solution is unsaturated, the solute will dissolve. If the solution is saturated, it won't. If the solution is supersaturated, crystals will very quickly form around the solute you've added.

Molarity (M)

Molarity is probably the most commonly used way of measuring concentration and is defined as the number of moles of solute per liters of solution.

Let's say that we have made a solution by adding water to 40 grams (1.0 mole) of sodium hydroxide until the final volume of the solution is one liter (to review mole calculations, head back to The Mole). Because we have one mole of solute in one liter of solution, the molarity is equal to (1 mole)/(1 liter) = 1 M. We refer to a solution with a molarity of one as being a "one molar" solution.

Molality (m)

Molality is defined as the number of moles of solute per kilogram of solvent. For example, if we were to add two kilograms of water to 4 moles of sugar, the molality would be equal to 4 moles/2 kilograms = 2 m ("two molal"). When doing calculations with molality, note that because the density of water is 1.0 g/mL under standard conditions, the number of kilograms of water is equal to the number of liters of water.

Normality (N)

The normality of a solution is defined as the number of moles of a reactive species, usually referred to as "equivalents" per liter of solution. The use of "equivalents" will depend on the reaction being performed, so some knowledge of the specific chemical process in a reaction is necessary before computing normality. At least, that's the "normal" way of solving this problem. (I couldn't resist.)

Mole Fraction (χ)

The mole fraction is defined as the number of moles of one component in a solution divided by the total number of moles of all components in the mixture. In equation form, we can express the mole fraction of one component in a solution as being:

• χ_A = ^{moles of A}⁄_{moles of A + moles of B + moles of C} + …

where A refers to the first component, B refers to the second component, and C refers to the third component. As the "…" indicates, this calculation can be extended to include any number of components in the mixture.

Parts Per Million (ppm) and Parts Per Billion (ppb)

Both parts per million and parts per billion are units of concentration most frequently used in environmental analysis. Because the solvent used is most frequently water, the concentration of a solution in ppm can be found by dividing the number of mg (0.001 g) of solute by the number of liters of water. Parts per billion can be determined by dividing the number of μg (10^-6 g) of solute by the number of liters of water.

A Quick Summary of Units of Concentration

The following table includes all of the units of concentration we've mentioned in this section, as well as how to find them.

Unit	Symbol	How It's Measured
molarity	M	moles of solute / liters of solution
molality	m	moles of solute / kilograms of solution
normality	N	"equivalents," which varies depending on the reaction being performed
mole fraction	χ	moles of A⁄moles of A + moles of B + …
parts per million	ppm	mg solute/L of water
parts per billion	ppb	μg solute/L of water