Fundamental Chemistry and Hydraulics - Mathematics and Statistics for the Environment - page 347

14.1.2.3 Concentrations
Because the properties of a solution depend largely on the relative amounts of solvent and solute, the
concentrations of each must be specified.

Note: Chemists use both relative terms, such as saturated and unsaturated, as well as more exact
concentration terms, such as weight percentages, molarity, and normality.

Although polar substances dissolve better than nonpolar substances in water, polar substances
dissolve in water only to a point; that is, only so much solute will dissolve at a given tempera-
ture. When that limit is reached, the resulting solution is saturated. At this point, the solution is in
equilibrium—no more solute can be dissolved. A liquid/solids solution is supersaturated when the
solvent actually dissolves more than an equilibrium concentration of solute (usually when heated).
Specifying the relative amounts of solvent and solute, or specifying the amount of one compo-
nent relative to the whole, usually gives the exact concentrations of solution. Solution concentrations
are sometimes specified as weight percentages:

Mass of solute
Totalmassofsol

%ofSolute = ×100 (14.3)

ute

To understand the concepts of mola r it y, molality, and normality, we must first understand the
concept of a mole. The mole is defined as the amount of a substance that contains exactly the same
number of items (i.e., atoms, molecules, or ions) as 12 g of carbon-12. By experiment, Avogadro
determined this number to be 6.02 × 10 23 (to three significant figures). If 1 mole of carbon atoms
equals 12 g, for example, what is the mass of 1 mole of hydrogen atoms? Note that carbon is 12
times as heavy as hydrogen; therefore, we need only 1/12 the weight of hydrogen to equal the same
number of atoms of carbon.

Note: One mole of hydrogen equals 1 gram.

By the same principle:

• One mole of CO 2 = 12 + 2(16) = 44 g
• One mole of Cl - = 35.5 g
• One mole of Ra = 226 g

In other words, we can calculate the mass of a mole if we know the formula of the substance.
Molarity ( M ) is defined as the number of moles of solute per liter of solution. The volume of a
solution is easier to measure in the lab than its mass:

M = Number of molesofsolute
Number of liters of solution

(14.4)

Molality ( m ) is defined as the number of moles of solute per kilogram of solvent:

Number of molesofsolute
Number of kilogramsofsolution

m = (14.5)

Note: Molality is not as frequently used as molarity, except in theoretical calculations.