Topic Overview

Math is the language of chemistry. It enables us to easily determine the amount of chemical needed for a reaction or the amount that will be produced. In this topic you will learn how to apply simple math relations to solving chemical problems.

The Mathematics of Formulas

Recall that the mass of an atom is a relative value based on the mass of a carbon-12 atom. All atoms are compared to this standard. Thus, a magnesium atom with an atomic mass of 24 amu is twice as massive as the standard carbon atom with an atomic mass of 12. This relationship will remain the same in any system of weights or masses. As long as there is a mass ratio of 12 parts of carbon to 24 parts of magnesium, equal numbers of carbon and magnesium are present, Twelve grams of carbon contain the same number of atoms as 24 grams of magnesium. These mass relationships of atoms are the basis for mass relations in compounds.

Formula Mass

Remember that compounds are represented by formulas that show the type and the number of atoms present in the compound. Because compounds are represented by formulas, the mass of the smallest unit of the compound is the formula mass, which is the sum of the atomic masses of all the atoms present. While the term molecular mass is often used to represent the mass of a unit of a compound, formula mass is preferred because ionic and network solids do not form discrete molecules. For example, sodium chloride (NaCl) is an ionic compound. No molecules of NaCl exist, so molecular mass does not apply to NaCl. However the formula mass can be calculated for a formula unit of the compound. The formula mass of NaCl is the mass of one atom of Na plus the mass of one atom of Cl in atomic mass unit (amu).

Gram Formula Mass The gram formula mass of a substance is simply the formula mass expressed in grams instead of atomic mass units. Thus, the gram formula of K₂CO₃ is 138 g. Some substance, such as sucrose (table sugar), form molecules. It is common to express the gram formula masses of molecular substances as gram molecular masses.

Percent Composition

Formulas represent the composition of a substance. Using the subscripts and atomic masses of the elements, the percent by mass of a substance can be calculated. The percent composition of a substance represents the composition as a percentage of each element compared with the total mass of the compound.

Hydrates Ionic substances often include definite amounts of water as part of the crystal structure. The water molecules are shown as part of the formula, such as CuSO₄ ⋅ 5H₂O. Crystals that contain attached water molecules are called hydrates, while substances without water are termed anhydrous. If it is necessary to calculate the percentage of water in such a crystal, treat the water molecule as a single unit.

The Mole

Chemists use a specific collective noun to define a particularly usable number of particles. A mole is defined as the number of atoms of carbon present in 12.000 grams of C-12. The number of particles in a mole is 6.02 × 10²³, which is called Avogadro’s number. While it would be impossible to individually count a mole of particles, the mass of one mole of a substance can be found determining its gram formula mass.

Converting Grams to Moles

Converting Moles to Grams

Finding Molecular Formulas from Empirical Formulas

When the molecular mass of a compound and its empirical formula are known, it is possible to determine the correct molecular formula. For example, the molecular mass of propene is 42 amu. The empirical formula of propene is CH₂, and the molecular mass of CH₂ is 14 amu. Divide the mass of the compound by the mass of the empirical formula. The result will be an integer. In this case it is 3. This tells you that the molecular formula is three times than the empirical formula. Simply multiply each subscript by the integer to find the molecular formula. The molecular formula in this case is C₃H₆.

Vocabulary

Formula mass - The sum of the atomic masses of all the atoms in a chemical formula. It is used to determine the mass of a single molecule or formula unit of a compound.

Gram formula mass - The formula mass expressed in grams, often used interchangeably with molar mass. It represents the mass of one mole of a substance.

Mole - A unit of measurement used in chemistry to express amounts of a substance. One mole of any substance contains approximately 6.022 x 10^23 elementary entities, such as atoms, molecules, or ions.

Percentage composition - The percentage by mass of each element in a compound. It is calculated by dividing the mass of each element in the compound by the total mass of the compound and multiplying by 100%.