## Moles of Molecules

James Richard Fromm

Chemistry is the area of science which deals with the interactions of atoms with one another. These interactions form the stable covalently-linked polyatomic structures called molecules and the stable lattices of ionic crystals. Each of the molecules which constitute a molecular substance is made up of atoms. This, the keystone of John Dalton's atomic-molecular theory, carries with it the consequence that the molar mass of a molecular substance must be the sum of the atomic masses of the atoms which compose the molecule.

Example. The molar mass of H2O is equal to twice the atomic mass of hydrogen plus the atomic mass of oxygen, or 2 + 16 = 18 g/mol. The molar mass of benzoic acid, C6H5COOH, is seven times the atomic mass of carbon (12), plus six times the atomic mass of hydrogen (1), plus twice the atomic mass of oxygen (16), which totals 122 g/mol. Using the more accurate atomic masses given in the table of atomic masses, the molar mass of water is 2(1.0079) + 1(15.9994)= 18.0152 g/mol and the molar mass of benzoic acid is 122.1232 g/mol.

Many substances do not form isolatable molecules but exist as crystal lattices. These lattices may easily dissociate into ions and dissolve in water, as NaCl does, or like SiO2 remain as insoluble crystals with strong covalent bonds. For these substances the molar mass used is the formula mass. The formula mass of any substance is the sum of the atomic masses which make up the empirical formula.

Example. Common salt has the empirical formula NaCl. The formula mass of NaCl is 22.98977 + 35.453 = 58.443 g/mol regardless of the actual structure of the crystal. This molar mass is called the formula mass of NaCl because it corresponds to the empirical formula rather than to any physical structure.

#### Percentage Composition of Compounds by Mass

The molar mass of a compound, molecule, or ion is the sum of the molar masses of the atoms which compose it. If the molar masses of the atoms (atomic masses) are known, as they are, then the molar mass M of any compound can be calculated from them. Knowledge of both the molar mass of a compound and the atomic masses of its constituent atoms permit chemists to calculate the elemental percentage composition by mass, usually called simply the percentage composition, of any compound. In fact, the atomic masses of the elements were originally determined by carrying out this procedure in reverse using the measured percentage compositions. Mass spectrometric methods have now generally replaced these earlier chemical methods of determining accurate relative atomic masses.

Example. The percentage composition of mercury (II) sulfide, HgS, is calculated as follows. The molar mass of HgS is:

200.59 + 32.06 = 232.65 g/mol.
% Hg = 100(200.59 g/mol)/(232.65 g/mol) = 86.22%
%S = 100(32.06 g/mol)/(232.65 g/mol) = 13.78%

Example. Copper(II) sulfate is sometimes dissolved in water to form a solution from which copper metal can be plated. We can compute the percentage composition of copper sulfate, and from the percentage composition we can calculate the mass of copper metal producible from 576.2 g of copper sulfate.

The empirical formula for copper(II) sulfate is CuSO4. Its molar mass is therefore 63.546 + 32.06 + 4(16) = 159.606.  The percentage composition by mass is:

63.546/159.606 x 100 = 39.81 % Cu
32.06/159.606 x 100 = 20.09 % S
64/159.606 x 100 = 40.10 % O

The mass of copper producible is therefore 576.2 g x 39.81% copper which is 229.4 g copper.

#### The Empirical Formula of a Compound

The empirical formula of a compound is the ratio of moles of each element present in the compound, expressed in the form of small whole numbers. The empirical formula of any compound can be expressed as small whole numbers because atoms are indivisible. If the ratio of moles were 1Fe:1.5O, as it is in iron (III) oxide, the empirical formula would be written as Fe2O3.

Example. An iron oxide is found to have the percentage composition 69.9% iron and 30.1% oxygen by mass. We can calculate which oxide of iron it is:

69.9/55.847 = 1.252 moles Fe
30.1/15.9994 = 1.881 moles O

The mole ratio is 1.502 moles O per mole Fe, so the compound is Fe2O3, hematite or iron (III) oxide.

Example. The percentage composition of a yellowish-red compound containing only vanadium and oxygen is found to be 56.01% vanadium and 43.98% oxygen. The empirical formula of the compound is calculated as follows. In 100 g of the compound there are 56.01 g V and 43.98 g O. There are then

56.01 g V/(50.9414 g V/mol V) = 1.099 mol V; 1.099/1.099 = 1.00
43.98 g O/(15.9994 g O/mol O) = 2.949 mol O; 2.749/1.099 = 2.50

A mole ratio of 1.00 V to 2.50 O is the empirical formula V2O5.

The empirical formula of a compound is the simplest integral ratio of atoms that can specify the ratios of numbers of atoms which are experimentally found to be those of the compound. The empirical formula for table salt, which is not a molecular substance, is NaCl. The empirical formula H2O specifies that there are two atoms of hydrogen to one atom of oxygen in water. The empirical formula for water is also the correct molecular formula for water. The empirical formula HO specifies that there is one atom of hydrogen to one atom of oxygen in hydrogen peroxide. The empirical formula for hydrogen peroxide is not the correct molecular formula for hydrogen peroxide. The correct molecular formula for hydrogen peroxide, H2O2, is a multiple of the empirical formula HO. Chemists prefer to use the correct molecular formula for a molecular substance whenever the correct molecular formula is known.

#### Molecular Formula of a Compound

The actual molecular formula of a compound is always a multiple of its empirical formula. Although P2O5 is a correct empirical formula, the actual molecular formula for this compound is believed to be P4O10. A given empirical formula might correspond to several different molecular formulae. The empirical formula CH could equally well correspond to C2H2, the gas ethene or acetylene, or to C6H6, the liquid benzene. Only with knowledge of the approximate, or exact, molar mass of the compound can the true molecular formula be determined.

Many common compounds, including table salt, exist as ionic crystals rather than in molecular form. These compounds do not really have a molecular formula and so the empirical formula is usually used for them. It is as reasonable to speak of the compound NaCl as the compound C2H2, although the latter is molecular while the former is not. When referring to the molar mass of a compound which is not molecular, the term formula mass or formula weight is often used, rather than molar mass, to emphasize the point that the mass given applies to one mole of formula units rather than to one mole of actual molecular species.