Chemical Formulae

Molecules are aggregates of individual atoms held together by chemical bonds (to be discussed in the next chapter). Thus, a symbolic representation of a molecule should be composed of the chemical symbols for the individual atoms that comprise the molecule. There are two types of chemical formulae that are commonly used to represent a molecule:

1.

Molecular Formula:

The molecular formula for a molecule expresses the precise number of each type of atom in that molecule.

Examples:

• CO$_2$ is the formula for a molecule of carbon dioxide.
• H$_2$O is the formula for a molecule of water.
• C$_6$H$_{12}$O$_6$ is the formula for molecule of glucose.

Note that the molecular formula is also the formula for the (bulk) substance, itself. That is, we say H$_2$O is the molecular formula for water or ice, indicating bulk water or ice. This is true as long as the bulk substance has well defined molecular subunits.

2.

Empirical Formula:

The empirical formula is the simplest formula for a molecule that still expresses the correct relative numbers or ratios of numbers of atoms in the molecule.

Example: The numbers of carbon, hydrogen and oxygen atoms in glucose (C$_6$H$_{12}$O$_6$) are in the ratio:

$$6:12:6$$

$$1:2:1$$

Hence, the empirical formula for glucose is

$${\rm CH}_2{\rm O}$$

Which contains more information?

Consider the empirical formula

$${\rm CH}_2$$

This is a correct empirical formula for the following molecules:

a.

ethylene: C$_2$H$_4$

b.

cyclopropane: C$_3$H$_6$

c.

cyclobutane: C$_4$H$_8$

d.

cyclohexane: C$_6$H$_{12}$

or any other molecule for which the number of carbon atoms and the number of hydrogen atoms are in the ratio of 1:2. From this example, it is clear that the molecular formula carries more information and is clearly preferable to an empirical formula.

Put another way, an empirical formula specifies a class of molecules, in which the numbers of atoms are in certain basic ratios, while the molecular formula precisely identifies a particular molecule.

Although preferable, a molecular formula is not always possible. For example, in liquids and solids, it may not always be possible to define precise molecular units, in which case an empirical formula is the only possible choice.

Sometimes, enough information about a substance is given to determine the empirical formula only. Consider the following example:

A 10.0 g sample of a sand-like substance is known to contain 46.01% iron (Fe) and 53.99% silicon (Si) by mass. What is the formula for the substance?

Solution: The mass of Fe and Si in the sample can be determined from the given percentages:

$${\rm mass\ of\ Fe} = 10.0 {\rm g} \times 0.4601 = 4.601 {\rm g}$$

$${\rm mass\ of\ Si} = 10.0 {\rm g} \times 0.5399 = 5.399 {\rm g}$$

We convert masses to moles, since we want to know how many of each type of atom there is in the substance (expressed in moles), and hence how many of each type of atom in a molecule. This is done using the molar masses of each atom type.

$${\rm moles\ of\ Fe} = {4.601 {\rm g} \over 55.847 {\rm g/mol}} = 0.08237 {\rm mol}$$

$${\rm moles\ of\ Si} = {5.399 {\rm g} \over 28.086 {\rm g/mol}} = 0.19223 {\rm mol}$$

The ratio is:

$$0.08237:0.192234$$

$$1:{7 \over 3}$$

$$3:7$$

So the formula, which is an empirical formula, is

$${\rm Fe}_3{\rm Si}_7$$

The reason it is only an empirical formula is that if the true formula were Fe$_6$Si$_{14}$, the same percentages by mass would still hold.