# Counting Atoms in Chemical Formulas

When expressing chemical information on paper, we will make frequent use of the chemical symbols in the periodic table.  For now, let us take the chemical symbol of an element to stand for one atom of that element.  Later, we will develop a different interpretation, but for now, the present one will suffice.

Examples:

H represents one atom of hydrogen

C represents one atom of carbon

Mg represents one atom of magnesium

We write chemical formulas for compounds.  A compound will be either ionic or molecular.  If molecular, the atoms are held together by sharing electrons.  Atoms held together by sharing electrons are said to be covalently bonded.  A group of covalently bonded atoms is called a molecule.

For molecular compounds, we can write a molecular formula which indicates the number of atoms of each element in the molecule.  For example, two atoms of hydrogen and one atom of oxygen combine (share electrons) to form a molecule of water.  As everyone knows, we represent water as H2O.  This formula tells us that 2 atoms of hydrogen and one atom of oxygen are present in the molecule.

Sometimes it is necessary to have more than one atom of an element, or more than one molecule of a compound.  In these cases, we can write a number in front of the element symbol or chemical formula to indicate the number of atoms or molecules involved.

2Al represents 2 atoms of aluminum

4 Mg represents 4 atoms of magnesium

5H2O represents 5 molecules of water

3C12H22O11 represents 3 molecules of sucrose (table sugar).

The numbers that appear in front of the symbols and formulas above are called coefficients. The coefficients tell us the number of atoms (for chemical symbols) or molecules (for molecular formulas) that we are dealing with.  The small numbers that appear somewhat below the chemical symbols within chemical formulas are called subscripts.  The subscripts tell us how many atoms of each element are in the molecule.  For both coefficients and subscripts, we generally don't write their value when it is equal to 1, because a 1 is "understood" if no coefficient or subscript is written.

Many elements (for example, aluminum and magnesium, as shown above) are monatomic, that is, they consist of individual atoms.  An aluminum can, for example, is a collection of a very large number of aluminum atoms (ignoring the label that has been painted on the can).

There are a few elements, however, that exist as molecules.  There are 7 elements that exist as diatomic molecules. That is, the fundamental particles that make up a sample of these elements are pairs of atoms, rather than individual atoms.

Oxygen exists as O2.

Nitrogen exists as N2.

Hydrogen exists as H2.

Fluorine exists as F2.

Chlorine exists as Cl2.

Bromine exists as Br2.

Iodine exists as I2.

There are also a few elements that exist as molecules that have more than 2 atoms:

The form of oxygen called ozone exists as O3.

The form of phosphorous called white phosphorous exists as P4.

Sulfur is normally encountered as S8.

Note that 2N and N2 do not mean the same thing.  2N represents 2 individual atoms of nitrogen that are NOT bonded to each other. But N2 represents a single entity that we call a molecule.  It consists of 2 nitrogen atoms that ARE bonded to each other.

You can count the number of atoms of each element in a chemical formula by multiplying the coefficient by the subscript, recognizing that those coefficients and subscripts that are not shown are equal to 1.  For example, if we write 2NH3 (which is 2N1H3) we calculate the number of atoms as follows:

For N we have 2 x 1 = 2

For H we have 2 x 3 = 6

Thus, in 2 molecules of NH3, you have a total of 2 N atoms and 6 H atoms.  This is shown in Figure 1. The compounds considered so far have all been molecular compounds.  Ionic compounds do not exist as molecules.  Rather than having atoms being joined together by sharing electrons, one or more atoms lose electrons (thereby becoming positive ions) and these electrons are then gained by one or more other atoms (thereby becoming negative ions).  Since opposite charges attract one another, the positive and negative ions are held together to form (at room temperature, and even well above) a solid crystal.

Ionic compounds always form in such a way that the total positive charge is equal to the total negative charge. In this way, the ionic crystal as a whole is electrically neutral.  Because there are no discrete molecules in such compounds, all we can do in expressing the chemical formula of these substances is to express the ratio of positive ions to negative ions.  Consider ordinary table salt as an example.  Chemically, we know it as sodium chloride, NaCl.  Sodium forms the ion Na+ and chlorine forms the ion Cl- (which we call the chloride ion).  Since these ions have equal and opposite charges, there must be an equal number of Na+ ions and Cl- ions.  The simplest way to express this is a one-to-one ratio.  Thus, the formula of sodium chloride is written NaCl.  On paper, ionic formulas often don't look any different than molecular formulas, but we must be aware that it is not correct to say that NaCl represents a molecule of sodium chloride.  Rather, we say that NaCl represents a formula unit of sodium chloride.  It is true that for every Na+ ion in the crystal, there is a Cl- ion.  However, we can not identify any particular Cl- ion as "belonging" to any particular Na+ ion.  In the case of a molecule, particular atoms can be identified as belonging to each other -- that is, being part of the same group of atoms that make up a particular molecule.

We take the formula unit of an ionic compound to represent the smallest possible amount of that compound, in the same way that we take a molecule to represent the smallest possible amount of a molecular compound.  Thus the smallest quantity of sodium chloride that we can have -- and still recognize it as sodium chloride -- is one sodium ion and one chloride ion.

Often, it is no more difficult to count the atoms in ionic formulas than it is in molecular formulas.  Consider the following examples:

MgCl2:

For Mg we have 1 x 1 = 1    (1 Mg2+ ion in formula)

For Cl we have 1 x 2 = 2    (2 Cl- ions in formula)

2Al2O3:

For Al we have 2 x 2 = 4    (4 Al3+ ions total in the two formula units)

For O we have 2 x 3 = 6    (6 O2- ions total in the two formula units)

It becomes slightly more difficult to count the atoms in ionic formulas when they contain polyatomic ions that occur more than once in the formula.   In these cases, the subscrips within the polyatomic ion must be multiplied by the subscript that appears outside the parentheses.  If a coefficient is present, it must also be multiplied, meaning sometimes there will be three numbers to multiply together to calculate the number of atoms of a particular element.  Consider the following examples:

(NH4)2CO3:

For N we have 1 x 2 = 2    (multiplying subscript of N by subscript of group)

For H we have 4 x 2 = 8    (multiplying subscript of H by subscript of group)

For C we have 1    (coefficient of formula, subscript of C and subscript of group are all 1)

For O we have 3    (subscript of O is 3, coefficient of formula and subscript of group are 1)

If you have trouble understanding the above, it may help to recall that (NH4)2CO3 is literally 1(NH4)2(CO3)1.  Written in this form, you can clearly see the coefficient in front of the formula, and the subscript of the carbonate group, both of which are 1.

A still more complicated case is when an element appears in more than one place in the formula.  For example, lets count the atoms in 5(NH4)2HPO4.  We must be careful because H atoms appear both in the NH4 group and in the HPO4 group.  The entire formula is taken 5 times, and each formula includes the NH4 group twice.  Overall, we have 10 NH4 groups and 5 HPO4 groups.

For N we have 5 * 1 * 2 = 10
(multiplying coefficeint, subscript within group, and subscript outside of group)

For H we have 5 * 4 * 2 + 5 * 1 * 1 = 40 + 5 = 45
(for each group, multiplying coefficient, subscript in group and subscript outside of group)

For P we have 5 * 1 * 1 = 5
(Multiplying coefficeint, subscript within group, and subscript outside group)

For O we have 5 * 4 * 1 = 20
(Multiplying coefficient, subscript within group, and subscript outside group)

If you have trouble understanding the above, it may help to recall that 5(NH4)2HPO4 is literally 5(NH4)2(HPO4)1.  Written in this way, the subscript of the HPO4 group is clearly visible.  However, while writing it this way may help with problem solving, we must keep in mind that 1's are not usually written as coefficients or subscripts.