Valency is a measure of the reactivity of an atom or molecule. You can derive the valency of many elements by looking at their positions in the periodic table, but this isn't true for all of them. It's also possible to calculate the valency of an atom or molecule by noting how it combines with other atoms or molecules with known valencies.
The Octet Rule
When determining the valency of an atom or molecule (one for which you can't use the periodic table to determine valency), chemists use the octet rule. According to this rule, atoms and chemicals combine in such a way as to produce eight electrons in the outer shell of whatever compound it is they form. An outer shell with eight electrons is full, which means the compound is stable.
When an atom or molecule has from one to four electrons in its outer shell, it has a positive valency, meaning it donates its free electrons. When the number of electrons is four, five, six or seven, you determine the valency by subtracting the electron number from 8. That's because it's easier for the atom or molecule to accept electrons to achieve stability. All the noble gases – except for helium – have eight electrons in their outermost shells and are chemically inert. Helium is a special case – it is inert, but it has only two electrons in its outermost shell.
The Periodic Table
Scientists have arranged all the elements that are currently known in a chart called the periodic table, and in many cases, you can determine valency by looking at the chart. For example, all the metals in column 1, including hydrogen and lithium, have a valency of +1, while all those in column 17, including fluorine and chlorine, have a valency of -1. The noble gases in column 18 have a valency of 0 and are inert.
You can't find the valency of copper, gold or iron using this method because they have multiple active electron shells. This is true for all the transitional metals in columns 3 through 10, the heavier elements in columns 11 through 14, the lanthanides (elements 57-71) and the actinides (elements 89-103).
Determining Valency from Chemical Formulae
You can determine the valency of a transitional element or a radical in a particular compound by noting how it combines with elements with known valency. This strategy is based on the octet rule, which tells us that elements and radicals combine so as to produce a stable outer shell of eight electrons.
As simple illustrations of this strategy, note that sodium (Na), with a valency of +1, combines readily with chlorine (Cl), which has a valency of -1, to form sodium chloride (NaCl), or table salt. This is an example of an ionic reaction in which an electron is donated by one atom and accepted by the other. However, it takes two sodium atoms to combine ionically with sulfur (S) to form sodium sulfide (Na2S), a strongly alkalizing salt used in the pulp industry. Because it takes two sodium atoms to form this compound, the valency of sulfur must be -2.
To apply this strategy to more complex molecules, it's important to first realize that elements sometimes combine to form reactive radicals which haven't yet achieved a stable outer shell of eight electrons. An example is the sulfate radical (SO4). This is a tetrahedral molecule in which the sulfur atom shares electrons with four oxygen atoms in what is called a covalent bond. In such a compound, you can't derive the valency of the atoms in the radical by looking at the formula. You can, however, determine the valency of the radical by the ionic compounds it forms. For example, the sulfate radical combines ionically with hydrogen to form sulfuric acid (H2SO4). This molecule contains two hydrogen atoms, each with a known valency of +1, so in this case, the valency of the radical is -2.
Once you have determined the valency of the radical, you can use it to calculate the valency of other elements and molecules with which it combines. For example, iron (Fe) is a transitional metal that can exhibit multiple valencies. When it combines with the sulfate radical to form ferrous sulfate, FeSO4, its valency must be +2, because the valency of the sulfate radical, as determined from the bond it forms with hydrogen, is -2.