Where are atoms that tend to gain electrons located in the periodic table of the elements?

Just take a look! Oxygen, sulfur, the halogens ... these elements all frequently form negative ions when reacted with, say, a metal, to form a salt through ionic bonding.

The rough explanation for this can be found in the trends exhibited by certain properties of elements moving through the table. One will find that, in the top right of the table, elements have very negative electron affinity and high electronegativity values.

Electron affinity is, in fact, the tendency of an atom of an element to gain an electron, expressed in terms of the enthalpy change when an electron is gained. One finds that for atoms likely to form negative ions, i.e. to gain electrons by a chemical process, this enthalpy change is negative - energy is liberated. We can roughly say here that the more exothermic a chemical change is, the more favourable it is and so the more likely it is to occur.

Electronegativity can also be related to this tendency, with electrons in the top right section of the table showing considerably higher values because of a particularly high nuclear charge density with respect to the atom as a whole. Although electronegativity applies within the context of covalent bonding electron withdrawal, this principal can also be used to understand why the halogens - and, of course, oxygen - are quite effective oxidising agents.