Anions are atoms or groups of atoms that have gained electrons. Having more negatively charged electrons than positively charged protons, they are negatively charged. The atoms that form ions most easily are the Group 17 (or VII) atoms, also called the halides: F, Cl, Br and I. All these form anions with a -1 charge. O, S, N and P also form anions, carrying charges of -2 (oxygen and sulfur) or -3 (N and P). Check the locations of these elements in the periodic table if you are not already familiar with them.
Most anions are composed from multiple atoms, and are called polyatomic ions (polyatomic = many atoms). Polyatomic ions are usually built around a core atom which is more often than not a non-metal, but some metals, notably manganese and chromium, form polyatomic ions as well. In most polyatomic ions, these atoms combine with oxygen and sometimes with hydrogen as well. As with every other generalisation, there are exceptions. For example, SCN-, the thiocyanate ion, is polyatomic, but has neither oxygen nor hydrogen. (Worse, NH4+ is polyatomic, but is a cation!) But back to the story.
The negative charge (the extra electron) in the polyatomic ion is shared around the entire ion. It is not associated with a particular nucleus in the ion, specifically not with the nucleus to which oxygen and/or hydrogen are attached. This is true whether the charge is single or multiple.
The Table of Common Ions lists the more common anions. (How about that?) Note that, with the exceptions of hydroxide (OH) and cyanide (CN-), all the names ending in -ide are monatomic. The rest are -ates or -ites. In the days of yore, chemists gathered samples of anions and then tried to give them some order. The rules they came up with went like this:
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Related Topic: Ions
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