The formula of mercury (l) dioxonitrate (III) is

The formula of a compound gives the type and number of atoms that are present in a molecule of that compound. To determine the formula of mercury (l) dioxonitrate (III), we need to determine the oxidation states of the atoms present in the compound. The symbol Hg represents the element mercury, which has a valence of +1 in this compound. The symbol NO\(_2\) represents the nitrite ion, which has a valence of -1. The Roman numeral III indicates that the compound contains three nitrite ions. To balance the charges of the mercury ion and the nitrite ions, we need two nitrite ions for every mercury ion. This gives us the formula Hg\(_2\)(NO\(_2\))\(_2\), and the correct option is (C) Hg\(_2\)(NO\(_2\))\(_2\).