I know that molecules such as NO2 is a free radical because of the one electron that is not bonded, but are molecules like H2O or O2 also free radicals as they have lone pairs of electrons?
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No. A free radical is an element, compound or ion with an odd number of electrons, which will make at least one electron unpaired. It's the unpaired electron which makes a substance a free radical, not non-bonding electrons. Many substances have nonbonding electrons, and if they are paired then the substance is not a free radical. Water is not a free radical. Oxygen has two lone pairs, but the emphasis is on pairs of electrons. It's a different matter for O2. Both atomic oxygen and molecular oxygen are radicals (diradicals) since they each have two unpaired electrons. The confusion lies in a common misconception. O2 molecules are not well represented by Lewis diagrams which show all of the electrons paired. Yet O2 is paramagnetic, which means that it has at least one unpaired electron. In fact O2 has two unpaired electrons. Only the molecular orbital diagram of O2 correctly shows the double bond and the two unpaired electrons for O2.