2,4-dinitrophenol (DNP) and trifluorocarbonylcyanide phenylhydrazone (FCCP) exemplify a class of compounds called uncoupling agents. They are so named because they permeabilize the inner mitochondrial membrane to protons, destroying the proton gradient and, in doing so, uncouple the electron transport system from the oxidative phosphorylation system. That is, electrons continue to pass through the electron transport system and reduce oxygen to water, but ATP is not synthesized in the process.
In the case of DNP, the phenolic group is usually dissociated at intracellular pH. However, a DNP molecule that approaches the inner mitochondrial membrane from the outside becomes protonated (because the pH is lower there). Protonation increases the hydrophobicity of DNP, allowing it to diffuse into the membrane and, by mass action, to pass through. Once inside, the higher pH of the matrix deprotonates the phenolic hydroxyl again. Thus, DNP has the effect of transporting H+ back into the matrix, bypassing the F0 proton channel and thereby preventing ATP synthesis.