The chemistry and kinetics of the nitridation of GaAs (100) surfaces by ${\mathrm{N}}_{2},$ ${\mathrm{N}}_{2}{\ensuremath{-}\mathrm{H}}_{2},$ and ${\mathrm{N}}_{2}{\ensuremath{-}\mathrm{N}\mathrm{H}}_{3}$ radio-frequency plasmas, in a remote configuration, are investigated in situ and in real time using spectroscopic ellipsometry. The effects of the surface temperature in the range 70--700 \ifmmode^\circ\else\textdegree\fi{}C and of the gas-phase chemistry on both the nitridation kinetics and the composition of the resulting GaN layer are highlighted. Pure ${\mathrm{N}}_{2}$ plasmas yield stoichiometric and smooth GaN layers with As segregation at the GaN/GaAs interface. The As segregation inhibits GaAs nitridation, because the N atoms scavenge the free As, and thereby limits the GaN thickness to a few angstroms. Thicker GaN layers (g100 \AA{}) are obtained by ${\mathrm{N}}_{2}{\ensuremath{-}\mathrm{H}}_{2}$ and ${\mathrm{N}}_{2}{\ensuremath{-}\mathrm{N}\mathrm{H}}_{3}$ plasmas, since hydrogen reduces the As segregation by the formation and desorption of ${\mathrm{AsH}}_{x}$ species. For the three plasma mixtures, the self-limiting nature of the GaAs nitridation process is revealed and explained using simple kinetic and chemical models based on the fact that the GaAs nitridation can be considered to be a topochemical reaction. Also demonstrated is the ineffectiveness of the nitridation at $Tg~600\ifmmode^\circ\else\textdegree\fi{}\mathrm{C},$ which is accompanied by the GaAs substrate decomposition and yields both a rough and Ga-rich GaN layer.