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The stability of the weakly ionized plasma and the transition from a stable homogeneous discharge to unstable filaments play an important role in gas laser physics, plasma-assisted combustion, chemical reforming, and material synthesis. Theoretical stability analysis and thermal-chemical mode analysis were performed to understand the mechanism of plasma thermal-chemical instability by using a zero-dimensional plasma system with both simplified and detailed chemical kinetics of H2/O2/N2 mixtures. The plasma dynamic and kinetic models accounted for multiple physical mechanisms in the chemically-reactive weakly ionized plasma, including ionization, attachment/detachment, recombination, vibrational and electronic energy relaxation, convective and diffusive species/heat removal, Joule heating, and detailed chemical kinetics. An analytical criterion and the explosive mode species/temperature pointers were formulated while the representative active species were identified for different thermal-chemical modes. The results showed that in addition to the classical thermal-ionization mechanism, various chemical modes from chemical heat imbalance and elementary kinetics significantly modified the time dynamics and the stability of the weakly ionized plasma. The present analysis provides insights and guidance to control plasma instability using chemical kinetics.

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