  Plasma-activated chemical transformations promise the efficient synthesis of
salient chemical products. However, the reaction pathways that lead to
desirable products are often unknown, and key quantum-state-resolved
information regarding the involved molecular species is lacking. Here we use
quantum cascade laser dual-comb spectroscopy (QCL-DCS) to probe
plasma-activated NH$_3$ generation with rotational and vibrational state
resolution, quantifying state-specific number densities via broadband spectral
analysis. The measurements reveal unique translational, rotational and
vibrational temperatures for NH$_3$ products, indicative of a highly reactive,
non-thermal environment. Ultimately, we postulate on the energy transfer
mechanisms that explain trends in temperatures and number densities observed
for NH$_3$ generated in low-pressure nitrogen-hydrogen (N$_2$-H$_2$) plasmas.
