= Solution
For fixed degeneracies and <ionization energy>,
$$
\frac{\mathrm d\ln K_c}{\mathrm dT}
=\frac{3}{2T}+\frac{E_I}{k_{\rm B}T^2}>0.
$$
Therefore \b[$K_c$ increases with <temperature>] in this model. Ionization costs positive <energy>, so it is suppressed at low <temperature> by its <Boltzmann factor>. At higher <temperature> that penalty becomes less important.
Ionization also creates an additional independently translating particle and more ways to distribute the particles and their momenta. This favours the ionized mixture through its translational and mixing <entropy>, consistent with the $T^{3/2}$ prefactor and increasing ionization at high <temperature>.
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