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Thermal rates for the C($^3$P) + O$_2$($^3 \Sigma_g^-$) $\leftrightarrow$CO($^1 \Sigma^+$)+ O($^1$D)/O($^3$P) reaction are investigated over a widetemperature range based on quasi classical trajectory (QCT) simulations on3-dimensional, reactive potential energy surfaces (PESs) for the $^1$A$'$,$(2)^1$A$'$, $^1$A$''$, $^3$A$'$ and $^3$A$''$ states. The forward rate matchesmeasurements at 15 K to 295 K whereas the equilibrium constant determined fromthe forward and reverse rates are consistent with those derived fromstatistical mechanics at high temperature. Vibrational relaxation, O+CO($\nu=1,2$) $\rightarrow$ O+CO$(\nu=0)$, is found to involve both, non-reactive andreactive processes. The contact time required for vibrational relaxation totake place is $\tau \geq 150$ fs for non-reacting and $\tau \geq 330$ fs forreacting (oxygen atom exchange) trajectories and the two processes are shown toprobe different parts of the global potential energy surface. In agreement withexperiments, low collision energy reactions for the C($^3$P) + O$_2$($^3\Sigma_g^-$, $v=0$) $\rightarrow$ CO($^1 \Sigma^+$)+ O($^1$D) lead toCO($^{1}\Sigma^{+}$, $v'=17$) with an onset at $E_{\rm c} \sim 0.15$ eV,dominated by the $^1$A$'$ surface with contributions from the $^3$A$'$ surface.Finally, the barrier for the CO$_{\rm A}$($^1\Sigma^+$) + O$_{\rm B}$($^3$P)$\rightarrow$ CO$_{\rm B}$($^{1}\Sigma^{+}$) + O$_{\rm A}$($^3$P) atom exchangereaction on the $^3$A$'$ PES yields a barrier of $\sim 7$ kcal/mol (0.300 eV),consistent with an experimentally reported value of 6.9 kcal/mol (0.299 eV).

The C($^3$P) + O$_2$($^3 \Sigma_g^-$) $\leftrightarrow$ CO$_2$  $\leftrightarrow$ CO($^1 \Sigma^+$)+ O($^1$D)/O($^3$P) Reaction: Thermal and  Vibrational Relaxation Rates from 15 K to 20000 K