To solve this problem, you'll need the thermodynamic properties ($\Delta H^\circ_f$ and $S^\circ$) for each of the species involved in the reaction: $\text{NO}_2$, $\text{CO}$, $\text{NO}$, and $\text{CO}_2$. Let me guide you step by step:

Steps to Solve:

1. Calculate $\Delta H^\circ_\text{rxn}$: Use the formula: $\Delta H^\circ_\text{rxn} = \sum \Delta H^\circ_f (\text{products}) - \sum \Delta H^\circ_f (\text{reactants})$

2. Calculate $\Delta S^\circ_\text{rxn}$: Use the formula: $\Delta S^\circ_\text{rxn} = \sum S^\circ (\text{products}) - \sum S^\circ (\text{reactants})$

3. Calculate $\Delta G^\circ_\text{rxn}$: Use the Gibbs free energy equation: $\Delta G^\circ_\text{rxn} = \Delta H^\circ_\text{rxn} - T \Delta S^\circ_\text{rxn}$ where $T$ is the temperature in Kelvin (convert $25^\circ C$ to $298 \, \text{K}$).

Let me know if you have the table of thermodynamic properties, or if you'd like me to use standard reference values to calculate these quantities for you. Alternatively, I can guide you through filling in each part based on your provided data.