Assume `DeltaH^(@)` and `DeltaS^(@)` to be independent of temperature, at what temperature with the reaction given below becomes spontaneous?
`N_(2)(g) + O_(2)(g) to 2NO(g)`
`DeltaH^(@) = 180.8 kJ mol^(-1)`

Explanation

To determine the temperature at which the reaction \(N_2(g) + O_2(g) \rightarrow 2NO(g)\) becomes spontaneous, we need to analyze the Gibbs free energy change (\(\Delta G\)) for the reaction. The reaction is spontaneous when \(\Delta G < 0\).

### Step-by-Step Solution:

1. **Understand the Gibbs Free Energy Equation**:
The Gibbs free energy change is given by the equation:
\[
\Delta G = \Delta H - T \Delta S
...