The gas-phase oxidation of nitric oxide proceeds according to the following overall balanced equation:

\[ 2\text{ NO}(g) + \text{O}_2(g) \rightarrow 2\text{ NO}_2(g) \]

A proposed two-step reaction mechanism for the process is shown below:

Step 1 (fast equilibrium):
\[ 2\text{ NO}(g) \underset{k_{-1}}{\overset{k_1}{\rightleftharpoons}} \text{N}_2\text{O}_2(g) \]

Step 2 (slow):
\[ \text{N}_2\text{O}_2(g) + \text{O}_2(g) \xrightarrow{k_2} 2\text{ NO}_2(g) \]

At a certain temperature, the elementary rate constants have the values \(k_1 = 4.0 \times 10^3\text{ M}^{-1}\text{s}^{-1}\), \(k_{-1} = 2.0 \times 10^2\text{ s}^{-1}\), and \(k_2 = 5.0 \times 10^1\text{ M}^{-1}\text{s}^{-1}\). The overall rate law is expressed as \(\text{Rate} = k_{\text{obs}} [\text{NO}]^2 [\text{O}_2]\). What is the value of the observed rate constant, \(k_{\text{obs}}\)?