A sample of pure \(\text{NO}_2\text{(g)}\) is introduced into a rigid, evacuated container at a constant temperature of \(298\text{ K}\) until its initial pressure reaches \(1.00\text{ atm}\). The dimerization reaction occurs according to the balanced equation below.

\[ 2\,\text{NO}_2\text{(g)} \rightleftharpoons \text{N}_2\text{O}_4\text{(g)} \]

After the system reaches chemical equilibrium, the partial pressure of \(\text{N}_2\text{O}_4\text{(g)}\) is measured to be \(0.40\text{ atm}\). What is the value of the equilibrium constant, \(K_p\), for the reaction at this temperature?