If it is assumed that the enthalpy of reaction, \(Q_{p}\), is a constant, show that the value of \(K_{p}\) is given by

\[K_{p}=\mathrm{e}^{-Q_{p} / \Re T+k}\]

where \(k\) is a constant.

For a particular reaction \(Q_{p}=-277346 \mathrm{~kJ} / \mathrm{kmol}\) and \(K_{p}=748.7\) at \(T=2000 \mathrm{~K}\). Evaluate \(K_{p}\) at the temperature of \(2500 \mathrm{~K}\). [26.64]