Integrated rate law equation for a first order gas phase reaction is given by (where \( P_i \) is initial pressure and \( P_t \) is total pressure at time \( t \))
\( k = \dfrac{2.303}{t} \times \dfrac{P_i}{(2P_i - P_t)} \)
\( k = \dfrac{2.303}{t} \times \log \!\left( \dfrac{2P_i - P_t}{P_i} \right) \)
\( k = \dfrac{2.303}{t} \times \log \!\ \dfrac{P_i}{(2P_i - P_t)} \ \)
\( k = \dfrac{2.303}{t} \times \dfrac{2P_i}{(2P_i - P_t)} \)