The initial pressure of the system before decomposition for a first order gas phase reaction A_ (g) B_ (g) + C_ (g) was P_i . After lapse of time 't', total pressure of the system increased by 'x' units and became P_t . The rate constant 'k' for the reaction is given as:

Step-by-step solution

The given gas phase reaction is A_ (g) B_ (g) + C_ (g) . At t = 0 , the initial pressure is P_i . Pressure of A = P_i , Pressure of B = 0 , Pressure of C = 0 . At time t , let the pressure of A decrease by x . Pressure of A = P_i - x Pressure of B = x Pressure of C = x Total pressure at time t is P_t = (P_i - x) + x + x = P_i + x . From this, we get x = P_t - P_i . The partial pressure of reactant A at time t is: P_A = P_i - x = P_i - (P_t - P_i) = 2P_i - P_t For a first order reaction, the rate constant k is given