For a first order gas phase reaction- A_ (g) 2 B_ (g) +C_ (g) P₀ be initial pressure of A and P_t the total pressure at time ' t '. Integrated rate equation is

Step-by-step solution

array lccc & & A_ (g) & 2 B_ (g) +C_ (g) Initial : & P₀ & 0 & 0 & P₀-P & 2 P & P array Total pressure at time (t)=P₀-P+2 P+P=P_t aligned & P_t=P₀+2 P & P_t-P₀=2 P P= P_t-P₀ 2 k= & 2.303 t [ P₀ P₀-P ]= 2.303 t [ P₀ P₀- ( P_t-P₀ 2 ) ] = & 2.303 t ( 2 P₀ 2 P₀-P_t+P₀ )= 2.303 t ( 2 P₀ 3 P₀-P_t ) aligned