The decomposition of N_(2)O_(5) according to following reaction is first order reaction : 2N_(2)O_(5)(g) rarr 4NO_(2)(g) + O_(2) (g) After 30 min. from start of the decomposition in a closed vessel, the total pressure developed is found to be 284.5 mm of Hg and on complete decomposition, the total pressure is 584.5 mm of Hg. Calculate the rate constant of the reaction.

The decomposition of N_(2)O_(5) according to following reaction is fir

1.	The decomposition of N_(2)O_(5) according to following reaction is first order reaction : 2N_(2)O_(5)(g) rarr 4NO_(2)(g) + O_(2) (g) After 30 min. from start of the decomposition in a closed vessel, the total pressure developed is found to be 284.5 mm of Hg and on complete decomposition, the total pressure is 584.5 mm of Hg. Calculate the rate constant of the reaction.
Answer» <P> Solution :`2N_(2)O_(5)(g)rarr4NO_(2)(g)+O_(2)(g)` `P_(0):` initial pressure , LET `P_(t)` : pressure at 30 MIN and `P_(oo)` : pressure at the end of decompositon. `rArr " "P_(t) =P)(0)+3x` `rArr " "x=(1)/(3) (P_(t)-P_(0)) and P_(oo) =2P_(0)+(1)/(2)P_(0)=(5)/(2)P_(0)` `rArr" "P_(0)=(2)/(5) P_(oo)` For the first order kinetics `k_("eff")t=2.303 log_(10)""(A_(0))/(A)` `A_(0):` initial concentration , A: final concentration Now `" "(A_(0))/(A) =(P_(0))/(P_(0)-2x)=((1)/(5)P_(oo))/((1)/(5)P_(oo)-2(P_(t)-2//5P_(oo))/(3))` `rArr" "(A_(0))/(A) =(3)/(5)((P_(oo))/(P_(oo)-P_(t)))` `rArr" "k_("eff") =(1)/(30)xx2.303 log_(10)""(3)/(5) XX(584.5)/(584.5-284.5)` `=5.204xx10^(-3)" min"^(-1)` k for the reaction `=(5.204)/(2)xx10^(-3)=2.602xx10^(-3)" min"^(-1)`