The decomposition of N_(2)O_(5) according to the equation2N_(2)O_(5)(g)rarr4NO_(2)(g)+O_(2)(g)is a first order reaction. After 30min, from the start of the decomposition in a closed vessel, total pressure developed is 284.5 mm Hg. On complete decomposition, total pressure is 584.5mm Hg. Calculate the rate constant of reaction .

The decomposition of N_(2)O_(5) according to the equation2N_(2)O_(5)(g

1.	The decomposition of N_(2)O_(5) according to the equation2N_(2)O_(5)(g)rarr4NO_(2)(g)+O_(2)(g)is a first order reaction. After 30min, from the start of the decomposition in a closed vessel, total pressure developed is 284.5 mm Hg. On complete decomposition, total pressure is 584.5mm Hg. Calculate the rate constant of reaction .
Answer» Solution :Given REACTION `2N_(2)O_(5)(g)rarr4NO_(2)(g)+O_(2)(g)` `""N_(2)O_(5)(g)rarr2NO_(2)(g)+(1)/(2)O_(2)(g)` `{:("Initial no.of moles:",""a,0,0),("No.of moles at TIME t:",(a-x),2x,x//2),("No. of moles after",,,),("COMPLETE decomposition",0,2a,a//2):}` `therefore` Total no.of moles after complete decomposition `=2a+(a)/(2)=(5)/(2)a` At a given volume and temperature , `pprop n` [ Assuming ideal behaviour of GAS mixture] According to the given data, `(5)/(2)a prop584.5mmHg""....[1]` and`(3)/(2)x prop284.5mmHg""....[2]` or, `thereforeaprop233.8mmHg and (3)/(2)xprop284.5-a` or, `(3)/(2)xprop284.5-233.8prop50.7"mmHg " thereforexprop33.8 mm HG` Therefore ,`(a-x)prop(233.8-33.8)"mmHg"` i.e., `(a-x)prop"mm Hg"` `thereforek=(2.303)/(t)log.(a)/(a-x)=(2.303)/(30)log.(233.8)/(200)` or,`k=5.21xx10^(-3)"min"^(-1)`