Consider the reaction `2N_(2)O_(5)(g)rarr4NO_(2)(g)+O_(2)(g)` whose rate can be expressed any one of the following expressions `(1) (-d[N_(2)O_(5)])/(dt)=k_(1)[N_(2)O_(5)] " or " (2) (d[NO_(2)])/(dt)=k_(2)[N_(2)O_(5)] " or " (3) (d[O_(2)])/(dt)=k_(3)[N_(2)O_(5)]`
Find the relation between `k_(1),k_(2) and k_(3)` .

Explanation

Reaction -rate `=-(1)/(2)(d[N_(2)O_(5)])/(dt)=(1)/(4)(d[NO_(2)])/(dt)=(d[O_(2)])/(dt)`
`therefore-(d[N_(2)O_(5)])/(dt)=(1)/(2)(d[NO_(2)])/(dt)=2(d[O_(2)])/(dt)`
or, `k_(1)[N_(2)O_(5)]=(k_(2))/(2)[N_(2)O_(5)] =2k_(3)[N_(2)O_(5)]thereforek_(1)=(k_(2))/(2)=2k_(3)`