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For a first order reaction involving dec...

For a first order reaction involving decomposition of `N_(2) O_(5)` the following information is available :
`2N_(2)O_(5)(g) rarr 4NO_(2) (g) +O_(2)(g) `
Rate =k `[N_(2)O_(5)]`
`N_(2)O_(5)(g) rarr 2NO_(2)(g) +1//2 O_(2) (g)`
Rate =k `[N_(2)O_(5))`
Which of the following expressions is true ?

A

k=k

B

k=2k

C

k=1/2k

D

k `gt k`

Text Solution

Verified by Experts

The correct Answer is:
B
(B) `2N_(2)O_(5)(g) rarr4NO_(2) +O_(2)(g) `
Rate = `=-(1)/(2)([N_(2)O_(5)])/(dt)=2k[N_(2)O_(5)]`
or Rate=` -(d[N_(2)O_(5)])/(dt)=2k[N_(2)O_(5)]`
For `N_(2)O_(5)rarr2NO_(2)+(1)/(2)O_(2)`
`-(d[N_(2)O_(5)])/(dt)=k[N_(2)O_(5)]`
or Rate `= - (d[N_(2)O_(5)])/(dt)= k[N_(2)O_(5)]`
Since rate must be same k = 2k
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