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The rate constant for the first order de...

The rate constant for the first order decomposition of `H_(2)O_(2)` is given by the following equation:
`logk=14.2-(1.0xx10^(4))/(T)K`
Calculate `E_(a)` for this reaction and rate constant k if its half-life period is 200 minutes.

Text Solution

Verified by Experts

From Arrhenius equation we get,
`logk=logA-(E_(a))/(2.303RT)" "...[1]`
The relation between k and T for the reaction is
`logk=14.2-(1.0xx10^(4))/(T)K" "...[2]`
Comparing equations (1) and (2), we have
`(E_(a))/(2.303R)=1xx10^(4)K thereforeE_(a)=191.47"kJ.mol"^(-1)`
For a first order reaction , `k=(0.693)/(t_(1//2))`
`thereforek=(0.693)/(200)"min"^(-1)=3.465xx10^(-3)"min"^(-1)`
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