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For a decomposition reaction the values ...

For a decomposition reaction the values of rate constant k at two different temperatures are given below :
`K_(1)=2.15xx10^(-8)L"mol"^(-1)s^(-1)"at " 650K`
`K_(2)=2.39xx10^(-7)L"mol"^(-1)s^(-1)"at " 700K`
Calclate the value of activation energy for this reaction.
`(R=8.314JK^(-1)"mol"^(-1))`

Text Solution

Verified by Experts

`"log"(k_(2))/(k_(1))=(E_(a))/(2.303k)((T_(2)-T_(1))/(T_(1)T_(2)))`
`E_(a)=((2.303xxRxxT_(1)xxT_(2))/(T_(2)-T_(1)))"log"(k_(2))/(k_(1))`
`E_(a)=(2.303xx8.314 J "mol"^(-1)k^(-1)xx650kxx700k)/(700k-650k)"log"(2.39xx10^(-8))/(2.15xx10^(-8))`
`E_(a)=(19.147xx650xx700)/(50)"log"(23.9-"log"2.15) J "mol"^(-1)`
`E_(a) 174237.7(1.3783-0.3324) J "mol"^(-1)`
`E_(a)=174237.7xx1.0459 J "mol"^(-1)`
`E_(a)=1822235.2 J "mol"^(-1)`
`E_(a)=182.24 KJ "mol"^(-1)`
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