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

Explanation

Substitute the values in the Arrhenius equation given below:
`"log"(k_(2))/(k_(1))=(E_(a))/(2.303R)[(T_(2)-T_(1))/(T_(1)T_(2))]`
`"or log"(2.39xx10^(-7))/(2.15xx10^(-8))=(E_(a))/(2.303xx8.314)[(700-650)/(650xx700)]`
`"or log "11.116=(E_(a))/(19.147)xx(50)/(650xx700) or 1.0461=(E_(a))/(19.147)xx(50)/(455000)`
or `E_(a)=(1.0461xx19.147xx455000)/(50)=182270J or 182.27kJ`