The decomposition of A into product has value of k as `4.5xx10^(3)s^(-1)` at 10 `""^(@)C` and energy of activation 60 kJ `"mol"^(-1)`. At what temperature would k be `1.5xx10^(4)s^(-1)`?

Explanation

`k_(1)=4.5xx10^(3)s^(-1), T_(1)=10+273K=283K, k_(2)=1.5xx10^(4)s^(-1), T_(2)=?, E_(a)=60"kJ mol"^(-1)`
Applying Arrhenius equation and substituting the values, we get
`"log"(k_(2))/(k_(1))=(E_(a))/(2.303R)((T_(2)-T_(1))/(T_(1)T_(2)))`
or `"log"(1.5xx10^(4))/(4.5xx10^(3))=(E_(a))/(RT)= -(60000"J mol"^(-1))/(2.303xx8.314JK^(-1)"mol"^(-1))((T_(2)-283)/(283T_(2)))`
or `log 3.333=3133.63 ((T_(2)-283)/(283T_(2))) or (0.5228)/(3133.63)=(T_(2)-283)/(283T_(2))`
or `0.0472T_(2)=T_(2)-283 or 0.9528T_(2)=283`
or `T_(2)=(283)/(0.9528)=297K=(297-273)""^(@)C=24""^(@)C`.