For a decomposition reaction the value of rate constant k at two different temperature 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 Calculate the value of activation energy for this reaction . (R=8.314"JK "^(-1)mol^(-1))

For a decomposition reaction the value of rate constant k at two diffe

1.	For a decomposition reaction the value of rate constant k at two different temperature 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 Calculate the value of activation energy for this reaction . (R=8.314"JK "^(-1)mol^(-1))
Answer» SOLUTION :Here `k_1=2.15xx10^(-8)"L mol"^(-1)s^(-1)""k_2=2.39xx10^(-7)"L mol"^(-1)s^(-1)` `T_1=650K, T_2=700 K and ""R=8.314"JK "^(-1)"mol"^(-1)` Using the formula `log k_2/k_1 = (E_a)/(2.303R)[(T_2-T_1)/(T_1T_2)]` `log (2.39xx10^(-7))/(2.15xx10^(-8))=E_a/(2.303xx8.314)[(700-650)/(650xx700)]` log `1.111xx10 = E_a/(19.147)xx50/(455000)` `1.0457=E_a/(19.147)XX1/(9100)` `E_a = 182202.812J " or " 182.203kJ`