For a decomposition reaction, the values of rate constant k at two different temperatures are given below:
` K_1 = 2.15 xx 10 ^(-8) L mol^(-1) s^(-1) at 650 K`
` K_2 = 2.39 xx 10^(-7) L mol s^(-1) at 700 K`
Calculate the value of activation energy for this reaction. (R = `8.314 JK ^(-1) mol^(-1)`)

Explanation

Applying Arrhenius equation,
`log "" (k_2)/(k_1)= (E_a)/( 2.303 R) ([T_2-T_1])/(T_1 T_2)`
Substituting the values
` log ( 2.39 xx 10^(-7) )/( 2.15 xx 10^(-8)) = (E_a)/(2.303 xx 8.314 )[(400-650 )/(650 xx 700 )]`
` or log 11.116 = (E_a)/( 19.147 ) xx (50)/(455000 )`
` or 1.046 = (E_a)/( 19.147 ) xx ( 50 )/( 455000 )`
` or 1.046 = (E_a)/( 19.147 ) xx (50 )/(455000 )`
` or E_a = ( 1.046 xx 19.147 xx 455000 )/(50 ) = 182252.6 J = 182.25 KJ`