(a)The rate constants of a reaction at 500 K and 700 K are 0.02 `s^(-1) and 0.07 s^(-1)` respectively. Calculate the value of Ea.
(b) Under what condition a bimolecular reaction behaves kinetically first order reaction ?

Explanation

(a) According to arrhenius equation
`log (K_2) /(k_1) =(E_(Act ))/( 2.303 R) [(T_2 -T_1)/(T_1 T_2)]`
`(K_2)/(K_1) = ( 0.07 )/( 0.02)=7/2`
`T_2 = 70 K`
`T_1 = 500 K`
`R=8.314 JK^(-1) Mol^(-1)`
` therefore log (7)/(2) = (E_(a))/(2.303 xx (8.314 )/( 1000 ) )[ (700 -500 )/( 700 xx 500 )]`
`E_a = log (7 )/(2) xx ( 2.303 xx 8.314 )/( 1000 ) xx (7000 xx 500 )/( 200 )`
`=( 0.5441 xx 2.303 xx 8.314 xx 700 xx 500)/( 1000 xx 200 )`
`=18.23 KJ mol^(-1)`
(b) This is possible only when the one of the reaction is present in large excess .