Activation energy (Ea) and rate constants (k1 and k2) of a chemical reaction at two different temperatures (T1 and T2) are related by
- k2k1 = - EaR ( 1T1 - 1T2 )
- k2k1 = - EaR ( 1T2 - 1T1 )
- k2k1 = - EaR ( 1T2 + 1T1 )
- k2k1 = EaR ( 1T1 - 1T2 )
Answer
(2) k2k1 = - EaR ( 1T2 - 1T1 ), (4) k2k1 = EaR ( 1T1 - 1T2 )
Solution
Arrhenius equation: k = A - EaRT
At T1: k1 = A - EaRT1; at T2: k2 = A - EaRT2
Subtracting:
k2k1 = EaR ( 1T1 - 1T2 ) ⇒ option (4)
Taking the minus sign outside:
k2k1 = - EaR ( 1T2 - 1T1 ) ⇒ option (2)
Option (1) has the wrong sign and option (3) has a sum instead of a difference.
Answer: (2), (4)