Question

Determine the activation energy in kJ/mol for a first order reaction if its specific rate constant 8.30e-05 s^-1 at 350.0 K and 3.25e+01 s^-1 at 560.0 K.

E_a = ______ kJ/mol

Answer 1

According to Arrhenius Equation , K = A e ^{-Ea / RT}

Where

K = rate constant

T = temperature

R = gas constant = 8.314 J/mol-K

E_a = activation energy

A = Frequency factor (constant)

Rate constant, K = A e ^{- Ea / RT}

                  log K = log A - ( E_a / 2.303RT )   ---(1)

If we take rate constants at two different temperatures, then

                log K = log A - ( E_a / 2.303RT )   --- (2)

    &         log K' = log A - (E_a / 2.303RT’)    ---- (3)

Eq (3 ) - Eq ( 2 ) gives

log ( K' / K ) = ( E_a / 2.303 R ) x [ ( 1/ T ) - ( 1 / T' ) ]

              E_a = [(2.303R x T x T’) / (T’ - T)] x log (K’ / K)  

Given K = 8.30x10^-5 s^-1

K' = 3.25x10⁺¹ s^-1

T = 350.0 K

T' = 560.0K

Plug the values we get   E_a = 99.9x10³ J/mol

= 99.9 kJ/mol