Question

For a given reaction, the rate constant is k'= 2.0 * 10^-4 L*mol^-1*s^-1 at T' = 298K and k= 4.5 * 10^-3 L*mol^-1*s^-1 at T=345K Calculate the Arrhenius parameter A

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 T = 345 , T' = 298 K , K = 4.5x10^-3 L mol^-1 s^-1 , K' = 2.0x10^-4 L mol^-1 s^-1

Plug the values we get  E_a = -56.634x10³ J

log A = log K + ( E_a / 2.303RT )

= -10.92

A = 10^-10.92 = 1.20x10^-11 L mol^-1 s^-1