Question

In: Chemistry

Determine the activation energy in kJ/mol for a first order reaction if its specific rate constant...

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

Expert Solution

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

queen_honey_blossom answered 1 year ago

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