For a reaction taking place in three steps, the rate constants are k1, k2 and k3 and overall rate constant is k=(k1k3/k2)⋅ If the energies of activation E1, E2 and E3 are 60 , 30 and 10 kJ mol-1 , respectively, then the overall energy of activation is

Question

For a reaction taking place in three steps, the rate constants are k1, k2 and k3 and overall rate constant is k=(k1k3/k2)⋅ If the energies of activation E1, E2 and E3 are 60 , 30 and 10 kJ mol-1 , respectively, then the overall energy of activation is (A)  30 kJ mol- 1  (B)  40 kJ mol- 1  (C)  60 kJ mol- 1  (D)  100 kJ mol- 1

Tardigrade Admin · Accepted Answer

Given, K=(k1k3/k2) From Arrhenius equation, k=Ae-Ea/RT Ae-Ea /RT=(Ae-E1 /RT⋅ Ae-E3 /RT/Ae-E2 /RT) ∴ Ea=E1+E3-E2=60+10-30 =70-30=40 kJ mol-1

$30 k J m o l^{- 1}$

$40 k J m o l^{- 1}$

$60 k J m o l^{- 1}$

$100 k J m o l^{- 1}$

Given, $K = \frac{k _{1} k _{3}}{k _{2}}$
From Arrhenius equation, $k = A e^{- E_{a} / RT}$
$A e^{- E_{a} / RT} = \frac{A e ^{- E_{1} / RT} \cdot A e ^{- E_{3} / RT}}{A e ^{- E_{2} / RT}}$
$∴ E_{a} = E_{1} + E_{3} - E_{2} = 60 + 10 - 30$
$= 70 - 30 = 40 k J m o l^{- 1}$

Q. For a reaction taking place in three steps, the rate constants are k1​,k2​ and k3​ and overall rate constant is k=k2​k1​k3​​⋅ If the energies of activation E1​,E2​ and E3​ are 60 , 30 and 10kJmol−1 , respectively, then the overall energy of activation is

30kJmol−1

40kJmol−1

60kJmol−1

100kJmol−1

Given, K=k2​k1​k3​​ From Arrhenius equation, k=Ae−Ea​/RT Ae−Ea​/RT=Ae−E2​/RTAe−E1​/RT⋅Ae−E3​/RT​ ∴Ea​=E1​+E3​−E2​=60+10−30 =70−30=40kJmol−1

$30 k J m o l^{- 1}$

$40 k J m o l^{- 1}$

$60 k J m o l^{- 1}$

$100 k J m o l^{- 1}$

Given, $K = \frac{k _{1} k _{3}}{k _{2}}$
From Arrhenius equation, $k = A e^{- E_{a} / RT}$
$A e^{- E_{a} / RT} = \frac{A e ^{- E_{1} / RT} \cdot A e ^{- E_{3} / RT}}{A e ^{- E_{2} / RT}}$
$∴ E_{a} = E_{1} + E_{3} - E_{2} = 60 + 10 - 30$
$= 70 - 30 = 40 k J m o l^{- 1}$