A reactant (A) forms two products A xrightarrowk1 B Activation energy Ea1 A xrightarrowk2 B Activation energy Ea2 If Ea2 = 2Ea1 then k1 and k2 are related as

Question

A reactant (A) forms two products A xrightarrowk1 B Activation energy Ea1 A xrightarrowk2 B Activation energy Ea2 If Ea2 = 2Ea1 then k1 and k2 are related as (A) k1=2k2eEa2/RT (B) k1=k2eEa1/RT (C) k2=k1eEa2/RT (D) k1=A k2eEa1/RT

Tardigrade Admin · Accepted Answer

A xrightarrowk1 B, A xrightarrowk2 B By Arrhenius equation, k1=AeEa1/RT and k2=AeEa2/RT [A' is Arrhenius constant] ∵(k1/k2)=(Ae-Ea1/RT/Ae-2Ea1/RT)=eEa1/RT ∴ k1=k2eEa1/RT

Q. A reactant $(A)$ forms two products
$A k_{1} B$ Activation energy $E_{a 1}$
$A k_{2} B$ Activation energy $E_{a 2}$
If $E_{a 2} = 2 E_{a 1}$ then $k_{1}$ and $k_{2}$ are related as

$k_{1} = 2 k_{2} e^{E_{a 2/ RT}}$

$k_{1} = k_{2} e^{E_{a 1/ RT}}$

$k_{2} = k_{1} e^{E_{a 2/ RT}}$

$k_{1} = A k_{2} e^{E_{a 1/ RT}}$

$A k_{1} B, A k_{2} B$
By Arrhenius equation, $k_{1} = A e^{E_{a 1/ RT}}$
and $k_{2} = A e^{E_{a 2/ RT}}$
[A' is Arrhenius constant]
$∵ \frac{k _{1}}{k _{2}} = \frac{A e ^{- E_{a 1} / RT}}{A e ^{- 2 E_{a_{1} / RT}}} = e^{E_{a 1/ RT}}$
$∴ k_{1} = k_{2} e^{E_{a 1/ RT}}$

Q. A reactant (A) forms two products Ak1​​B Activation energy Ea1​ Ak2​​B Activation energy Ea2​ If Ea2​=2Ea1​ then k1​ and k2​ are related as

k1​=2k2​eEa2/RT​

k1​=k2​eEa1/RT​

k2​=k1​eEa2/RT​

k1​=Ak2​eEa1/RT​

Ak1​​B,Ak2​​B By Arrhenius equation, k1​=AeEa1/RT​ and k2​=AeEa2/RT​ [A' is Arrhenius constant] ∵k2​k1​​=Ae−2Ea1​/RT​Ae−Ea1​/RT​=eEa1/RT​ ∴k1​=k2​eEa1/RT​