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Arrhenius Equation

Ak1→B, Activa...

Question

$A_{1}$ B, Activation Energy $E a_{1}$
$A_{2}$ C, Activation Energy $E a_{2}$
If $E a_{2} = 2 E a_{1}$ , then $k_{1}$ and $k_{2}$ are related as:

A

k_{1} = 2 k_{2} e^{E a_{2} / R T}

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B

k_{2} = k_{1} e^{E a_{1} / R T}

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C

k_{2} = - k_{1} e^{k a_{2} / R T}

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D

k_{1} = k_{2} e^{E a_{1} / R T}

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Solution

The correct option is C $k_{1} = k_{2} e^{E a_{1} / R T}$
The rate constant $k$ and the activation energy $E_{a}$ can be related by the Arrhenius equation.
$\Rightarrow k_{1} = {A e}^{- E_{a} / R T} ⟶ (1) \Rightarrow k_{2} = {A e}^{- E_{a} / R T} ⟶ (2) N o w, E_{a_{2}} = {2 E}_{a_{1}}$
Putting in $(2) . k_{2} = {A e}^{- 2 E_{a_{1}} / R T} ⟶ (3)$
From $(3) & (1) \frac{k_{2}}{k_{1}} = \frac{{A e}^{- 2 E_{a_{1}} / R T}}{{A e}^{- E_{a_{1}} / R T}} k_{2} = {k_{1} e}^{- E_{a_{1}} / R T}$
Hence, the constant $k_{1}$ and $k_{2}$ are related as $k_{2} = {k_{1} e}^{- E_{a_{1}} / R T}$

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Similar questions

Q. A reactant (A) forms two products.

A k_{1} - \to B

, Activation energy

E a_{1}

A k_{2} - \to C

, Activation energy

E a_{2}

E a_{2} = 2 E a_{1}

k_{1}

k_{2}

are related as:

(A)

forms two products:

A k_{1} - ---- \to B

, Activation energy

E_{a_{1}}

and Pre-exponential factor

A

A k_{2} - ---- \to C

, Activation energy

E_{a_{2}}

and Pre-exponential factor

A

E_{a_{2}} = 2 E_{a_{1}}

k_{1}

k_{2}

will be related as:

Q. For reaction;

A \to B

, the rate of constant

k_{1} = A_{1} e^{- E a_{1} / R T}

and for the reaction;

P \to Q

, the rate constant

k_{2} = A_{2} e^{- E a_{2} / R T}

A_{1} = 10^{8}, A_{2} = 10^{10}

E a_{1} = 600, E a_{2} = 1200

, then the temperature at which

k_{1} = k_{2}

Q. For two reactions, activation energies are

E_{a_{1}}

E_{a_{2}}

; rate constants are

k_{1}

k_{2}

at the same temperature. If

k_{1} > k_{2}

Q. For a reaction

A ⟶ B

, the rate constant

k_{1} = A_{1} e^{- {E a}_{1} / (R T)}

and for the reaction

X ⟶ Y

, the rate constant

k_{2} = A_{2} e^{- {E a}_{2} / (R T)}

A_{1} = 10^{8}, A_{2} = 10^{10}

{E a}_{1} = 600 c a l / m o l, {E a}_{2} = 1800 c a l / m o l

, then the temperature at which

k_{1} = k_{2}

R = 2 c a l / k m o l

)

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