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Question: A reactant (1) forms two products : \(A\overset{\quad k_{1}\quad}{\rightarrow}B,\) Activation Energ...

A reactant (1) forms two products :

Ak1B,A\overset{\quad k_{1}\quad}{\rightarrow}B, Activation Energy Ea1 ;

Ak2C,A\overset{\quad k_{2}\quad}{\rightarrow}C, Activation Energy Ea2 If Ea2 = 2 Ea1, then k1 and k2 are related as :

A

k2=k1eEa1/RTk_{2} = k_{1}e^{Ea_{1}/RT}

B

k2=k1eEa2/RTk_{2} = k_{1}e^{Ea_{2}/RT}

C

k1=k2eEa1/RTk_{1} = k_{2}e^{Ea_{1}/RT}

D

k1=k2eEa1/RTk_{1} = k_{2}e^{Ea_{1}/RT}

Answer

k1=k2eEa1/RTk_{1} = k_{2}e^{Ea_{1}/RT}

Explanation

Solution

K1=A1eEa1/RTK_{1} = A_{1}e^{- Ea_{1}/RT}

K2=A2eEa2/RTK_{2} = A_{2}e^{- Ea_{2}/RT}

K1K2=A1A2e(Ea2Ea1)/RT\frac{K_{1}}{K_{2}} = \frac{A_{1}}{A_{2}}e^{\left( {E_{a}}_{2} - E_{a1} \right)/RT}

K1=K2A×eEa1/RTK_{1} = K_{2}A \times e^{Ea1/RT}