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Rate Constant

For the two p...

Question

For the two parallel reactions $A_{1} B$ and $A_{2} C$ , determine the activation energy $E^{'}$ for the disapperance of A is given in terms of activation energies $E_{1}$ and $E_{2}$ for the two paths .

A

E^{'} = \frac{k_{1} E_{1} + k_{2} E_{2}}{k_{1} + k_{2}}

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B

E^{'} = \frac{k_{1} E_{1} - k_{2} E_{2}}{k_{1} - k_{2}}

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C

E^{'} = \frac{k_{2} E_{1} - k_{1} E_{2}}{k_{1} - k_{2}}

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D

E^{'} = \frac{k_{1} E_{2} + k_{2} E_{2}}{k_{1} + k_{2}}

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Solution

The correct option is A $E^{'} = \frac{k_{1} E_{1} + k_{2} E_{2}}{k_{1} + k_{2}}$
For the two parallel reactions $A_{1} B$ and $A_{2} C$ , the activation energy $E^{'}$ for the disapperance of A is given in terms of activation energies $E_{1}$ and $E_{2}$ for the two paths, by the following expression.
$E^{'} = \frac{k_{1} E_{1} + k_{2} E_{2}}{k_{1} + k_{2}}$
The rate constant for the overall reaction is the sum of the rate constants for two parallel reactions. $k = k_{1} + k_{2}$ .
Also $A = A_{0} e^{- k t} = A_{0} e^{- (k_{1} + k_{2}) t}$

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