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Factors Affecting the Rate of a Chemical Reaction

At a certain ...

Question

At a certain temperature, the first order rate constant $k_{1}$ is found to be smaller than the second order rate constant $k_{2}$ . If the energy of activation $E_{1}$ of the first order reaction is greater than energy of activation $E_{2}$ of the second order reaction, then with increase in temperature:

k_{1}

will increase faster than

k_{2}

, but always will remain less than

k_{2}

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k_{2}

will increase faster than

k_{1}

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k_{1}

will increase faster than

k_{2}

and becomes equal to

k_{2}

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k_{1}

will increase faster than

k_{2}

and becomes greater than

k_{2}

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Solution

The correct option is A $k_{1}$ will increase faster than $k_{2}$ , but always will remain less than $k_{2}$
The relationship between the energy of activation of the reaction and the rate constant of the reaction is $\frac{d (l n k)}{d T} = \frac{E_{a}}{R T^{2}}$
With increase in the energy of activation, the increase in the rate constant of the reaction will be faster with increase in temperature.
Hence, $k_{1}$ will increase faster than $k_{2}$ , but always will remain less than $k_{2}$ .

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At a certain temperature, the first order rate constant k1 is found to be smaller than the second order rate constant k2. If the energy of activation E1 of the first order reaction is greater than energy of activation E2 of the second order reaction, then with increase in temperature: