Consider the following statements related to the temperature dependence of rate constants. Identify the correct statements:
$A.$ The Arrhenius equation holds true only for an elementary homogeneous reaction.
$B.$ The unit of $A$ is the same as that of $k$ in the Arrhenius equation.
$C.$ At a given temperature,a low activation energy means a fast reaction.
$D.$ $A$ and $E_a$ as used in the Arrhenius equation depend on temperature.
$E.$ When $E_a > RT$,$A$ and $E_a$ become interdependent.
Choose the correct answer from the options given below:

  • A
    $A, C$ and $D$ Only
  • B
    $B, D$ and $E$ Only
  • C
    $B$ and $C$ Only
  • D
    $A$ and $B$ Only

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According to the Arrhenius equation,which of the following statements are correct?
$(A)$ $A$ high activation energy usually implies a fast reaction.
$(B)$ Rate constant increases with increase in temperature. This is due to a greater number of collisions whose energy exceeds the activation energy.
$(C)$ Higher the magnitude of activation energy,stronger is the temperature dependence of the rate constant.
$(D)$ The pre-exponential factor is a measure of the rate at which collisions occur,irrespective of their energy.

For a first-order reaction $A \to P$,the rate constant equation is given by $\log K = -2000 \, (1/T) + 6.0$. The pre-exponential factor $A$ and the activation energy $E_a$ are,respectively:

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