The Arrhenius equation models the rate constant $(k)$ of a chemical reaction as an exponential function that depends on a pre$-$exponential factor $(A),$ reaction activation energy

barrier $(E_a),$ and reaction temperature $(T).R$ is the ideal gas constant, and $e$ is a constant called Euler's number that forms the base of the exponential expression. The equation

can be written as:

$k=A{e}^{-\frac{E_a}{RT}}$

Note that $-\frac{E_a}{RT}$ is an exponent on $e.$ Use the Arrhenius equation to derive an expression for the activation energy, $E_a,$ of a reaction in terms of temperature $(T),$ the rate

constant $(k),$ and the frequency factor $(A),$ and select an equivalent equation from the list below.

$E_a=-\frac{lnk}{RT}+lnA$

$E_a=RTlnk-$RTlnA

$E_a=A{e}^{-\frac{k}{RT}}$

$E_a=-\frac{RTlnk}{A}$

$E_a=-RTlnk+$RTlnA

$E_a=-RTlnk+lnA$

$E_a=-RTlnk$