A certain reaction has an activation energy of 70.0 kJ/mol and a frequency factor of A = 1.40 xx 10^12 "M"^(-1)"s"^(-1). What is the rate constant, k, of this reaction at 22.0 °"C"?

Jul 26, 2017

Given ${E}_{a}$, $A$, and $k$, the reaction follows Arrhenius behavior, and thus the Arrhenius equation applies:

$k = A {e}^{- {E}_{a} / R T}$,

where the variables above are all known, except that $T$ is in $\text{K}$. This is a second order reaction (how do we know?).

There is no further rearrangement necessary; we already have the form of the equation we need.

$\textcolor{b l u e}{k} = \left(1.40 \times {10}^{12} \text{M"^(-1)cdot"s"^(-1))e^(-"70.0 kJ/mol"//"0.008314472 kJ/mol"cdot"K" // "295.15 K}\right)$

$= \textcolor{b l u e}{5.73 \times {10}^{- 1} {\text{M"^(-1)cdot"s}}^{- 1}}$

And we should recognize that exponentials have no units, i.e. ${e}^{x}$ is such that $x$ is unitless, and thus ${e}^{x}$ is unitless.