Question

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"`?

Answer 1

Given `E_a`, `A`, and `k`, the reaction follows Arrhenius behavior, and thus the Arrhenius equation applies:

`k = Ae^(-E_a//RT)`,

where the variables above are all known, except that `T` is in `"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.

`color(blue)(k) = (1.40 xx 10^(12) "M"^(-1)cdot"s"^(-1))e^(-"70.0 kJ/mol"//"0.008314472 kJ/mol"cdot"K" // "295.15 K")`

`= color(blue)(5.73 xx 10^(-1) "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.