We’re being asked to calculate the **half-life (t _{1/2})** of a first-order reaction with a rate constant of

Recall that ** half-life** is the time needed for the amount of a reactant to decrease by 50% or one-half. The half-life of a first-order reaction is given by:

$\overline{){{\mathbf{t}}}_{\raisebox{1ex}{$\mathbf{1}$}\!\left/ \!\raisebox{-1ex}{$\mathbf{2}$}\right.}{\mathbf{=}}\frac{\mathbf{ln}\mathbf{2}}{\mathbf{k}}}$

The desorption (leaving of the surface) of a single molecular layer of n-butane from a single crystal of aluminum oxide was found to be first order with a rate constant of 0.128/s at 150 K.

What is the half-life of the desorption reaction?

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