We’re being asked to determine the time it would take for the 99% of the protein sample to decompose.

The integrated rate law for a first-order reaction is as follows:

$\overline{){\mathbf{ln}}{\mathbf{}}{\mathbf{\left[}\mathbf{A}\mathbf{\right]}}_{{\mathbf{t}}}{\mathbf{=}}{\mathbf{-}}{\mathbf{kt}}{\mathbf{+}}{\mathbf{ln}}{\mathbf{}}{{\mathbf{\left[}}{\mathbf{A}}{\mathbf{\right]}}}_{{\mathbf{0}}}}$

where:

**[A] _{t}** = concentration at time t

The protein that you’ve just isolated is unstable; it decomposes through a first-order process with k = 0.02 min^{-1}. How long will it take for 99% of a 1 mL sample of the protein, with initial concentration 87 μM, to decompose?

A. 0.05 sec

B. 0.5 min

C. 230 sec

D. 86 min

E. 3.8 hr

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