We’re being asked to determine the **time it would take for the concentration of A to decrease from 0.860 M to 0.310 M**.

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

We’re given:

A first order reaction has a rate constant of 0.500 s^{–1}. How long, in seconds, would it take for the concentration of A to decrease from 0.860 M to 0.310 M?

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