A reaction has a rate constant of 0.0185 s ^{-1} and the only reactant has an initial concentration of 0.135 M. What is the concentration in molarity of this reactant after 125 seconds?

A. 4.84 x 10^{-5 }

B. 0.0134

C. 0.103

D. 0.310

E. 4.84

We’re being asked to **calculate the concentration of reactant** remaining from **0.135 M** after **125 seconds**. The rate constant of the reaction is **0.0185 s ^{–1}**.

We don’t know the order of the reaction but we can quickly figure it out from the rate constant.

Recall that the unit for the rate constant is given by:

$\overline{){\mathbf{k}}{\mathbf{=}}{{\mathbf{M}}}^{\mathbf{n}\mathbf{-}\mathbf{1}}{\mathbf{\xb7}}{{\mathbf{s}}}^{\mathbf{-}\mathbf{1}}}$

where **n** = order of the reaction.

The given rate constant only has **s ^{–1}** as its units, which means

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

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

where:

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

**k** = rate constant

**t** = time

**[A] _{0}** = initial concentration