# Solution: 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. 0.0134C. 0.103D. 0.310E. 4.84

###### Problem

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

###### Solution

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:

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

where n = order of the reaction

The given rate constant only has –1 as its units, which means n = 1 and the reaction follows first-order kinetics.

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

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