# Problem: A second-order reaction starts with an initial concentration of 0.100 mol/L of the reactant. If the rate constant is 3.6 × 10–2 L/(mol • s), what is the time required to decrease the initial concentration to 0.050 mol/L?A) 280 sB) 420 sC) 19.3 sD) 1.39 sE) 830 s

###### FREE Expert Solution

We’re being asked to determine the time required to decrease the initial concentration of the reactant to 0.050 mol/L.

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

$\overline{)\frac{\mathbf{1}}{{\mathbf{\left[}\mathbf{A}\mathbf{\right]}}_{\mathbf{t}}}{\mathbf{=}}{\mathbf{kt}}{\mathbf{+}}\frac{\mathbf{1}}{{\mathbf{\left[}\mathbf{A}\mathbf{\right]}}_{\mathbf{0}}}}$

where:

[A]t = concentration at time t

k = rate constant

t = time (unknown)

[A]0 = initial concentration

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###### Problem Details

A second-order reaction starts with an initial concentration of 0.100 mol/L of the reactant. If the rate constant is 3.6 × 10–2 L/(mol • s), what is the time required to decrease the initial concentration to 0.050 mol/L?

A) 280 s

B) 420 s

C) 19.3 s

D) 1.39 s

E) 830 s