We are asked to **calculate the rate of the decomposition after 0.1 ****min**

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

$\overline{){\mathbf{rate}}{\mathbf{}}{\mathbf{=}}{\mathbf{}}{\mathbf{k}}\mathbf{\left[}{\mathbf{C}}_{\mathbf{2}}{\mathbf{H}}_{\mathbf{6}}{\mathbf{N}}_{\mathbf{2}}\mathbf{\right]}}$

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

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

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

The decomposition of azomethane (C_{2}H_{6}N_{2}) follows first-order kinetics with a rate constant of 40 min^{−1}. If you start with a concentration of 0.2 M C_{2}H_{6}N_{2}, what is the rate of the decomposition after 0.1 min?

A. 1.46 × 10^{−1} M min^{−1}

B. 4 M min^{−1}

C. 4.46 × 10^{2} M min^{−1}

D. 0.4 M min^{−1}

E. 3.66 × 10−3 M min−1

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