We’re being asked to **determine the concentration of XY** after **55.0 s** given an initial concentration of **0.050 M**.

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

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

The decomposition of XY is second order in XY and has a rate constant of 7.02×10^{−3} *M*^{-1} s^{-1} at a certain temperature. If the initial concentration of XY is 0.050 M, what is the concentration of XY after 55.0 s?

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