# Problem: For the decomposition of gaseous dinitrogen pentoxide,2N2O5(g) ⟶ 4NO2(g) + O2(g)the rate constant is k = 2.8 x 10-3 s-1 at 60°C. The initial concentration of N2O5 is 1.58 mol/L. (a) What is [N2O5] after 5.00 min?

###### FREE Expert Solution

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

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

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:

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

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###### Problem Details

For the decomposition of gaseous dinitrogen pentoxide,

2N2O5(g) ⟶ 4NO2(g) + O2(g)

the rate constant is k = 2.8 x 10-3 s-1 at 60°C. The initial concentration of N2O5 is 1.58 mol/L.

(a) What is [N2O5] after 5.00 min?