We’re being asked to **determine the rate constant (k) of N _{2}O_{5}**.

Recall that ** half-life** is the time needed for the amount of a reactant to decrease by 50% or one-half.

The half-life of a first-order reaction is given by:

$\overline{){{\mathbf{t}}}_{\raisebox{1ex}{$\mathbf{1}$}\!\left/ \!\raisebox{-1ex}{$\mathbf{2}$}\right.}{\mathbf{}}{\mathbf{=}}{\mathbf{}}\frac{\mathbf{ln}\mathbf{2}}{\mathbf{k}}}$

where:

**t**_{1/2} = half-life

**k** = decay constant

The half-life of N_{2}O_{5}_{ }(g) at a 25 °C is 4.03 x 10^{4 }s.

a) Find the rate constant (k) for the first-order decomposition of N_{2}O_{5 }(g) at 25 °C.

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