We are asked to** determine the fraction of N _{2}O_{5 }molecules that remain unreacted after 24h**

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

**k** = rate constant

**t** = time, **[A] _{0}** = initial concentration.

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

The rate constant is 1.72 x 10^{-5} s^{-1}

b) Determine the fraction of N_{2}O_{5 }molecules that remain unreacted after 24h.