The unit of rate constant of the decomposition reaction $2{\mathrm{N}}_2{\mathrm{O}}_5\to 2{\mathrm{NO}}_2+{\mathrm{O}}_2$ which is first order with respect to ${\mathrm{N}}_2{\mathrm{O}}_5$ is

For a first order reaction ,

$k=\frac{2.303}{t}\log \frac{[R{]}_0}{\left[R\right]}$

The unit of rate constant of the decomposition reaction $2{\mathrm{N}}_2{\mathrm{O}}_5\to 2{\mathrm{NO}}_2+{\mathrm{O}}_2$ which is first order with respect to ${\mathrm{N}}_2{\mathrm{O}}_5$ is ${\mathrm{S}}^{-1}$.