#### Zero-Order Reactions

As for other reaction orders, an equation for zero-order half-life may be derived from the integrated rate law: $$[A]_t =−kt+[A]_0 $$

For a half-life, $ t=t_{\frac{1}{2}}$ and $[A]_t=\frac{1}{2}[A]_0$

Substituting into the integrated rate law: $$ \frac{1}{2}[A]_0 =−k t_{\frac{1}{2}} +[A]_0 $$

And rearranging:

$$ \frac{[A]_0}{2} =−k t_{\frac{1}{2}} +[A]_0 \\

k t_{\frac{1}{2}} =\frac{[A]_0}{2} $$

$$t_{\frac{1}{2}} =\frac{[A]_0}{2k} \label{eq1}\tag{1}$$

As for all reaction orders, the half-life for a zero-order reaction is inversely proportional to its rate constant. However, the half-life of a zero-order reaction increases as the initial concentration increases.