For a given reaction ${\mathrm{t}}_{1/2}=\frac{1}{\mathrm{Ka}}$. The order of the reaction is 

${\mathrm{t}}_{1/2}=\frac{1}{\mathrm{Ka}}$ for second order reactions. 

${\mathrm{t}}_{1/2}=\frac{1}{\mathrm{K}\left(\mathrm{a}\right)}\Rightarrow {\mathrm{t}}_{1/2}\propto \frac{1}{{\left[\mathrm{a}\right]}^1}$

$\Rightarrow {\mathrm{t}}_{1/2}\propto {\left[\mathrm{a}\right]}^{-1}$

Also, 

$\begin{array}{l}{\mathrm{t}}_{1/2}\propto {\left[\mathrm{a}\right]}^{1-\mathrm{n}}\\ ={\left[\mathrm{a}\right]}^{-1}\Rightarrow 1-\mathrm{n}=-1\\ \mathrm{n}=2\end{array}$