## Chemistry 9th Edition

If the initial reaction rate doubles when the concentration of a reactant is quadrupled, the reaction order is $\frac{1}{2}$. A reactant with a $-1$ order will have its reaction rate decreased by a factor of $\frac{1}{2}$ when the concentration of the reactant is increased by a factor of $2$.
If the rate doubles when the concentration quadruples, then the reaction order can be found with the equation $2 = 4^n$. It follows that $n=log_24=2$. If a reactant has a $-1$ order and the concentration is increased by a factor of $2$, then the reaction rate increases by a factor of $2^{-1}$ or $\frac{1}{2}$.