# How do I determine the units of the rate constant for a zero order, first order, second order, and third order reaction?

Jun 12, 2017

You will need to be able to write a general rate law and solve for the units...

$r \left(t\right) = k {\left[A\right]}^{n}$

$r \left(t\right)$ is the initial rate as a function of time $t$, $k$ is the rate constant, $\left[A\right]$ is the concentration of $A$, and $n$ is the order of $A$.

Since $A$ is assumed the only reactant for simplicity, its order IS the reaction order. If the units of time are $\text{s}$, and of concentration are $\text{M}$, then:

${\text{M"/"s" = [???] cdot "M}}^{n}$

=> [???]

$=$ $\textcolor{b l u e}{\text{units of rate constant in general}}$

$= \textcolor{b l u e}{\text{M"^(1 - n)/"s}}$

So,

• zero order should simply be $\text{M"^(1 - 0)/"s" = "M/s}$.
• first order should be $\text{M"^(1 - 1)/"s" = 1/"s}$.

Can you work out second order and third order?