# What are the rate of reaction units?

May 15, 2018

For any reaction? Concentration per unit time.

What units of time do you want? Seconds? Minutes? Hours? Well, whatever you can measure with a stopwatch I suppose... Know what makes sense given the numerical value of the rate you are looking at. Is it about the picosecond-time-scale autoionization of water? The 10-second time-scale of the reaction of crystal violet with sodium hydroxide? The billions-of-years-time-scale of the uranium-238 decay chain?

What unit of concentration do you want? Molecules per unit volume? Molarity? Your choice... depends on whether you are a statistical mechanical chemist or a more typical experimentalist.

The rate of reaction is given as $r \left(t\right)$ in a rate law as:

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

$= - \frac{1}{a} \frac{\Delta \left[A\right]}{\Delta t} = - \frac{1}{b} \frac{\Delta \left[B\right]}{\Delta t} = \frac{1}{c} \frac{\Delta \left[C\right]}{\Delta t} = \frac{1}{d} \frac{\Delta \left[D\right]}{\Delta t}$

for the reaction

$a A + b B \to c C + \mathrm{dD}$

where:

• $k$ is the rate constant (constant with respect to temperature).
• $\left[\text{ }\right]$ is the concentration of a given reactant.
• $m$ is the order of reactant $A$.

And we know that $\left[\text{ }\right]$ is concentration and $t$ is time... so by definition of the rate of change of concentration over time

$\frac{\Delta \left[\text{ }\right]}{\Delta t}$

being the slope of a concentration vs. time plot, the units are clearly

$\text{concentration"/"time}$