Inconsistency in Elementary Bi-Molecular Reaction Rate Expressions
If the reaction is
$$\ce{2A -&gt; P},$$
then the rates are defined to be related as
$$
  -\frac{1}{2}\frac{\mathrm{d}\ce{A}}{\mathrm{d}t} 
  = \frac{\mathrm{d}\ce{P}}{\mathrm{d}t}
$$
and this is true throughout the reaction. The rate at which $\ce{P}$ is produced is half that at which $\ce{A}$ is consumed. Normally therefore a factor of 2 is expected with the rate constant. With any other usage an explanation should be added so as not to confuse things.
In the general case
$$\ce{aA + bB -&gt; pP + qQ},$$
then
$$ 
  -\frac{1}{a}\frac{\mathrm{d}\ce{A}}{\mathrm{d}t} 
  = -\frac{1}{b}\frac{\mathrm{d}\ce{B}}{\mathrm{d}t} 
  = \frac{1}{p}\frac{\mathrm{d}\ce{P}}{\mathrm{d}t} 
  = \frac{1}{q}\frac{\mathrm{d}\ce{Q}}{\mathrm{d}t}
  = \frac{\mathrm{d}x}{\mathrm{d}t},
$$
where at any time $t$, $ax$ moles of $\ce{A}$ and $bx$ of $\ce{B}$  are consumed and $px$ of $\ce{P}$ are produced, where $x$ is the extent of reaction.