Is the rate of a zero order reaction always independent of the concentration of its reactants? Consider the following reaction :
$\ce{A + B}$ $\rightarrow$ $\ce{Products}$
where order of the reaction w.r.t. $\ce{A}$ is $-1$ and order of the reaction w.r.t. $\ce{B}$ is $+1$. So, overall order of the reaction $=(-1)+(1) = 0$. So, it is a zero order reaction. My teachers told me that in a zero order reaction, the rate of the reaction is independant of concentration of the reactants. Below I have derived the integrated rate law for the above reaction. You can clearly see that in the integrated rate law there are terms of concentration of $\ce{A}$ and
$\ce{B}$. Obviously, the integrated rate law is telling us that the rate of the reaction depends on the concentration of the reactants. Then why does everyone say that in a zero order reaction the rate of the reaction is independant of concentration of the reactants. Why?
When you look at the overall reaction, it is if you have an equal concentration of each reactant, then by the reaction progressing or adding equal amounts of both, the reaction rate won't change. For example, if you have 2M of both A and B, $[A]^{-1}[B]^1 = 1/2*2=1$, and increasing the concentration to 3M for both won't change the rate since $1/3*3=1$. The differential rate law applies to only one single species, so unless you have equimolar amounts of each reactant or make an approximation using an excess of one, you cannot apply the differential rate law.