Does concentration of zero-order reactant affect half-life?


> 
> Two substances $\ce{A}$ and $\ce{B}$ react with each other in such a way that $\ce{A}$ is $50\,\%$ consumed in $\pu{33 min}$ and $75\,\%$ consumed in $\pu{66 min}.$ Changing the concentration of $\ce{B}$ has no effect on the results. Which statement is true?
> 
> 
> 


And the answer is:



> 
> This reaction is first order in $\ce{A}$ and zero-order in $\ce{B}.$
> 
> 
> 


I understand why $\ce{A}$ is first order but I don't get why $\ce{B}$ is zero order. The equation for the half-life of a zero order reactant is $$t\_{1/2} = \frac{[\ce{B}]\_0}{2k}.$$


Doesn't this mean that the concentration for a zero-order reactant would affect the half-life?





> 
> Changing the concentration of $\ce{B}$ has no effect on the results.
> 
> 
> 


This statement could only mean one thing: $\ce{B}$ does not participate in the reaction. Obviously, if $\ce{B}$ does participate in the reaction, and you change the concentration of $\ce{B}$ to $0,$ the reaction won't happen.



> 
> The equation for the half-life of a zero order reactant is $$t\_{1/2} = \frac{[\ce{B}]\_0}{2k}.$$
> 
> 
> 


Zero order reaction have no half-life. Only 1st order reaction has half-life.


 3

Exactly! The concentration of B during the reaction does not effect the half life. If you see for the zero order reactions, the half life can be written as $\frac{B\_{\text{initial}}}{2K}$ in which B & K are constants. So for zero order reactions, half life does not depend upon the concentration of reactants at any time (after start of the reaction).


 1

Let the rate law for the reaction be $$r = k[\ce{A}]^n[\ce{B}]^m$$



> 
> Changing the concentration of B has no effect on the results.
> 
> 
> 


What are the results? Is it the rate? or is it the half life?


***Finding the value of $\mathbf{m}$***


**1. If it is the rate, then**


It is obvious that $m$ should be zero.


**2. If it is the half life, then**


For this to happen, $m$ should be equal to $1$$^\*$, because only for a first order or a *pseudo* first order reaction, half life is independent of initial concentration of reactant.




---


\*This is correct only if A is in excess


 0