# 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?

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?

• How can we conclude that $A$ is first order? Apr 26, 2021 at 23:30
• Some information is missing. You ask : Which statement is true ? OK. But there are no statements to consider for a choice !... Jun 29, 2021 at 19:55

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.

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).

• But you are changing the initial concentration of B. I thought first order half lives were not affected by the initial concentration. Jan 19, 2016 at 18:04

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