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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?

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

3 Answers 3

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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.

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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).

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  • $\begingroup$ But you are changing the initial concentration of B. I thought first order half lives were not affected by the initial concentration. $\endgroup$
    – user99364
    Jan 19, 2016 at 18:04
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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

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