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Chapter 12: Problem 6

For the reaction \(\mathrm{A}+\mathrm{B} \rightarrow \mathrm{C},\) explain at least two ways in which the rate law could be zero order in chemical A.

Short Answer

Expert verified
There are at least two ways in which the rate law could be zero order in chemical A for the reaction A + B → C. One way is the presence of a catalyst or enzyme that becomes saturated with reactant A, making the reaction rate independent of A's concentration. Another possibility is a fast equilibration of a pre-reaction step that determines the overall reaction rate, causing the concentration of an intermediate product to remain constant despite changes in A's concentration. Additionally, a competing reaction pathway with a different rate law may also lead to the overall rate law becoming zero order for A if the other pathway's rate is much greater and independent of A's concentration.

Step by step solution

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1. Presence of a catalyst or enzyme

A catalyst or an enzyme can make the reaction zero order with respect to A. When the catalyst or enzyme is present in the reaction mixture, it can become saturated with reactant A, causing it to bind with A at its maximum capacity. In this situation, the reaction rate will not increase with an increase in A's concentration since the catalyst or enzyme sites are fully occupied and functioning at their maximum rate.
02

2. Fast equilibration of a pre-reaction step

One possibility is that the reaction involves a fast pre-equilibrium step that determines the overall reaction rate. Suppose there is a fast equilibrium reaction occurring before the slow, rate-determining step: \(A + B \rightleftharpoons D\) \(D \rightarrow C\) The overall reaction will still be A + B → C. However, as D forms quickly from A + B and is also consumed quickly in the slow step (D → C), the concentration of D will remain constant even if A's concentration changes. This scenario will lead to the rate law being zero order with respect to A, as the rate will be determined by the slow step and will not depend on A's concentration.
03

3. A competing reaction pathway

Another possibility is that there exists a competing reaction pathway with a different rate law, also producing C. For example, consider the following two pathways: \(A + B \rightarrow C\) (pathway 1) \(A + X \rightarrow C\) (pathway 2) If the rate of pathway 2 is much greater than that of pathway 1 and pathway 2's rate doesn't depend on the concentration of A, the overall rate law may become zero order for A. For example, if pathway 2 is a first-order reaction concerning X and the concentration of X is much higher than B, the overall rate of the reaction will depend mostly on pathway 2, making it independent of reactant A's concentration.

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