Question

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

In two possible scenarios, the rate law for the reaction A + B → C could be zero-order in chemical A. First, if the reaction is one-step and A is present at a high enough concentration that it saturates the reactive sites, adding more A has no effect on the reaction rate, making the reaction zero-order in A with the rate law: rate = k [B]^n. Second, if the reaction is a two-step reaction with A being involved only in the second step along with chemical C, the reaction rate is mainly determined by the first step and depends only on the concentration of B, not A, resulting in zero-order dependence on A.

Step-by-step solution

1. Reaction is one step, and A is saturated

One possible situation in which the rate law is zero-order in A is if the reaction is a one-step reaction, and A is present at a high enough concentration that it saturates the reactive sites. In this scenario, adding more A has no effect on the reaction rate because all available reactive sites are already occupied. As a result, the rate law for the reaction becomes rate = k [B]^n, showing that it is zero-order in A.

2. A is involved in only the second step with chemical C in a two-step reaction

Another possibility for the rate law to be zero-order in A is if the reaction is a two-step reaction, in which A is involved only in the second step along with chemical C. In the first step, B reacts with another molecule to form C, and in the second step, A and C react to form the final products. Since the second step is generally faster than the first step, the reaction rate is primarily determined by the first step, not by A. This means that the rate law for this reaction would depend only on the concentration of B and not on A, making the reaction zero-order in A. In both scenarios, the rate of the reaction is independent of the concentration of chemical A, and hence the rate law shows zero-order dependence on A.