Consider the following overall reaction which is experimentally observed to be second order in AB and zero order in C:
AB+C -> A+BC
Determine whether the mechanism below is valid for this reaction
AB+ AB -> AB(sub 2) + A slow
AB(sub2) + C -> AB+BC fast
It's valid, for all you kids googling the answers to your homework :P
Well, this seems like an interesting mechanism! Let's see if it holds up to scrutiny.
First, we have the slow step: AB + AB -> AB2 + A
In this step, two AB molecules come together to form AB2 and release an A molecule. This step is certainly feasible, but it doesn't quite match with the rate equation we observe experimentally, which is second order in AB.
According to the rate equation, the reaction is second order in AB but zero order in C. However, in the proposed mechanism, the rate-determining step involves two AB molecules. This would make the overall reaction third order (since it involves two AB molecules and one C molecule).
So, based on these observations, the proposed mechanism does not seem to be valid for this reaction. But hey, at least it provided us with some amusement in the process!
To determine whether the proposed mechanism is valid for the given overall reaction, we need to compare the rate law predicted by the mechanism with the experimentally observed rate law.
First, let's write the rate law for the proposed mechanism using the rate-determining step, which is the slow step:
Rate = k * [AB][AB]
According to the mechanism, the concentration of AB2 remains constant throughout the reaction, and it is not included in the rate law. Therefore, we don't need to consider [AB2] in the rate law.
Next, let's write the rate law for the overall reaction based on the given information:
Rate = k' * [AB]^2 * [C]^0
Since the rate is second order in AB and zero order in C, the rate law becomes:
Rate = k' * [AB]^2
Comparing the rate law predicted by the mechanism and the rate law observed experimentally, we can see that they don't match. The proposed mechanism predicts a rate law that includes the concentration of [AB] squared, whereas the experimentally observed rate law doesn't contain [AB]^2.
Therefore, based on this comparison, we can conclude that the proposed mechanism is not valid for the given reaction.
To determine whether the proposed mechanism is valid for the given reaction, we need to analyze the overall reaction and compare it to the proposed elementary steps in the mechanism. Let's break it down step by step:
Overall reaction: AB + C -> A + BC
Proposed mechanism:
Step 1 (slow): AB + AB -> AB2 + A
Step 2 (fast): AB2 + C -> AB + BC
Now, let's check if the proposed mechanism satisfies the observed rate law for the reaction, which is second order in AB and zero order in C.
In the slow step (Step 1), the rate-determining step, we see that two AB molecules react to form AB2 and a molecule of A. The rate of this step is determined by the concentration of AB, which matches the observed second-order dependence on AB in the rate law.
In the fast step (Step 2), AB2 reacts with C to regenerate AB and form BC. However, the rate of this step is not relevant to the overall rate law since it is fast and does not involve AB or C. Hence, it matches the observed zero-order dependence on C.
Therefore, based on this analysis, we can conclude that the proposed mechanism is valid for the given reaction.