X2 + Y2 ➔ X2Y2 rate = k[X2] A reaction and its experimentally determined rate law are represented ab — Kinetics Chemistry Question

STEPS:

1. Understand the relationship between reaction mechanisms and rate laws: A reaction mechanism is a sequence of individual, elementary steps that describes how reactants are converted into products. The rate-determining step (RDS) is the slowest elementary step in this sequence. It acts as the kinetic bottleneck, meaning the rate law of this step dictates the rate law of the entire overall reaction.
2. Determine the rate law for an elementary step: For any elementary step, the rate law is determined directly by its molecularity. The coefficients of the reactant species in the balanced elementary equation are used as their reaction orders in the rate law.
3. Analyze Mechanism 1:
* Identify the rate-determining step: Step 1 is marked as the slow step ($\text{X}_2 \rightarrow 2\text{X}$), making it the RDS.
* Write its rate law: Since it is a unimolecular step involving only one molecule of reactant $\text{X}_2$, its rate law is written as:
$$\text{rate} = k[\text{X}_2]$$
This matches the experimentally determined rate law of the overall reaction.
* Verify stoichiometry: To be valid, the sum of the elementary steps must equal the overall reaction:
$$\text{X}_2 \rightarrow \bcancel{2\text{X}}$$
$$\bcancel{\text{X}} + \text{Y}_2 \rightarrow \bcancel{\text{XY}_2}$$
$$\bcancel{\text{X}} + \bcancel{\text{XY}_2} \rightarrow \text{X}_2\text{Y}_2$$
Adding these steps together and canceling the intermediates (two $\text{X}$ atoms and one $\text{XY}_2$ molecule) yields:
$$\text{X}_2 + \text{Y}_2 \rightarrow \text{X}_2\text{Y}_2$$
This matches the overall balanced equation. Thus, Mechanism 1 is consistent.
4. Analyze Mechanism 2:
* Identify the rate-determining step: Step 1 is also marked as the slow step ($\text{X}_2 \rightarrow 2\text{X}$), making it the RDS.
* Write its rate law: Its rate law is determined solely by this first step:
$$\text{rate} = k[\text{X}_2]$$
This also matches the experimentally determined rate law of the overall reaction.
* Verify stoichiometry: Add the elementary steps together:
$$\text{X}_2 \rightarrow \bcancel{2\text{X}}$$
$$\bcancel{\text{X}} + \text{Y}_2 \rightarrow \bcancel{\text{XY}} + \bcancel{\text{Y}}$$
$$\bcancel{\text{X}} + \bcancel{\text{XY}} \rightarrow \bcancel{\text{X}_2\text{Y}}$$
$$\bcancel{\text{X}_2\text{Y}} + \bcancel{\text{Y}} \rightarrow \text{X}_2\text{Y}_2$$
Adding these steps and canceling all intermediates (two $\text{X}$ atoms, one $\text{XY}$ molecule, one $\text{Y}$ atom, and one $\text{X}_2\text{Y}$ molecule) yields:
$$\text{X}_2 + \text{Y}_2 \rightarrow \text{X}_2\text{Y}_2$$
This matches the overall balanced equation. Thus, Mechanism 2 is also consistent.
5. Conclude: Since both Mechanism 1 and Mechanism 2 yield the correct overall stoichiometric equation and share a slow rate-determining first step that produces the rate law $\text{rate} = k[\text{X}_2]$, both proposed mechanisms are consistent, which matches Option C.

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WHY_OTHERS_WRONG:

• A is incorrect: This option claims only Mechanism 1 is consistent. However, Mechanism 2 also meets all criteria for consistency, as its slow rate-determining first step correctly produces the experimental rate law and its steps successfully sum to the overall stoichiometry.
• B is incorrect: This option claims only Mechanism 2 is consistent. However, Mechanism 1 also meets all criteria for consistency, as its slow rate-determining first step correctly produces the experimental rate law and its steps successfully sum to the overall stoichiometry.
• D is incorrect: This option claims neither mechanism is consistent. However, as demonstrated in the steps above, both mechanisms are fully consistent because they both satisfy the stoichiometric and kinetic requirements of the reaction.