Consider the gas-phase reaction: H₂(g) + I₂(g) → 2 HI(g) The reaction was experimentally determined to be first order in H₂ and first order in I₂. Consider the proposed mechanisms. Proposed mechanism I: H₂(g) + I₂(g) → 2 HI(g) Single step Proposed mechanism II: I₂(g) Δk1k-12 I(g) Fast H₂( g) + 2 I( g) → k22 HI( g) Slow a. Show that both of the proposed mechanisms are valid.

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insert step 1> Identify the overall reaction and the rate law from the experimental data. The overall reaction is H2(g) + I2(g) → 2 HI(g), and the rate law is rate = k[H2][I2], indicating first order in both H2 and I2.

insert step 2> Analyze Proposed Mechanism I: This is a single-step mechanism where the rate law can be directly written from the stoichiometry of the reaction. Since the reaction is elementary, the rate law is rate = k[H2][I2], which matches the experimental rate law.

insert step 3> Analyze Proposed Mechanism II: This involves two steps. The first step is the fast equilibrium I2(g) ⇌ 2 I(g), and the second step is the slow step H2(g) + 2 I(g) → 2 HI(g).

insert step 4> For Proposed Mechanism II, write the rate law for the slow step, which is the rate-determining step: rate = k2[H2][I]^2.

insert step 5> Use the equilibrium expression from the fast step to express [I] in terms of [I2]: K_eq = [I]^2/[I2], so [I]^2 = K_eq[I2]. Substitute this into the rate law for the slow step to show that rate = k'[H2][I2], where k' = k2K_eq, which matches the experimental rate law.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Reaction Order

Reaction order refers to the power to which the concentration of a reactant is raised in the rate law of a chemical reaction. In this case, the reaction is first order in both H2 and I2, meaning that the rate of reaction is directly proportional to the concentration of each reactant. Understanding reaction order is crucial for analyzing how changes in concentration affect the reaction rate.

Mechanism of Reaction

A reaction mechanism is a step-by-step description of the pathway taken by reactants to form products. It includes elementary steps that detail how bonds are broken and formed. Evaluating proposed mechanisms involves determining if they can account for the observed reaction order and rate, which is essential for validating their correctness.

Rate Law and Rate Constants

The rate law expresses the relationship between the rate of a chemical reaction and the concentration of its reactants, often incorporating rate constants for each step in a mechanism. For the proposed mechanisms, the rate constants (k1, k-1, k2) play a critical role in determining the overall rate of the reaction and validating the mechanisms based on the experimental data provided.