What rate law corresponds to the proposed mechanism for the formation of hydrogen iodide, which can be written in simplified form as: I2 Δk1k-1 2I (Fast), I + H2 Δk2k-2 H2I (Fast), H2I + I ¡k3 2HI (Slow)?

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Identify the slow step in the mechanism, as it determines the rate law. In this case, the slow step is: \( \text{H}_2\text{I} + \text{I} \xrightarrow{k_3} 2\text{HI} \).

Write the rate law based on the slow step. The rate of the reaction is determined by the concentration of the reactants in the slow step: \( \text{Rate} = k_3 [\text{H}_2\text{I}][\text{I}] \).

Express the intermediate \( \text{H}_2\text{I} \) in terms of the initial reactants using the fast equilibrium steps. From the second fast step: \( \text{I} + \text{H}_2 \rightleftharpoons \text{H}_2\text{I} \), we have \( K_2 = \frac{[\text{H}_2\text{I}]}{[\text{I}][\text{H}_2]} \).

Solve for \( [\text{H}_2\text{I}] \) in terms of \( [\text{I}] \) and \( [\text{H}_2] \) using the equilibrium constant \( K_2 \): \( [\text{H}_2\text{I}] = K_2 [\text{I}][\text{H}_2] \).

Substitute \( [\text{H}_2\text{I}] \) from the previous step into the rate law: \( \text{Rate} = k_3 K_2 [\text{I}]^2 [\text{H}_2] \). This is the rate law for the overall reaction.

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Rate Law

A rate law expresses the relationship between the rate of a chemical reaction and the concentration of its reactants. It is typically formulated as rate = k[A]^m[B]^n, where k is the rate constant, and m and n are the orders of the reaction with respect to reactants A and B. Understanding how to derive the rate law from a proposed reaction mechanism is crucial for predicting how changes in concentration affect the reaction rate.

Reaction Mechanism

A reaction mechanism is a step-by-step description of the pathway taken during a chemical reaction, detailing each elementary step involved. Each step can have different rates, and the slowest step, known as the rate-determining step, dictates the overall reaction rate. Analyzing the proposed mechanism helps in identifying which steps contribute to the rate law and how intermediates are involved.

Elementary Steps and Rate-Determining Step

Elementary steps are individual reactions that occur in a mechanism, each with its own rate constant. The rate-determining step is the slowest step in the mechanism, which limits the overall rate of the reaction. In the given mechanism, identifying the slow step allows us to derive the rate law by focusing on the concentrations of the reactants involved in that step, while considering the fast steps as equilibria.

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Rate Law Determination

Related Practice

Textbook Question

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 b. What kind of experimental evidence might lead you to favor mechanism II over mechanism I?

Textbook Question

Consider the reaction: 2 NH₃(aq) + OCl^-(aq) → N₂H₄(aq) + H₂O(l) + Cl^- (aq) This three-step mechanism is proposed: NH₃(aq) + OCl^- (aq) Δk1k2 NH₂Cl(aq) + OH- (aq) Fast NH₂Cl(aq) + NH₃(aq) →k3 N₂H₅⁺ (aq) + Cl^- (aq) Slow N₂H₅⁺ (aq) + OH^-(aq) →k4 N₂H₄(aq) + H₂O(l) Fast a. Show that the mechanism sums to the overall reaction.

Textbook Question

A certain substance X decomposes. Fifty percent of X remains after 100 minutes. How much X remains after 200 minutes if the reaction order with respect to X is (c) second order?

Textbook Question

The half-life for radioactive decay (a first-order process) of plutonium- 239 is 24,000 years. How many years does it take for one mole of this radioactive material to decay until just one atom remains?