What rate law corresponds to the proposed mechanism for the formation of hydrogen bromide, which can be written in a simplified form as: Br2(g) → 2Br(g) (Fast) Br(g) + H2(g) → HBr(g) + H(g) (Slow) H(g) + Br2(g) → HBr(g) + Br(g) (Fast)?

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Identify the slow step in the mechanism, as it determines the rate law. In this case, the slow step is: Br(g) + H2(g) → HBr(g) + H(g).

Write the rate law based on the slow step. The rate law is determined by the reactants in the slow step: rate = k[Br][H2].

Recognize that the concentration of Br is not typically known, so we need to express it in terms of known quantities.

Use the fast equilibrium step to express [Br] in terms of [Br2]. The fast step is: Br2(g) ⇌ 2Br(g).

Assume the fast step reaches equilibrium quickly, allowing us to use the equilibrium expression: [Br]^2 = K[Br2], where K is the equilibrium constant. Solve for [Br] and substitute into the rate law.

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 the rate law is essential 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. It outlines the individual elementary steps, including which are fast and which are slow. The slowest step, known as the rate-determining step, primarily influences the overall rate law of the reaction, making it crucial for determining the rate law from a proposed mechanism.

Elementary Steps

Elementary steps are the individual reactions that occur in a reaction mechanism. Each step represents a single molecular event, and the overall reaction is the sum of these steps. The rate law can often be derived from the elementary steps, particularly focusing on the slowest step, which dictates the rate of the overall reaction.

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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 a. Show that both of the proposed mechanisms are valid.

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

Phosgene (Cl2CO), a poison gas used in World War I, is formed

by the reaction of Cl2 and CO. The proposed mechanism for the

reaction is:

Cl2Δ2 Cl (fast, equilibrium)

Cl + COΔClCO (fast, equilibrium)

ClCO + Cl2¡Cl2CO + Cl (slow)

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?