Problem 71 - Chemistry The Central Science

Question

The following mechanism has been proposed for the gasphase reaction of \(\mathrm{H}_{2}\) with ICl: $$\begin{array}{c}{\mathrm{H}_{2}(g)+\mathrm{ICl}(g) \longrightarrow \mathrm{HI}(g)+\mathrm{HCl}(g)} \\ {\mathrm{HI}(g)+\mathrm{ICl}(g) \longrightarrow \mathrm{I}_{2}(g)+\mathrm{HCl}(g)}\end{array}$$ \(\begin{array}{l}{\text { (a) Write the balanced equation for the overall reaction. }} \\ {\text { (b) Identify any intermediates in the mechanism. (c) If }}\end{array}\) the first step is slow and the second one is fast, which rate law do you expect to be observed for the overall reaction?

Step-by-Step Solution

Answer

The balanced equation for the overall reaction is \(H_2(g) + 2ICl(g) \longrightarrow I_2(g) + 2HCl(g)\). The intermediate in this mechanism is HI. The expected rate law for the overall reaction, given that the first step is slow and the second step is fast, is \(Rate = k[H_2][ICl]\), where k is the rate constant and [H_2] and [ICl] are the concentrations of H_2 and ICl, respectively.

Step 1: Write Balanced Equation for Overall Reaction

Add the two given steps of the reaction mechanism and then cancel any species that appear on both sides of the equation. This will provide us with the balanced equation for the overall reaction. Given steps: \(1. \quad H_2(g) + ICl(g) \longrightarrow HI(g) + HCl(g)\) \(2. \quad HI(g) + ICl(g) \longrightarrow I_2(g) + HCl(g)\) Add the two steps: \(H_2(g) + 2ICl(g) + HI(g) \longrightarrow HI(g) + HCl(g) + I_2(g) + HCl(g)\) Now, cancel species that appear on both sides: \(HI\) appears on both sides and can be cancelled. This leaves us with the balanced equation for the overall reaction: \(H_2(g) + 2ICl(g) \longrightarrow I_2(g) + 2HCl(g)\)

Step 2: Identify Intermediates

Intermediates are species that are produced in one step of a mechanism and consumed in another step. Analyze the given mechanism steps and identify any intermediates. From the two given steps, we can see that HI is produced in the first step and consumed in the second step. Therefore, HI is an intermediate in this mechanism.

Step 3: Determine Rate Law

We are given that the first step is slow and the second step is fast. The slow step determines the rate law for the overall reaction because it acts as the bottleneck in the reaction progress. Our rate law will depend only on the reactants in this slow step: Given slow step: \(H_2(g) + ICl(g) \longrightarrow HI(g) + HCl(g)\) The rate law can be written in the form: \(Rate = k[H_2][ICl]\) where k is the rate constant, and [H_2] and [ICl] are the concentrations of H_2 and ICl, respectively. This is the expected rate law for the overall reaction.

Key Concepts

Gas-Phase Reaction

A gas-phase reaction occurs when reactants in a gaseous state interact to form products. These reactions are influenced by the properties of gases, such as temperature and pressure. In the given problem, the reaction between hydrogen gas \(H_2(g)\) and iodine chloride \(ICl(g)\) is a typical example.

• The process involves different transition states, where molecules collide, leading to transformations.
• It's crucial to understand that the outcome depends on these collisions' energy and orientation.

Gas-phase reactions often have unique dynamics compared to those occurring in liquid or solid phases. The speed and efficiency of these reactions are also contingent on the reactants' concentrations and the inherent kinetics of the involved molecules.

Intermediates

Intermediates are crucial to understanding reaction mechanisms. They are species formed in one step and consumed in another, thus not appearing in the overall balanced equation. In our problem:

• \(HI\) is generated during the first step \(H_2(g) + ICl(g) \to HI(g) + HCl(g)\).
• Then, it is consumed in the second step \(HI(g) + ICl(g) \to I_2(g) + HCl(g)\).

As an intermediate, \(HI\) doesn't appear in the final balanced equation \(H_2(g) + 2ICl(g) \to I_2(g) + 2HCl(g)\).
Understanding intermediates allows chemists to deeply know how each step contributes to the overall reaction, aiding in predicting and controlling reaction behaviors.

Rate Law

The rate law expresses how the rate of a chemical reaction relates to the concentration of its reactants. In our scenario, the reaction's rate is determined by the slowest or 'rate-determining' step. For our gas-phase reaction:

• The slow step is \(H_2(g) + ICl(g) \to HI(g) + HCl(g)\).
• This determines the rate law as \(Rate = k[H_2][ICl]\).

Here, \(k\) is the rate constant, and [H_2] and [ICl] are the reactants' concentrations.

The rate law helps predict the reaction speed and analyze how changes in concentration affect reaction dynamics. Understanding the rate law is crucial for controlling industrial chemical processes and optimizing lab reactions.