Problem 67 - Chemistry: The Central Science

Question

The following mechanism has been proposed for the gas-phase reaction of \(\mathrm{H}_{2}\) with ICl: $$ \begin{aligned} &\mathrm{H}_{2}(g)+\mathrm{ICl}(g) \longrightarrow \mathrm{HI}(g)+\mathrm{HCl}(g) \\ &\mathrm{HI}(g)+\mathrm{ICl}(g) \rightarrow \mathrm{I}_{2}(g)+\mathrm{HCl}(g) \end{aligned} $$ (a) Write the balanced equation for the overall reaction. (b) Identify any intermediates in the mechanism. (c) Write rate laws for each elementary reaction in the mechanism. (d) If the first step is slow and the second one is fast, what rate law do you expect to be observed for the overall reaction?

Step-by-Step Solution

Answer

In summary, the overall balanced equation for the reaction is: H2(g) + 2 ICl(g) → I2(g) + 2 HCl(g). The intermediate in the mechanism is HI(g). The rate laws of the elementary reactions are Rate(1) = k1[H2][ICl] and Rate(2) = k2[HI][ICl]. The rate law for the overall reaction, considering the first step slow and the second step fast, is Rate(overall) = k1[H2][ICl].

Step 1: Balance the Overall Reaction

Add the two elementary reactions given in the mechanism to find the overall reaction. The overall reaction is found by adding together the reactants and products of each reaction, and then canceling out any intermediate species that appear on both sides of the equation. (1) H2(g) + ICl(g) → HI(g) + HCl(g) (2) HI(g) + ICl(g) → I2(g) + HCl(g) --------------------------------------- Overall: H2(g) + 2 ICl(g) → I2(g) + 2 HCl(g)

Step 2: Identify the Intermediates

The intermediates are species that are produced in one elementary reaction and consumed in a subsequent elementary reaction. By comparing the species in the elementary reactions, we can identify the intermediates. In this case, HI is produced in reaction (1) and consumed in reaction (2), so HI is an intermediate.

Step 3: Write Rate Laws for Each Elementary Reaction

For each elementary reaction, use the reactants' concentrations and the reaction rate constant (k) to write the rate law. Rate laws express the relationship between the reaction rate and the concentration of the reacting species. The reaction order represents the dependency of the reaction rate on the concentration of a reactant. In elementary reactions, the reaction orders correspond to the stoichiometric coefficients of the reactants. (a) For the first elementary reaction: Rate(1) = k1[H2][ICl] (b) For the second elementary reaction: Rate(2) = k2[HI][ICl]

Step 4: Determine the Rate Law for the Overall Reaction

If the first step is slow (rate-determining) and the second one is fast, the overall reaction rate will be determined by the rate of the slow step. In this case, the slow step is the first elementary reaction, so the rate law for the overall reaction is the same as the rate law for the first elementary reaction: Rate(overall) = k1[H2][ICl] The rate law of the overall reaction is Rate = k1[H2][ICl], considering the first step to be slow.

Key Concepts

Elementary Reactions

In the world of chemical reactions, an **elementary reaction** is like a single step in a dance routine. Each elementary reaction describes a specific collision or interaction between molecules that leads to a change in their structure. Unlike complex reactions that can involve multiple steps and intermediates, elementary reactions are straightforward.

When we analyze a mechanism, it often consists of multiple elementary reactions. These smaller steps collectively illustrate how reactants transform into products. For example, in the proposed mechanism for the reaction between \(\mathrm{H}_{2}\) and \(\mathrm{ICl}\), there are two elementary reactions:

• \(\mathrm{H}_{2}(g) + \mathrm{ICl}(g) \rightarrow \mathrm{HI}(g) + \mathrm{HCl}(g)\)
• \(\mathrm{HI}(g) + \mathrm{ICl}(g) \rightarrow \mathrm{I}_{2}(g) + \mathrm{HCl}(g)\)

Each of these represents a basic, indivisible act in the overall dance of the molecules.

Analyzing elemental reactions is crucial as it not only helps us understand the molecular dance but also aids in predicting how quickly they occur under certain conditions.

Rate Laws

**Rate laws** are mathematical equations that help us predict the speed of a chemical reaction. Essentially, a rate law expresses the rate of a reaction as a function of the concentration of its reactants. For elementary reactions, the rate law is straightforward.

If you have a reaction like \(\mathrm{A}(g) + \mathrm{B}(g) \rightarrow \mathrm{C}(g)\), the rate of the reaction can often be described as:
\[ \text{Rate} = k[\mathrm{A}][\mathrm{B}] \]
Here, \(k\) is the rate constant, and \([\mathrm{A}][\mathrm{B}]\) represents the concentrations of reactants A and B.

In the context of the gas-phase reaction between \(\mathrm{H}_{2}\) and \(\mathrm{ICl}\), the rate law for the first elementary reaction is:
\[ \text{Rate(1)} = k_1[\mathrm{H}_{2}][\mathrm{ICl}] \]
And for the second elementary reaction:
\[ \text{Rate(2)} = k_2[\mathrm{HI}][\mathrm{ICl}] \]
Rate laws are crucial in understanding how reactant concentrations influence the speed of reactions. They provide insight into which step in a mechanism is the slowest, helping us determine the rate-determining step of a reaction.

Intermediate Species

In many chemical reactions, there are species that exist only momentarily. These are known as **intermediate species**. They form during one step of the reaction and get consumed in a following step, thus never appearing in the final equation. Think of them as temporary participants that facilitate the progress of the overall mechanism.

For the reaction of \(\mathrm{H}_{2}\) with \(\mathrm{ICl}\), the intermediate species identified is \(\mathrm{HI}\). It is produced in the first elementary reaction and then consumed in the second:

• Step 1: \(\mathrm{H}_{2}(g) + \mathrm{ICl}(g) \rightarrow \mathrm{HI}(g) + \mathrm{HCl}(g)\)
• Step 2: \(\mathrm{HI}(g) + \mathrm{ICl}(g) \rightarrow \mathrm{I}_{2}(g) + \mathrm{HCl}(g)\)

Because intermediates like \(\mathrm{HI}\) are not seen in the final reaction equation, they can be elusive. However, understanding these species is essential, as they often hold the key to comprehending the pathway and sequence of steps in a chemical mechanism.

Recognizing intermediates enables chemists to better understand reaction dynamics and the overall route from reactants to products.