Problem 79 - Chemistry Matter and Change

Question

A two-step mechanism has been proposed for the decomposition of nitryl chloride \(\left(\mathrm{NO}_{2} \mathrm{CL}\right)\) Step \(1 : \mathrm{NO}_{2} \mathrm{Cl}(\mathrm{g}) \rightarrow \mathrm{NO}_{2}(\mathrm{g})+\mathrm{Cl}(\mathrm{g})\) Step \(2 : \mathrm{NO}_{2} \mathrm{Cl}(\mathrm{g})+\mathrm{Cl}(\mathrm{g}) \rightarrow \mathrm{NO}_{2}(\mathrm{g})+\mathrm{Cl}_{2}(\mathrm{g})\) What is the overall reaction? Identify any intermediates in the reaction sequence, and explain why they are called intermediates

Step-by-Step Solution

Answer

The overall reaction for the decomposition of nitryl chloride (NO₂Cl) is: \(NO_2Cl(g) \rightarrow NO_2(g) + \frac{1}{2} Cl_2(g)\) The Cl(g) species is an intermediate in this reaction mechanism, as it is produced in one step and consumed in the next one.

Step 1: Write Down the Elementary Steps

Write down the given elementary steps in the reaction mechanism. Step 1: NO₂Cl(g) → NO₂(g) + Cl(g) Step 2: NO₂Cl(g) + Cl(g) → NO₂(g) + Cl₂(g)

Step 2: Sum up the Elementary Steps

Add the two elementary steps to eliminate any species that appear as products in one step and reactants in another step. These species are called intermediates. \(NO_2Cl(g) \rightarrow NO_2(g) + Cl(g)\) \(+(+) \hspace{20pt}\) \(NO_2Cl(g) + Cl(g) \rightarrow NO_2(g) + Cl_2(g)\) After summing the two steps, we get: \(2 NO_2Cl(g) \rightarrow 2 NO_2(g) + Cl_2(g)\)

Step 3: Simplify the Overall Reaction

Simplify the overall reaction by dividing through by the common factor (in this case, 2): \(2 NO_2Cl(g) \rightarrow 2 NO_2(g) + Cl_2(g) \hspace{20pt} \div 2\) This simplifies to: \(NO_2Cl(g) \rightarrow NO_2(g) + \frac{1}{2} Cl_2(g)\)

Step 4: Identify Intermediates

The intermediates are the species that are produced in one step and consumed in the next step. In this mechanism, the Cl(g) species is an intermediate, as it is formed in Step 1 and consumed in Step 2. The overall reaction for the decomposition of nitryl chloride (NO₂Cl) is: \(NO_2Cl(g) \rightarrow NO_2(g) + \frac{1}{2} Cl_2(g)\) The Cl(g) species is an intermediate in this reaction mechanism.

Key Concepts

Elementary Steps in a Reaction

When we talk about reaction mechanisms, it's essential to understand "elementary steps." These steps are the most fundamental reactions that occur in a sequence leading to the overall transformation. Each elementary step shows how molecules interact on a very basic level. In our example of the decomposition of nitryl chloride, we have two elementary steps:

• Step 1: \(NO_2Cl(g) \rightarrow NO_2(g) + Cl(g)\)
• Step 2: \(NO_2Cl(g) + Cl(g) \rightarrow NO_2(g) + Cl_2(g)\)

The key idea is that you can't simplify them further—they happen just as written. Each step involves breaking or forming specific bonds. They help us build a clear picture of how reactants turn into products, making complex reactions more manageable. Understanding these steps is crucial for figuring out the overall reaction and identifying intermediates.

Role of Intermediates

Intermediates are unique species that appear partway through a reaction mechanism but do not appear in the overall balanced equation. In the decomposition of nitryl chloride, the species \(Cl(g)\) serves as an intermediate. It is produced in Step 1 but consumed in Step 2, showing its transient nature.

• Produced in one step and used up in another, intermediates are essential to the flow of a reaction sequence.
• They help bridge elementary steps, ensuring continuity in a reaction.

Intermediates can provide insight into reaction rates and pathways. For chemists, identifying intermediates is crucial for understanding the speed and efficiency of reactions. They help decipher more complicated reaction mechanisms by pinpointing specific transitional phases.

Understanding the Overall Reaction

The overall reaction is the sum of all its elementary steps, revealing the net transformation from reactants to products. In the decomposition of nitryl chloride, after canceling out the intermediates (\(Cl(g)\)), adding the steps gives us:
\[2 NO_2Cl(g) \rightarrow 2 NO_2(g) + Cl_2(g)\]
Finally, by simplifying, we divide everything by 2, leading to the overall balanced equation:
\[NO_2Cl(g) \rightarrow NO_2(g) + \frac{1}{2} Cl_2(g)\]
This overall reaction shows the direct result of the process, omitting fleeting intermediates. It provides a clear depiction of the starting materials and final products. Understanding the overall reaction is vital for chemists as it summarizes the whole transformation efficiently, allowing for the calculation of stoichiometry and understanding the chemical changes that have occurred. Through this, one gains a broad view of the chemical kinetics involved.