Problem 80 - Chemistry: The Central Science

Question

The addition of \(\mathrm{NO}\) accelerates the decomposition of \(\mathrm{N}_{2} \mathrm{O}\), possibly by the following mechanism: $$ \begin{aligned} \mathrm{NO}(g)+& \mathrm{N}_{2} \mathrm{O}(g) \longrightarrow \mathrm{N}_{2}(g)+\mathrm{NO}_{2}(g) \\ 2 \mathrm{NO}_{2}(g) & \longrightarrow 2 \mathrm{NO}(g)+\mathrm{O}_{2}(g) \end{aligned} $$ (a) What is the chemical equation for the overall reaction? Show how the two steps can be added to give the overall equation. (b) Is NO serving as a catalyst or an intermediate in this reaction? (c) If experiments show that during the decomposition of \(\mathrm{N}_{2} \mathrm{O}, \mathrm{NO}_{2}\) does not accumulate in measurable quantities, does this rule out the proposed mechanism?

Step-by-Step Solution

Answer

The overall chemical equation for the reaction is \(NO(g) + N_2O(g) \rightarrow N_2(g) + O_2(g)\). NO is serving as a catalyst in this reaction, as it is consumed in the first step and regenerated in the second step without being altered in the overall reaction. The lack of measurable quantities of \(NO_2\) does not rule out the proposed mechanism, as it could be consistent with a faster second step preventing \(NO_2\) from accumulating.

Step 1: a) Overall chemical equation

To get the overall chemical equation, we'll add the two given equations as follows: Step 1: \(NO(g) + N_2O(g) \rightarrow N_2(g) + NO_2(g)\) Step 2: \(2NO_2(g) \rightarrow 2NO(g) + O_2(g)\) Sum the two equations: \(NO(g) + N_2O(g) + 2NO_2(g) \rightarrow N_2(g) + NO_2(g) + 2NO(g) + O_2(g)\) Now, cancel out the molecules that appear on both sides of the equation: \(NO(g) + N_2O(g) \rightarrow N_2(g) + O_2(g)\) So the overall chemical equation is: \(NO(g) + N_2O(g) \rightarrow N_2(g) + O_2(g)\)

Step 2: b) NO as catalyst or intermediate

A catalyst is a substance that increases the rate of a reaction and remains unchanged after the reaction. An intermediate is a substance that is produced in one step of a reaction and consumed in a subsequent step. From the given mechanism: Step 1: \(NO(g)\) is a reactant and not produced in any other reaction, and \(NO_2(g)\) is a product. Step 2: \(NO_2(g)\) is a reactant and it gets consumed to produce \(NO(g)\). Since \(NO(g)\) is consumed in the first step and regenerated in the second step without being altered in the overall reaction, it is a catalyst in this reaction.

Step 3: c) Interpretation of experimental results

If experiments show that during the decomposition of \(N_2O\), \(NO_2\) does not accumulate in measurable quantities, it doesn't necessarily rule out the proposed mechanism. In the reaction mechanism, \(NO_2\) is produced in the first step and consumed in the second step. If the second step is faster than the first step, \(NO_2\) would be consumed immediately after being produced, preventing it from accumulating in measurable quantities. This would be consistent with the proposed mechanism. Therefore, the lack of measurable quantities of \(NO_2\) does not rule out the proposed mechanism.

Key Concepts

Catalysts

Catalysts are fascinating substances that play a crucial role in speeding up chemical reactions. They achieve this by providing an alternative reaction pathway with a lower activation energy than the uncatalyzed reaction.
This means that reactants can be converted to products more quickly and efficiently, without the catalyst itself being consumed in the process.

• For example, in the given reaction mechanism, NO acts as a catalyst.
• It facilitates the decomposition of N\( _2 \) O without altering the overall reaction products.
• Since NO is regenerated in the mechanism, it fulfills its role as a catalyst.

Catalysts are incredibly important in both industrial and biological processes, offering a smart and resourceful way to promote reactions while remaining unchanged.

Chemical Equations

Chemical equations are the symbolic representation of a chemical reaction, showing the reactants transforming into products. They provide valuable insight into the specific substances involved and their stoichiometric relationships.
By balancing a chemical equation, we ensure that the law of conservation of mass is respected, which means that the same number of atoms for each element appear on both sides of the equation.

• In the original exercise, the mechanism involves two steps expressed in chemical equations.
• Combining these provides the overall balanced equation for the decomposition of N\( _2 \) O:

\[ NO(g) + N_2O(g) \rightarrow N_2(g) + O_2(g) \]Chemical equations are essential tools in chemistry that allow us to follow and understand the processes happening at the molecular level.

Reaction Intermediates

Reaction intermediates are species that are formed during the conversion of reactants into products but do not appear in the overall balanced equation.
They are temporary entities, consumed in later stages of the mechanism, and provide insight into the detailed steps of a reaction.

• In the exercise, NO\( _2 \) is an example of a reaction intermediate.
• It is produced in the first step of the mechanism and quickly consumed in the next step.
• Intermediates are crucial for deducing reaction mechanisms and understanding how reactions proceed.

So, intermediates help paint the full picture of how a reaction unfolds at the microscopic level, even though they don't appear in the final equation.

Decomposition Reactions

Decomposition reactions are a type of chemical reaction where a single compound breaks down into two or more simpler substances.
These reactions are often driven by energy in the form of heat, light, or electricity, leading to the breakdown of complex molecules.

• The decomposition of N\( _2 \) O is a typical example of this type of reaction, where it breaks down into nitrogen and oxygen gases.
• Such reactions are fundamental in various fields, including chemistry, biology, and environmental science.

Decomposition reactions are an essential concept because they help us understand how complex molecules can be transformed into simpler, more stable structures, revealing the dynamics of chemical change.