Problem 76 - Chemistry: Principles and Reactions

Question

Write the rate expression for each of the following elementary steps: (a) \(\mathrm{NO}+\mathrm{O}_{3} \longrightarrow \mathrm{NO}_{2}+\mathrm{O}_{2}\) (b) \(2 \mathrm{NO}_{2} \longrightarrow 2 \mathrm{NO}+\mathrm{O}_{2}\) (c) \(\mathrm{K}+\mathrm{HCl} \longrightarrow \mathrm{KCl}+\mathrm{H}\)

Step-by-Step Solution

Answer

Question: Write the rate expression for each of the following elementary reactions: (a) NO + O3 → NO2 + O2 (b) 2NO2 → 2NO + O2 (c) K + HCl → KCl + H Answer: (a) Rate = k [NO][O3] (b) Rate = k [NO2]^2 (c) Rate = k [K][HCl]

Step 1: Reaction (a) - Identify Reactants and Molecularity

In the first reaction, we have \(\mathrm{NO}\) and \(\mathrm{O}_{3}\) as reactants. Each reactant has a molecularity of 1 because there is only one molecule involved in the reaction.

Step 2: Reaction (a) - Write Rate Expression

For reaction (a), the rate expression is given by: $$ \text{Rate} = k [\mathrm{NO}]^1 [\mathrm{O}_{3}]^1 $$

Step 3: Reaction (b) - Identify Reactants and Molecularity

In the second reaction, we have \(\mathrm{NO}_{2}\) as the reactant. It has a molecularity of 2 because there are two molecules involved in the reaction.

Step 4: Reaction (b) - Write Rate Expression

For reaction (b), the rate expression is given by: $$ \text{Rate} = k [\mathrm{NO}_{2}]^2 $$

Step 5: Reaction (c) - Identify Reactants and Molecularity

In the third reaction, we have \(\mathrm{K}\) and \(\mathrm{HCl}\) as reactants. Each reactant has a molecularity of 1 because there is only one molecule involved in the reaction.

Step 6: Reaction (c) - Write Rate Expression

For reaction (c), the rate expression is given by: $$ \text{Rate} = k [\mathrm{K}]^1 [\mathrm{HCl}]^1 $$ To summarize, the rate expressions for the given elementary reactions are: (a) \(\text{Rate} = k [\mathrm{NO}] [\mathrm{O}_{3}]\) (b) \(\text{Rate} = k [\mathrm{NO}_{2}]^2\) (c) \(\text{Rate} = k [\mathrm{K}] [\mathrm{HCl}]\)

Key Concepts

Chemical Kinetics

Chemical kinetics is an essential aspect of chemistry that studies the speed or rate at which a chemical reaction occurs and determines the factors influencing it. This field helps us understand how various conditions like temperature, concentration, and presence of catalysts can affect the rate of a reaction.

Understanding chemical kinetics allows us to predict how long it will take for a reaction to complete and what yield of products we can expect over time. It also plays a pivotal role in industries, where the efficiency of chemical processes can mean the difference between a profitable operation and a costly one.

When we talk about rate expressions, such as, \( \text{Rate} = k [\mathrm{NO}] [\mathrm{O}_{3}] \), the \(k\) in the equation represents the rate constant, which is specific to each reaction and can be influenced by external conditions. The rate constant is central to kinetical analyses, as it is a quantification of how fast the reaction proceeds under certain conditions.

Elementary Reaction Steps

Elementary reaction steps are the simplest reactions in which reactants convert to products in a single step and with a single transition state. These steps are crucial building blocks to understanding complex reactions, which happen in multiple stages.

An important feature of elementary reactions is how their rate expressions reflect the stoichiometry of the reactants involved. For example, the elementary reaction for the formation of \(\mathrm{NO}_{2}\) and \(\mathrm{O}_{2}\) from \(\mathrm{NO}\) and \(\mathrm{O}_{3}\) has a rate expression directly related to the concentrations of the reactants.

In a multi-step reaction, however, the overall rate expression can be more complex and is not always apparent from the stoichiometry of the overall reaction. Kinetic studies, often involving experiments, are utilized to determine the individual steps and their respective rate expressions.

Reaction Molecularity

Reaction molecularity refers to the number of reactant particles involved in an elementary reaction step. It is a key concept in understanding how reactants interact to form products.

Unimolecular and Bimolecular Reactions

Reactions can be classified as unimolecular or bimolecular. A unimolecular reaction involves a single molecule undergoing a transformation, while a bimolecular reaction involves two reactant molecules colliding and reacting together.

Using the reactions provided as examples, the conversion of \(\mathrm{NO}_{2}\) to \(\mathrm{NO}\) and \(\mathrm{O}_{2}\) in reaction (b) is a bimolecular step, as it involves two \(\mathrm{NO}_{2}\) molecules. The rate expression (\text{Rate} = k [\mathrm{NO}_{2}]^2) highlights this by squaring the concentration of \(\mathrm{NO}_{2}\).

Molecularity can also provide insights into the underlying reaction mechanism and is a fundamental concept that links the microscopic interactions of molecules to the macroscopic observable rate of a reaction.