Problem 73
Question
What is the molecularity of each of the following elementary reactions? Write the rate law for each. (a) \(\mathrm{Cl}_{2}(g) \longrightarrow 2 \mathrm{Cl}(g)\) (b) \(\mathrm{OCl}^{-}(a q)+\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{HOCl}(a q)+\mathrm{OH}^{-}(a q)\) (c) \(\mathrm{NO}(g)+\mathrm{Cl}_{2}(g) \longrightarrow \mathrm{NOCl}_{2}(g)\)
Step-by-Step Solution
Verified Answer
(a) Unimolecular; Rate = k[Cl2]
(b) Bimolecular; Rate = k[OCl⁻][H2O]
(c) Bimolecular; Rate = k[NO][Cl2]
1Step 1: Reaction (a): Cl2(g) -> 2 Cl(g)
In this elementary reaction, a molecule of Cl2(g) dissociates into two Cl(g) atoms. As only one molecule is involved in this reaction, it is a unimolecular reaction.
Now, let's write the rate law for this reaction. The rate law is an equation that expresses the reaction rate as a function of the concentration of the reactants. For a unimolecular reaction, the rate law is given by:
Rate = k[Reactant]
Where Rate is the reaction rate, k is the rate constant and [Reactant] is the concentration of the reactant:
Rate = k[Cl2]
2Step 2: Reaction (b): OCl⁻(aq) + H2O(l) -> HOCl(aq) + OH⁻(aq)
In this elementary reaction, two molecules are involved: one OCl⁻(aq) ion and one H2O(l) molecule. As two molecules are participating in the reaction, it is a bimolecular reaction.
The rate law for a bimolecular reaction is given by:
Rate = k[Reactant1][Reactant2]
Applying this to our reaction:
Rate = k[OCl⁻][H2O]
3Step 3: Reaction (c): NO(g) + Cl2(g) -> NOCl2(g)
In this elementary reaction, two molecules are involved: one NO(g) molecule and one Cl2(g) molecule. As two molecules are involved in this reaction, it is a bimolecular reaction.
The rate law for a bimolecular reaction is given by:
Rate = k[Reactant1][Reactant2]
Applying this to our reaction:
Rate = k[NO][Cl2]
The molecularity and rate laws for each reaction are as follows:
(a) Unimolecular; Rate = k[Cl2]
(b) Bimolecular; Rate = k[OCl⁻][H2O]
(c) Bimolecular; Rate = k[NO][Cl2]
Key Concepts
Elementary ReactionsRate LawUnimolecular ReactionBimolecular Reaction
Elementary Reactions
An elementary reaction is a basic chemical reaction where reactants convert to products in a single step and with a single transition state. These reactions are the building blocks of complex reactions and proceed without any intermediate or side reactions, making their rate laws directly dependent on the stoichiometry of the reaction.
Understanding the molecularity of an elementary reaction is crucial, as it refers to the number of reactant particles involved in the reaction. Molecularity can be unimolecular, involving a single molecule, bimolecular, involving two reacting species, or even termolecular, involving three. However, termolecular reactions are quite rare because the probability of three particles colliding simultaneously with the correct orientation is low.
Understanding the molecularity of an elementary reaction is crucial, as it refers to the number of reactant particles involved in the reaction. Molecularity can be unimolecular, involving a single molecule, bimolecular, involving two reacting species, or even termolecular, involving three. However, termolecular reactions are quite rare because the probability of three particles colliding simultaneously with the correct orientation is low.
Rate Law
The rate law is a mathematical relationship linking the rate of a reaction to the concentrations of the reactants. For an elementary reaction, the rate law can be deduced from the reaction's molecularity. It describes how the reaction rate is proportional to the concentration of the reactants raised to a power, usually equal to the number of molecules or atoms undergoing the transformation.
It's expressed in the general form: \[ Rate = k[Reactant_1]^{m}[Reactant_2]^{n}... \] Here, \(k\) is the rate constant indicative of the reaction speed, and \(m\), \(n\), etc., are the orders of the reaction with respect to each reactant. For elementary reactions, these orders correspond exactly to the molecularity, indicating the reaction mechanism directly reflects the observed kinetics.
It's expressed in the general form: \[ Rate = k[Reactant_1]^{m}[Reactant_2]^{n}... \] Here, \(k\) is the rate constant indicative of the reaction speed, and \(m\), \(n\), etc., are the orders of the reaction with respect to each reactant. For elementary reactions, these orders correspond exactly to the molecularity, indicating the reaction mechanism directly reflects the observed kinetics.
Unimolecular Reaction
In a unimolecular reaction, a single reactant molecule undergoes a transformation to form the product. This type of elementary reaction has a molecularity of one, meaning it involves only one reacting species. A classic example is the decomposition of a molecule into two or more molecules or atoms.
The rate law for a unimolecular reaction takes the simple form: \[ Rate = k[Reactant] \] When observing a unimolecular reaction, the rate is directly proportional to the concentration of the single reactant. The simplicity of unimolecular reactions often makes them a preferred model for studying the fundamental aspects of reaction kinetics.
The rate law for a unimolecular reaction takes the simple form: \[ Rate = k[Reactant] \] When observing a unimolecular reaction, the rate is directly proportional to the concentration of the single reactant. The simplicity of unimolecular reactions often makes them a preferred model for studying the fundamental aspects of reaction kinetics.
Bimolecular Reaction
Bimolecular reactions involve two reactant molecules that collide and interact to form products, making them have a molecularity of two. Such reactions are prevalent and a core part of chemical kinetics, as they describe a wide range of chemical processes, from simple atomic collisions to complex biological interactions.
The rate law for a bimolecular reaction follows the form: \[ Rate = k[Reactant_1][Reactant_2] \] This indicates that the rate is proportional to the product of the concentrations of the two reactants. Therefore, the probability of reaction depends on the likelihood of the two reactant molecules encountering each other, which is a function of their concentrations.
The rate law for a bimolecular reaction follows the form: \[ Rate = k[Reactant_1][Reactant_2] \] This indicates that the rate is proportional to the product of the concentrations of the two reactants. Therefore, the probability of reaction depends on the likelihood of the two reactant molecules encountering each other, which is a function of their concentrations.
Other exercises in this chapter
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What are the differences between an intermediate and a transition state?
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What is the molecularity of each of the following elementary reactions? Write the rate law for each. (a) \(2 \mathrm{NO}(g) \longrightarrow \mathrm{N}_{2} \math
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