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Chapter 14: Problem 65

(a) What is meant by the term elementary reaction? (b) What is the difference between a unimolecular and a bimolecular elementary reaction? (c) What is a reaction mechanism? (d) What is meant by the term rate determining step?

Short Answer

Expert verified
(a) An elementary reaction is a single molecular event occurring during a chemical reaction, typically in a single step. (b) Unimolecular and bimolecular elementary reactions differ based on the number of molecules involved. Unimolecular reactions involve one molecule transitioning, while bimolecular reactions involve two molecules colliding and reacting. (c) A reaction mechanism is a sequence of elementary reactions or steps describing the pathway of reactants converting into products at the molecular level. (d) The rate-determining step is the slowest elementary step in a reaction mechanism, determining the overall reaction rate and influencing factors affecting reaction rates.

Step by step solution

01

(a) Elementary Reaction

An elementary reaction is a single molecular event that occurs during a chemical reaction. It represents the most basic process at the molecular level, involving the rearrangement or interaction of atoms or molecules, and typically occurs within a single step.
02

(b) Unimolecular and Bimolecular Elementary Reactions

Unimolecular and bimolecular elementary reactions are categories of elementary reactions based on the number of molecules involved in the reaction event. A unimolecular elementary reaction involves the transition of a single molecule from one chemical species to another, either through decomposing or rearranging. A bimolecular elementary reaction, on the other hand, involves two molecules colliding and reacting to form new chemical species. In general, the two types can be represented by the following equations: - Unimolecular: \(A \rightarrow products\) - Bimolecular: \(A + B \rightarrow products\)
03

(c) Reaction Mechanism

A reaction mechanism is a sequence of elementary reactions or steps that describes the pathway by which reactants are converted into products at the molecular level. It provides detailed information about the intermediate species formed during the reaction, as well as the energy changes and activation energies associated with each elementary step. The reaction mechanism helps explain the observed rate law and overall reaction kinetics.
04

(d) Rate-Determining Step

The rate-determining step (RDS) is the slowest elementary step in a reaction mechanism, which effectively determines the overall reaction rate. Since all other steps in the mechanism occur relatively faster than the RDS, the progress of the reaction is limited by the rate at which the RDS occurs. By understanding the RDS, chemists can gain insights into the factors that influence the reaction rates and predict how the reaction conditions can be optimized to improve reaction efficiency.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Unimolecular Reactions
Unimolecular reactions are a type of elementary reaction where a single molecule undergoes a transformation. This transformation can involve rearrangement of its atoms, or breaking into smaller pieces.

Imagine a molecule as a complex structure that can change by itself, without needing to collide with another molecule. A classic example would be the decomposition of a molecule like nitrous oxide (\( NO_2 \)) which breaks down to form a simpler product or products.
  • Occurs in one molecule
  • No external collisions needed
  • Can involve rearrangement or decomposition
Such reactions are crucial in many industrial processes and occur naturally in environments like the Earth's atmosphere. The term "uni" in unimolecular indicates that only one reactant is involved in the slow step of the reaction.
Bimolecular Reactions
Bimolecular reactions are elementary reactions involving two separate molecules. These two molecules collide and react together to form new products.

This collision is necessary for the reaction to occur. It鈥檚 like a dance between two partners who must meet in the right conditions to create something new. An example is the reaction of hydrogen and iodine to form hydrogen iodide.
  • Requires collision between two molecules
  • More common than unimolecular reactions
  • Dependent on concentration of both reactants
The term "bi" emphasizes that two reactant species are involved, making it a crucial type of mechanism in chemical processes where transformation requires interaction between different molecules.
Reaction Mechanism
Understanding a reaction mechanism involves exploring the step-by-step sequence of elementary reactions that lead to the final product. Think of it as a detailed map that shows every small reaction that happens from start to finish.

Each step in this map involves the interaction of molecules in specific ways, showing how intermediates are formed along the way. Reaction mechanisms can be complex, with many steps, or quite simple with only a few.
  • Sequence of elementary steps
  • Describes how reactants turn into products
  • Shows energy changes and intermediates
By examining mechanisms, chemists gain insights into the physical conditions needed to control the reaction rate and the possible side reactions that might occur.
Rate-Determining Step
The concept of the rate-determining step (RDS) is pivotal in understanding reaction speeds. The RDS is the slowest step within a reaction mechanism. It functions like a bottleneck, controlling how fast the entire reaction proceeds.

Think of a multi-step process like a factory line, where the slowest machine dictates the pace of production. Similarly, the slowest step in a chemical reaction limits how fast reactants can form products.
  • Slowest step in a reaction sequence
  • Determines overall reaction rate
  • Vital for understanding and optimizing reaction conditions
Knowing the RDS helps chemists determine which part of the reaction pathway to optimize, thereby improving efficiency and effectiveness in both lab and industrial settings.

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Most popular questions from this chapter

(a) What are the units usually used to express the rates of reactions occurring in solution? (b) As the temperature increases, does the reaction rate increase or decrease? (c) As a reaction proceeds, does the instantaneous reaction rate increase or decrease?

Suppose that a certain biologically important reaction is quite slow at physiological temperature \(\left(37^{\circ} \mathrm{C}\right)\) in the absence of a catalyst. Assuming that the collision factor remains the same, by how much must an enzyme lower the activation energy of the reaction to achieve a \(1 \times 10^{5}\) -fold increase in the reaction rate?

The rate of a first-order reaction is followed by spectroscopy, monitoring the absorbance of a colored reactant at \(520 \mathrm{nm}\). The reaction occurs in a 1.00-cm sample cell, and the only colored species in the reaction has an extinction coefficient of \(5.60 \times 10^{3} \mathrm{M}^{-1} \mathrm{~cm}^{-1}\) at \(520 \mathrm{nm} .\) (a) Calculate the initial concentration of the colored reactant if the absorbance is 0.605 at the beginning of the reaction. (b) The absorbance falls to 0.250 at \(30.0 \mathrm{~min} .\) Calculate the rate constant in units of \(\mathrm{s}^{-1}\). (c) Calculate the half-life of the reaction. (d) How long does it take for the absorbance to fall to \(0.100 ?\)

The dimerization of \(\mathrm{C}_{2} \mathrm{~F}_{4}\) to \(\mathrm{C}_{4} \mathrm{~F}_{8}\) has a rate constant \(k=0.045 \mathrm{M}^{-1} \mathrm{~s}^{-1}\) at \(450 \mathrm{~K} .\) (a) Based on the unit of \(k\) what is the reaction order in \(\mathrm{C}_{2} \mathrm{~F}_{4} ?(\mathbf{b})\) If the initial concentration of \(\mathrm{C}_{2} \mathrm{~F}_{4}\) is \(0.100 \mathrm{M}\), how long would it take for the concentration to decrease to \(0.020 \mathrm{M}\) at \(450 \mathrm{~K}\) ?

Urea \(\left(\mathrm{NH}_{2} \mathrm{CONH}_{2}\right)\) is the end product in protein metabolism in animals. The decomposition of urea in \(0.1 \mathrm{M} \mathrm{HCl}\) occurs according to the reaction $$ \mathrm{NH}_{2} \mathrm{CONH}_{2}(a q)+\mathrm{H}^{+}(a q)+2 \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow 2 \mathrm{NH}_{4}^{+}(a q)+\mathrm{HCO}_{3}^{-}(a q) $$ The reaction is first order in urea and first order overall. When \(\left[\mathrm{NH}_{2} \mathrm{CONH}_{2}\right]=0.200 \mathrm{M},\) the rate at \(61.05^{\circ} \mathrm{C}\) $$ \text { is } 8.56 \times 10^{-5} \mathrm{M} / \mathrm{s} $$ (a) What is the rate constant, \(k\) ? (b) What is the concentration of urea in this solution after \(4.00 \times 10^{3} \mathrm{~s}\) if the starting concentration is \(0.500 \mathrm{M}\) ? (c) What is the half-life for this reaction at \(61.05^{\circ} \mathrm{C}\) ?
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