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Chapter 13: Problem 75

Sketch a potential-energy diagram for the reaction of nitric oxide with ozone. $$ \mathrm{NO}(g)+\mathrm{O}_{3}(g) \longrightarrow \mathrm{NO}_{2}(g)+\mathrm{O}_{2}(g) $$ The activation energy for the forward reaction is \(10 \mathrm{~kJ} ;\) the \(\Delta H^{\circ}\) is \(-200 \mathrm{~kJ}\). What is the activation energy for the reverse reaction? Label your diagram appropriately. {-}$

Short Answer

Expert verified
The activation energy for the reverse reaction is 210 kJ.

Step by step solution

01

Understand the Reaction Pathway

The reaction path involves reactants (NO and O鈧�) converting to products (NO鈧� and O鈧�). This path is reflected in a potential energy diagram with reactants on the left and products on the right.
02

Identify Energy Values

Identify the known energy values: the activation energy for the forward reaction is 10 kJ and the change in enthalpy (螖H掳) for the reaction is -200 kJ.
03

Activation Energy in Potential-Energy Diagram

In a potential-energy diagram, the activation energy of the forward reaction is the energy difference between the transition state and the reactants. The transition state is the highest energy point along the reaction path.
04

Apply 螖H掳

The 螖H掳 of -200 kJ indicates that the products are at a lower energy level than the reactants by 200 kJ. This is shown by drawing the products 200 kJ lower on the diagram relative to the reactants.
05

Calculate Activation Energy for Reverse Reaction

For the reverse reaction (NO鈧� + O鈧� to NO + O鈧�), the activation energy is the energy difference between the transition state and the products. Since the products are lower by 200 kJ and the forward activation energy is 10 kJ, the reverse activation energy is 10 kJ + 200 kJ = 210 kJ.
06

Sketch the Energy Diagram

Draw the potential-energy diagram with an initial energy level for reactants, a peak representing the transition state at 10 kJ above the reactants, and a final energy level for the products 200 kJ below the reactants. Label each segment accordingly: reactants, products, activation energy (forward and reverse), and 螖H掳.

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Key Concepts

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

Activation Energy
Activation energy is a crucial concept in understanding how chemical reactions occur. It refers to the minimum amount of energy required for reactants to transform into products through a chemical reaction. In a potential energy diagram, this is depicted as the energy difference between the reactants and the highest point on the curve, known as the transition state. Activation energy can be thought of as an energy barrier that must be overcome for a reaction to proceed.
  • For the forward reaction, it is given as 10 kJ.
  • The reverse reaction, in this case, requires 210 kJ, as the products are at a lower energy level compared to the reactants by 200 kJ.
This concept helps us understand why some reactions occur faster than others and how conditions such as temperature can affect reaction rates.
Enthalpy Change
Enthalpy change, denoted as 螖H, indicates the overall energy change during a chemical reaction. Specifically, it tells us whether a reaction is endothermic or exothermic. In this exercise, the 螖H掳 value is -200 kJ, which means the reaction releases energy and is exothermic.
  • Exothermic reactions, like this one, result in products that are lower in energy compared to the reactants.
  • This energy difference is represented on a potential energy diagram by the vertical distance between the reactants and products.
Understanding enthalpy change is important for predicting whether reactions occur spontaneously and for estimating the heat exchange with the surroundings during the process.
Transition State
The transition state is a key concept in chemical reaction dynamics. It represents the point along the reaction pathway where the energy is at its highest. In a potential energy diagram, the transition state can be observed at the peak of the curve between the reactants and products.
  • The transition state is a temporary state that cannot be isolated.
  • It signifies the most unstable configuration the reactants pass through on their way to becoming products.
Understanding the transition state helps chemists design catalysts that lower the activation energy needed, speeding up reactions.
Energy Levels
Energy levels in a chemical reaction context represent the potential energy of reactants and products at different stages of the reaction. They help visualize how energy changes throughout the reaction process in a potential energy diagram.
  • The initial energy level in our exercise starts with the reactants, NO and O鈧�.
  • After overcoming the activation energy, which includes reaching the transition state, products NO鈧� and O鈧� are formed at a lower energy level by 200 kJ.
Studying these energy levels gives insight into the energy requirements and efficiency of chemical reactions.
Chemical Reaction Dynamics
Chemical reaction dynamics delve into the details of reaction mechanisms and the role of energy. By analyzing potential energy diagrams, one can understand the movement and transformation of atoms during a reaction. The process reveals how molecules collide, form a transition state, and rearrange into products.
  • Reaction dynamics help predict reaction pathways and speed.
  • They are critical for optimizing reactions in industrial and laboratory settings to achieve desired products efficiently.
This knowledge allows scientists and engineers to manipulate conditions such as temperature and catalysts to control and improve reaction outcomes.

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Most popular questions from this chapter

The thermal decomposition of nitryl chloride, \(\mathrm{NO}_{2} \mathrm{Cl}\), $$ 2 \mathrm{NO}_{2} \mathrm{Cl}(g) \longrightarrow 2 \mathrm{NO}_{2}(g)+\mathrm{Cl}_{2}(g) $$ is thought to occur by the mechanism shown in the following equations: $$ \mathrm{NO}_{2} \mathrm{Cl} \stackrel{k_{1}}{\longrightarrow} \mathrm{NO}_{2}+\mathrm{Cl} $$ (slow step) $$ \mathrm{NO}_{2} \mathrm{Cl}+\mathrm{Cl} \stackrel{k_{2}}{\longrightarrow} \mathrm{NO}_{2}+\mathrm{Cl}_{2} $$ (fast step) What rate law is predicted by this mechanism?

Briefly discuss the factors that affect the rates of chemical reactions. Which of the factors affect the magnitude of the rate constant? Which factor(s) do not affect the magnitude of the rate constant? Why?

A study of the decomposition of azomethane, \(\mathrm{CH}_{3} \mathrm{NNCH}_{3}(g) \longrightarrow \mathrm{C}_{2} \mathrm{H}_{6}(g)+\mathrm{N}_{2}(g)\) gave the following concentrations of azomethane at various times: \(\begin{array}{rl}\text { Time } & {\left[\mathrm{CH}_{3} \mathrm{NNCH}_{3}\right]} \\ 0 \mathrm{~min} & 1.50 \times 10^{-2} \mathrm{M} \\\ 10 \mathrm{~min} & 1.29 \times 10^{-2} \mathrm{M} \\ & 1.10 \times 10^{-2} \mathrm{M}\end{array}\) \(20 \mathrm{~min} \quad 1.10 \times 10^{-2} M\) $$ 30 \mathrm{~min} \quad 0.95 \times 10^{-2} \mathrm{M} $$ Obtain the average rate of decomposition in units of \(M / \mathrm{s}\) for each time interval.

At \(330^{\circ} \mathrm{C},\) the rate constant for the decomposition of \(\mathrm{NO}_{2}\) is \(0.775 \mathrm{~L} /(\mathrm{mol} \cdot \mathrm{s})\). If the reaction is second order, what is the concentration of \(\mathrm{NO}_{2}\) after \(2.5 \times 10^{2}\) seconds if the starting concentration was \(0.050 M ?\) What is the halflife of this reaction under these conditions?

For the decomposition of one mole of nitrosyl chloride, \(\Delta H=38 \mathrm{~kJ}\). $$ \mathrm{NOCl}(g) \longrightarrow \mathrm{NO}(g)+\frac{1}{2} \mathrm{Cl}_{2}(g) $$ The activation energy for this reaction is \(100 \mathrm{~kJ}\) a, Is this reaction exothermic or endothermic? b. What is the activation energy for the reverse reaction? c. If a catalyst were added to the reaction, how would this affect the activation energy?
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