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# 18.3: Potential Energy Diagrams

Difficulty Level: At Grade Created by: CK-12

## Lesson Objectives

The student will:

• define internal energy.
• describe and draw the difference between endothermic and exothermic potential energy diagrams.
• draw and label the parts of a potential energy diagram.

## Vocabulary

• endothermic reaction
• exothermic reaction
• internal energy
• potential energy diagram

## Introduction

In this lesson, we go beyond the theoretical perspectives of the collision theory to consider how particle collisions can be represented in energy diagrams. Potential energy diagrams are used in the study of kinetics to show how the potential energy changes during collisions of reactants and products. The features of such diagrams will be the focus of this lesson.

## Internal Energy of Reactants and Products, ΔH

Potential energy diagrams illustrate the potential energy of the reactants and products for a chemical reaction and how this energy changes during a reaction. Take a look at the potential energy diagram of the reaction shown below.

The y\begin{align*}y\end{align*}-axis represents the potential energy. The potential energy measures the energy stored within the bonds and phases of the reactants and products. This potential energy is a part of the internal energy. In chemical reactions, the internal energy represents the total energy of the system and is often called enthalpy. The x\begin{align*}x\end{align*}-axis represents the reaction progress. Chemical reactions proceed (or are read) from left to right. Therefore, looking at the potential energy diagram, the reactants are usually found to the left on the diagram and the products on the right.

The enthalpy of a substance is sometimes called heat content. The potential energy stored in the bonds of the substance was thought of as heat stored as potential energy. When a reaction occurs, the enthalpy or heat content of the reactants changes into the enthalpy or heat content of the products. The enthalpy of the reactants and products is almost never the same. Therefore, when a reaction occurs, there is a change in the amount of potential energy stored in the bonds between the reactants and the products. If the bonds of the products store more energy than the bonds of the reactants, then energy must be taken in during the reaction. If the bonds of the products store less potential energy than the bonds of the reactants, then excess potential energy will be left over and will come out of the reaction as kinetic energy. The difference in the enthalpy or heat content of the reactants and that of the products is expressed as H\begin{align*}\triangle H\end{align*}, or the change in enthalpy. Since this energy is either taken in or given off during the reaction, it is also called the heat of reaction.

## Exothermic and Endothermic Potential Energy Diagrams

There are two types of potential energy diagrams. These two types center on the difference between the energies of the reactants and products. Consider the figure below. An endothermic reaction is shown on the left, and an exothermic reaction is shown on the right.

The definition of H\begin{align*}\triangle H\end{align*} is the heat content (enthalpy) of the products minus the heat content (enthalpy) of the reactants, H=HproductsHreactants\begin{align*}\triangle H = H_{\mathrm{products}} - H_{\mathrm{reactants}}\end{align*}. When the enthalpy of the reactants is greater than the enthalpy of the products, heat will be given off by the reaction, so the H\begin{align*}\triangle H\end{align*} will be negative. The opposite is true when the enthalpy of the products is greater than the enthalpy of the reactants.

If the difference between the potential energy of the products and the reactants is positive, or H>0\begin{align*}\triangle H > 0\end{align*}, the reaction is considered to be endothermic (kinetic energy is absorbed and becomes potential energy in the bonds) and is represented by the left figure above. If the difference between the potential energy of the products and the reactants is negative, or H<0\begin{align*}\triangle H < 0\end{align*}, the reaction is considered to be exothermic (excess potential energy from the bonds is left over and comes out into the surroundings as kinetic energy) and is represented by the right figure above.

## Activation Energy Barrier

Recall that the activation energy represents the minimum amount of energy required to overcome the energy barrier. This energy must be supplied from the collision energy of the reactant molecules. If the molecules do not have sufficient collision energy to provide the activation energy, then the reaction must be heated to increase the kinetic energy of the reactants in order for the reaction to occur. For instance, hydrogen gas and oxygen gas can be kept in the same container at room temperature for long periods of time without reacting. Even though the molecules are colliding, they do not react since there is insufficient activation energy.

In potential energy diagrams, the symbol for activation energy is often designated as Ea\begin{align*}E_a\end{align*}. Look at the two exothermic reactions whose potential energy diagrams are represented in figures A and B below, and notice the activation energy marked in each.

When a reaction has a low activation energy, like in figure A above, most of the reactant molecules have sufficient kinetic energy to react, and the reaction will most likely be rapid (a high reaction rate). When a reaction has a high activation energy, like in figure B above, most of the reactant molecules will not have enough energy to react, and the reaction will most likely be very slow.

## Activated Complex

Remember that the activated complex is a transitional state between the reactants and products. The transitional complex is a short-lived, very unstable species that is the intermediate between the reactants and products. The activated complex contains the highest amount of energy of all of the species in the reaction. Its position is therefore at the top of the activation energy barrier, as is illustrated below.

Example:

Consider the reaction between H2\begin{align*}\mathrm{H}_2\end{align*} and I2\begin{align*}\mathrm{I}_2\end{align*}.

H2(g)+I2(g)2 HI(g)     H=50.kJ\begin{align*}\mathrm{H}_{2(g)} + \mathrm{I}_{2(g)} \rightarrow 2 \ \mathrm{HI}_{(g)} \ \ \ \ \ \triangle H = 50.\text{kJ}\end{align*}

Under certain circumstances, the enthalpy of the reactants is 20 kJ/mol\begin{align*}20 \ \mathrm{kJ/mol}\end{align*}, the activation energy is 80 kJ\begin{align*}80 \ \mathrm{kJ}\end{align*}, and the enthalpy of reaction is 30 kJ\begin{align*}30 \ \mathrm{kJ}\end{align*}. Draw a potential energy diagram with the following properly labeled:

1. the axes
2. the activation energy
3. the change in enthalpy
4. the activated complex

Solution:

Example:

From the potential energy diagram above, list the values for

1. the enthalpy of the reactants
2. the enthalpy of the products
3. the threshold energy
4. the activation energy
5. the change in enthalpy

Solution:

1. 20 kJ/mol\begin{align*}20 \ \mathrm{kJ/mol}\end{align*}
2. 50 kJ/mol\begin{align*}50 \ \mathrm{kJ/mol}\end{align*}
3. 100 kJ/mol\begin{align*}100 \ \mathrm{kJ/mol}\end{align*}
4. 80 kJ/mol\begin{align*}80 \ \mathrm{kJ/mol}\end{align*}
5. 30 kJ/mol\begin{align*}30 \ \mathrm{kJ/mol}\end{align*}

## Lesson Summary

• Potential energy diagrams show how the potential energy changes during reactions from reactants and products.
• Exothermic reactions have a potential energy difference between the products and reactants that is negative.
• Endothermic reactions have a potential energy difference between the products and reactants that is positive.
• In potential energy diagrams, the symbol for activation energy is often designated as Ea\begin{align*}E_a\end{align*}.
• The activated complex is positioned at the top of the activation energy barrier.

Visit the website below for an animation on exothermic and endothermic reactions.

## Review Questions

1. Define and explain the importance of the activation energy.

Use the diagram below to answer questions 2 through 6.

1. Which letter represents the activation energy barrier?
1. a
2. b
3. c
4. d
2. Which statement best describes the reaction?
1. The reaction is exothermic in the forward reaction.
2. The reaction is endothermic in the forward reaction.
3. The reaction is exothermic in the reverse reaction.
4. The reaction is exothermic only at high temperatures.
3. Which letter represents the change in enthalpy for the reaction?
1. b
2. c
3. d
4. e
4. Which letter represents the activated complex for the reaction?
1. a
2. b
3. c
4. d
5. What is an activated complex?
1. a transitional species that can eventually be isolated
2. a transitional species of that must be made before the products can be formed
3. a reactant molecule breaking into a product molecule
4. part of the activation energy barrier
6. For the following reaction, the activation energy is 60 kJ\begin{align*}60 \ \mathrm{kJ}\end{align*}: A2(g)+2 B(g)2 AB(g)\begin{align*}A_{2(g)} + 2 \ B_{(g)} \rightarrow 2 \ AB_{(g)}\end{align*}. Draw a potential energy diagram properly labeling the following:
1. the axes
2. the reactants and products
3. the activation energy
4. the enthalpy

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