Chemistry
Representations of Equilibrium
In chemistry, representations of equilibrium refer to visual or symbolic depictions of the balanced state reached in a reversible chemical reaction. These representations often include chemical equations, graphs, and diagrams to illustrate the dynamic nature of equilibrium, where the rates of the forward and reverse reactions are equal. They help in understanding the relationship between reactants and products at equilibrium.
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11 Key excerpts on "Representations of Equilibrium"
- Stella Vosniadou, Erik De Corte, Robert Glaser, Heinz Mandl(Authors)
- 2012(Publication Date)
- Routledge(Publisher)
4M:Chem. In this section, we describe the system and show how it implements the multiple, linked representation approach to learning chemical equilibrium. In the subsequent section, we examine preliminary evidence that supports the effectiveness of this approach.The environment currently includes four chemical systems: a physical equilibrium, a gas-phase equilibrium, a solution equilibrium, and a heterogeneous equilibrium. These are structured progressively so that students can move from a simple mental model of equilibrium to a more elaborate, complex understanding of the concept (White, 1993).Development on the system continues, but we estimate that in its current form it would take up to 8 hours in lecture and another 5–6 hours in laboratory sessions to thoroughly explore the completed portions. It is designed both for use with projection equipment in the lecture hall and individual work stations in classroom laboratories. In lecture, it is designed to make the class more interactive and engaging. In the classroom laboratory, it allows students, working individually or in small groups, to conduct structured, in-depth investigations of chemical phenomena.FIG. 3.1. Screen display of 4M:Chem showing multiple, linked representations (original in color).The symbol systems or representations that we use include: chemical notation, video of the reactions, molecular-level animations, dynamic graphs, displays of absorption spectra, and tabular data (see Fig. 3.1 for a sample screen display). The software allows learners to act on a chemical system and see the results of these actions propagate across the multiple representations. Let us examine how the use of these representations, individually and together, might act to influence understanding.Symbolic Elements and EventsThere is an operational space we present on the screen called the control window. It contains one representation of the chemical system that students have selected from a menu of available systems; it is expressed in the standard notation of chemists:The equation expresses a relationship between two symbolic entities. The entities and their relationship are, perhaps, yet to be understood by the students. The buttons present the students with two symbolic actions that can be performed on the system: “heat” or “cool.” These symbolic elements and buttons are what we term the literal features
eBook - PDF- Paul Flowers, Klaus Theopold, Richard Langley, William R. Robinson(Authors)
- 2019(Publication Date)
- Openstax(Publisher)
INTRODUCTION CHAPTER 13 Fundamental Equilibrium Concepts 13.1 Chemical Equilibria 13.2 Equilibrium Constants 13.3 Shifting Equilibria: Le Châtelier’s Principle 13.4 Equilibrium Calculations Imagine a beach populated with sunbathers and swimmers. As those basking in the sun get too hot, they enter the surf to swim and cool off. As the swimmers tire, they return to the beach to rest. If the rate at which sunbathers enter the surf were to equal the rate at which swimmers return to the sand, then the numbers (though not the identities) of sunbathers and swimmers would remain constant. This scenario illustrates a dynamic phenomenon known as equilibrium, in which opposing processes occur at equal rates. Chemical and physical processes are subject to this phenomenon; these processes are at equilibrium when the forward and reverse reaction rates are equal. Equilibrium systems are pervasive in nature; the various reactions involving carbon dioxide dissolved in blood are examples (see Figure 13.1). This chapter provides a thorough introduction to the essential aspects of chemical equilibria. 13.1 Chemical Equilibria LEARNING OBJECTIVES By the end of this section, you will be able to: • Describe the nature of equilibrium systems • Explain the dynamic nature of a chemical equilibrium The convention for writing chemical equations involves placing reactant formulas on the left side of a reaction Figure 13.1 Transport of carbon dioxide in the body involves several reversible chemical reactions, including hydrolysis and acid ionization (among others). CHAPTER OUTLINE arrow and product formulas on the right side. By this convention, and the definitions of “reactant” and “product,” a chemical equation represents the reaction in question as proceeding from left to right. Reversible reactions, however, may proceed in both forward (left to right) and reverse (right to left) directions.
eBook - ePubInnovations in Science and Mathematics Education
Advanced Designs for Technologies of Learning
- Michael J. Jacobson, Robert B. Kozma(Authors)
- 2012(Publication Date)
- Routledge(Publisher)
For example, the primary surface feature of the video window is that the color changes when the equilibrium is effected in some way (e.g., the temperature or the pressure increases) and the color stops changing when equilibrium is reached. This surface feature would support an understanding that an increase in the temperature or the pressure results in a change in the chemical system and that after a while the system stops changing. The primary surface features in the graph window are the two lines of different colors that increase or decrease over time and then plateau. Students who use the graph window could take these surface features as meaning that the relative amounts of the two species increase or decrease and then stop changing. In the animation window, the continuous interaction of the “balls” or “molecules” represent the dynamic quality of the system such that more reactions lead to products than to reactants, but at equilibrium the relative amounts of reactants and products stay the same and the reactions between reactants and products continue at the same rate.The second principal that we tested is that the nature of understanding derived from multiple, linked representations is additive, at least to some extent. That is, we expected that students who use videos, graphs, and animations will have an understanding of chemical equilibrium that is a combination of the understanding derived from the individual representations.To examine the effects of the different representations in our software environment, we enlisted students enrolled in an introductory chemistry course in a community college who were randomly assigned to four different versions of 4M:Chem. Seventeen students completed the study.Procedure
We configured the software in four different ways so we could isolate the effects of the different types of representations on student learning. Specifically, three groups of students were assigned to conditions in which they were given the chemical equations for each experiment along with one other dynamic representational form: either the Videos (V), the dynamic Graphs (G), or the Animations (A). A fourth group received video, graphs, and animations.The content was organized around principles related to chemical equilibrium and addressed common misconceptions that college students have regarding this concept (Kozma et al., 1990). Students in all groups received a manual that structured their experience with the software. After explaining the instructional purpose of the unit and how the software operated, the manual directed the students through a series of experiments related to the concept of equilibrium, characteristics of the state of chemical equilibrium, and how equilibrium is affected by changes in temperature, pressure, and concentration—what is referred to as Le Chatelier’s Principle.
eBook - PDF- Paul Flowers, Klaus Theopold, Richard Langley, William R. Robinson(Authors)
- 2015(Publication Date)
- Openstax(Publisher)
In this chapter, you will learn how to predict the position of the balance and the yield of a product of a reaction under specific conditions, how to change a reaction's conditions to increase or reduce yield, and how to evaluate an equilibrium system's reaction to disturbances. Chapter 13 | Fundamental Equilibrium Concepts 717 13.1 Chemical Equilibria By the end of this section, you will be able to: • Describe the nature of equilibrium systems • Explain the dynamic nature of a chemical equilibrium A chemical reaction is usually written in a way that suggests it proceeds in one direction, the direction in which we read, but all chemical reactions are reversible, and both the forward and reverse reaction occur to one degree or another depending on conditions. In a chemical equilibrium, the forward and reverse reactions occur at equal rates, and the concentrations of products and reactants remain constant. If we run a reaction in a closed system so that the products cannot escape, we often find the reaction does not give a 100% yield of products. Instead, some reactants remain after the concentrations stop changing. At this point, when there is no further change in concentrations of reactants and products, we say the reaction is at equilibrium. A mixture of reactants and products is found at equilibrium. For example, when we place a sample of dinitrogen tetroxide (N 2 O 4 , a colorless gas) in a glass tube, it forms nitrogen dioxide (NO 2 , a brown gas) by the reaction N 2 O 4 (g) ⇌ 2NO 2 (g) The color becomes darker as N 2 O 4 is converted to NO 2 . When the system reaches equilibrium, both N 2 O 4 and NO 2 are present (Figure 13.2). 718 Chapter 13 | Fundamental Equilibrium Concepts This OpenStax book is available for free at http://cnx.org/content/col11760/1.9 Figure 13.2 A mixture of NO 2 and N 2 O 4 moves toward equilibrium.
eBook - ePub- Michel Soustelle(Author)
- 2015(Publication Date)
- Wiley-ISTE(Publisher)
3.3. Representation of the evolution of an equilibrium with the temperature
As temperature is an important variable of chemical equilibrium, users have attempted to represent the evolution of a chemical equilibrium with changing temperature. Two methods are discussed below.3.3.1. Diagram in van ’t Hoff coordinates
The first mode of representation is based on relation [3.28 ], applied in convention (I). The method involves representing, in standard pressure conditions (in practice at the pressure of 1 bar), the logarithm of the equilibrium constant as a function of the inverse of temperature. This representation gives us practically a straight line, because the standard enthalpy Δr h0 and standard entropy Δr s0 of the reaction are practically independent of the temperature. Hence, the slope of that line may be −Δr h0 / R, and its ordinate at the origin may be Δr s0 / R by virtue of relation [3.28 ].Representation of the evolution of an equilibrium with temperature as a van ’t Hoff diagramFigure 3.5.Figure 3.5 shows such a line in the case of an endothermic reaction (positive reaction enthalpy).3.3.2. Ellingham diagrams
The second mode of representation of the evolution of an equilibrium with the temperature is the generalized Ellingham diagram, which we shall now examine in detail.3.3.2.1. Ellingham representation
Consider the context of the pure-substance reference (I). The principle of that diagram is, at standard pressure, to plot the standard Gibbs energy Δr g0 for the reaction in the plane [T, RT lnQ(I) ] (Figure 3.6(a) ). Using relation [3.44 ], we can see that if the standard enthalpy Δr h0 and standard entropy Δr s0 of the reaction are practically independent of temperature (these are the so-called Ellingham approximations), the representative curve is a segment of straight line whose slope is the opposite of the standard entropy Δr s0 and the intercept is the standard enthalpy Δr h0
- Kevin Dahm, Donald Visco(Authors)
- 2014(Publication Date)
- Cengage Learning EMEA(Publisher)
While Zumdahl acknowledges this limitation, quantitative accounting for departures from ideal solution behavior is be-yond the scope of a typical freshman chemistry course. However, in Chapters 9 through 13, we have learned to model deviations from the ideal gas and ideal solution models, largely in the context of phase equilibrium. In this section, we will see how to apply the same principles to reaction equilibrium, devise a model for chemical reaction equ- ilibrium, and demonstrate its equivalence to Equation 14.44 for the ideal solution case. 14.3.1 The Equilibrium Constant Our discussions of chemical equilibrium began in Chapter 8, when we established that spontaneous processes progress in a direction that decreases the Gibbs free energy and that a system is at equilibrium when the Gibbs free energy reaches a minimum. The change in Gibbs free energy for a system can be written as dG 5 2 S dT 1 V dP 1 o i m i dN i (14.45) This equation is valid whether changes in the number of moles of a compound ( dn i ) occur because of material entering or leaving the system, or because of chemical reactions occurring inside the system. Our goal is to develop a way of modeling chemical reactions at specific condi-tions (e.g., T and P ) of interest, so let us assume a chemical reaction occurs in a closed system at constant temperature and pressure, like the system in Example 14-1. For this case, Equation 14.45 simplifies to dG 5 o i m i dN i (14.46) Since we are modeling a closed system, changes in the number of moles of a species can only occur by chemical reaction, which means they are related to each other by stoichiometry.
eBook - PDF- John A. Olmsted, Gregory M. Williams, Robert C. Burk(Authors)
- 2020(Publication Date)
- Wiley(Publisher)
676 Principles of Chemical Equilibrium LEARNING OBJECTIVES Upon completion of this chapter you should be able to: • explain the dynamic nature of equilibrium in terms of reversibility • understand some of the properties of equilibrium constants • relate the equilibrium position to thermodynamic quantities • predict the effects on the equilibrium position of changing concentrations or temperature • solve quantitative equilibrium problems • perform equilibrium calculations on reactions in aqueous solution CHAPTER CONTENTS 14.1 Describing Chemical Equilibria 14.2 Properties of Equilibrium Constants 14.3 Thermodynamics and Equilibrium 14.4 Shifts in Equilibrium 14.5 Working with Equilibria 14.6 Equilibria in Aqueous Solutions CHAPTER 14 Craig Aurness/Corbis/VCG/Getty Images fotokostic/iStock/Getty Images. 14.1 Describing Chemical Equilibria 677 14.1 Describing Chemical Equilibria The detailed chemistry describing the synthesis of ammonia is complex, so we introduce the principles of equilibrium using the chemistry of nitrogen dioxide. Molecules in a sample of nitrogen dioxide are always colliding with one another. As described in Chapter 13, a collision in the correct orientation can result in bond formation, producing an N 2 O 4 molecule: 2 NO 2 ⟶ N 2 O 4 In a vessel that contains only NO 2 molecules, the production of N 2 O 4 is the only reaction that takes place. However, once N 2 O 4 molecules are present, the reverse reaction can also occur. An N 2 O 4 molecule can fragment after collisions give it sufficient energy to break the N N bond. These fragmentations regenerate NO 2 : N 2 O 4 ⟶ 2 NO 2 Figure 14.1 depicts these two processes from the molecular perspective. Dynamic Equilibrium Collisions between NO 2 molecules produce N 2 O 4 and consume NO 2 . At the same time, decomposition of N 2 O 4 produces NO 2 and consumes N 2 O 4 . When the concentration of N 2 O 4 is very low, the decomposition occurs less often than the formation reaction.
eBook - PDF- Juan J. de Pablo, Jay D. Schieber(Authors)
- 2014(Publication Date)
- Cambridge University Press(Publisher)
10 Reaction equilibrium Reactions are an essential component of chemical engineering, and reaction engineering itself is a very broad discipline [43 , 107 ]. However, before we study the time evolution of chemical reactions, it is important to know the final equilibrium state that a system can reach. The equilibrium state of a chemical reaction is determined by thermodynamic principles. In this chapter we examine the thermodynamic principles that govern chemical reactions, and find methods for calculating the final composition of a mixture that results from chemical reactions. The methods consist of two general steps: determination of the equilibrium constant(s) from ther-modynamic properties of the constituent chemical compounds; and determination of the chemical composition of the equilibrium mixture from the initial composition and the equilibrium constant(s). In general, finding this composition requires the use of models with good estimates for the activities (or fugacities) of the constituent species, as shown in the previous two chapters. The equilibrium constant depends only on the temperature and the species present, not on the composition. We also consider how thermodynamic driving forces can influence reaction rates. However, few details are given in this book, since that is a topic best left for other courses and textbooks. Denat-uration of DNA strands is discussed in Section 10.9, where denaturation is applied to polymerase chain reactions (PCR). PCR is a technique that can be used to amplify small amounts of genetic material. Finally, in the last section, Section 10.10, connections are made to statistical mechanics. 10.1 A SIMPLE PICTURE: THE REACTION COORDINATE ......................................................................................................................
eBook - PDF- Edward J. Neth, Paul Flowers, Klaus Theopold, Richard Langley, William R. Robinson(Authors)
- 2019(Publication Date)
- Openstax(Publisher)
INTRODUCTION CHAPTER 13 Fundamental Equilibrium Concepts 13.1 Chemical Equilibria 13.2 Equilibrium Constants 13.3 Shifting Equilibria: Le Châtelier’s Principle 13.4 Equilibrium Calculations Imagine a beach populated with sunbathers and swimmers. As those basking in the sun get too hot, they enter the surf to swim and cool off. As the swimmers tire, they return to the beach to rest. If the rate at which sunbathers enter the surf were to equal the rate at which swimmers return to the sand, then the numbers (though not the identities) of sunbathers and swimmers would remain constant. This scenario illustrates a dynamic phenomenon known as equilibrium, in which opposing processes occur at equal rates. Chemical and physical processes are subject to this phenomenon; these processes are at equilibrium when the forward and reverse reaction rates are equal. Equilibrium systems are pervasive in nature; the various reactions involving carbon dioxide dissolved in blood are examples (see Figure 13.1). This chapter provides a thorough introduction to the essential aspects of chemical equilibria. We now have a good understanding of chemical and physical change that allow us to determine, for any given process: 1. Whether the process is endothermic or exothermic 2. Whether the process is accompanied by an increase of decrease in entropy 3. Whether a process will be spontaneous, non-spontaneous, or what we have called an equilibrium process Recall that when the value ∆G for a reaction is zero, we consider there to be no free energy change—that is, no Figure 13.1 Transport of carbon dioxide in the body involves several reversible chemical reactions, including hydrolysis and acid ionization (among others). CHAPTER OUTLINE free energy available to do useful work. Does this mean a reaction where ΔG = 0 comes to a complete halt? No, it does not.
eBook - PDF- Gary D. Christian, Purnendu K. Dasgupta, Kevin A. Schug(Authors)
- 2013(Publication Date)
- Wiley(Publisher)
Chapter Six GENERAL CONCEPTS OF CHEMICAL EQUILIBRIUM “The worst form of inequality is to try to make unequal things equal.” — Aristotle Learning Objectives WHAT ARE SOME OF THE KEY THINGS WE WILL LEARN FROM THIS CHAPTER? ● The equilibrium constant (key equations: 6.12, 6.15), pp. 194 ● Calculation of equilibrium concentrations, p. 195 ● Using Excel Goal Seek to solve one-variable equations, p. 197 ● The systematic approach to equilibrium calculations: mass balance and charge balance equations, p. 204 ● Activity and activity coefficients (key equation: 6.19), p. 211 ● Thermodynamic equilibrium constants (key equation: 6.23), p. 217 Even though in a chemical reaction the reactants may almost quantitatively react to form the products, reactions never go in only one direction. In fact, reactions reach an equilibrium in which the rates of reactions in both directions are equal. In this chapter we review the equilibrium concept and the equilibrium constant and describe general approaches for calculations using equilibrium constants. We discuss the activity of ionic species along with the calculation of activity coefficients. These values are required for calculations using thermodynamic equilibrium constants, that is, for the diverse ion effect, described at the end of the chapter. They are also used in potentiometric calculations (Chapter 13). 6.1 Chemical Reactions: The Rate Concept In 1863 Guldberg and Waage described what we now call the law of mass action, which states that the rate of a chemical reaction is proportional to the “active masses” of the reacting substances present at any time. The active masses may be concentrations or pressures. Guldberg and Waage derived an equilibrium constant by defining equilibrium as the condition when the rates of the forward and reverse reactions are equal.
eBook - PDF- Gary D. Christian, Purnendu K. Dasgupta, Kevin A. Schug(Authors)
- 2020(Publication Date)
- Wiley(Publisher)
Chapter 5 GENERAL CONCEPTS OF CHEMICAL EQUILIBRIUM “The worst form of inequality is to try to make unequal things equal.” —Aristotle KEY THINGS TO LEARN FROM THIS CHAPTER The equilibrium constant (key Equations: 5.12, 5.15) Calculation of equilibrium concentrations Using Excel Goal Seek to solve one-variable equations The systematic approach to equilibrium calculations: mass balance and charge balance equations Activity and activity coefficients (key Equation: 5.19) Thermodynamic equilibrium constants (key Equation: 5.23) Even though in a chemical reaction the reactants may almost quantitatively react to form the products, reactions never go in only one direction. In fact, reactions reach an equilibrium in which the rates of reactions in both directions are equal. In this chapter we review the equilibrium concept and the equilibrium constant and describe gen- eral approaches for calculations using equilibrium constants. We discuss the activity of ionic species along with the calculation of activity coefficients. These values are required for calculations using thermodynamic equilibrium constants, that is, for the diverse ion effect, described at the end of the chapter. They are also used in potentio- metric calculations (Chapter 20). 5.1 Chemical Reactions: The Rate Concept In 1863 Guldberg and Waage described what we now call the law of mass action, which states that the rate of a chemical reaction is proportional to the “active masses” of the reacting substances present at any time. The active masses may be concentrations or pressures. Guldberg and Waage derived an equilibrium constant by defining equilib- rium as the condition when the rates of the forward and reverse reactions are equal.
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