8 Key excerpts on "Free Energy and Equilibrium"

• 

  eBook - ePub

  General Chemistry for Engineers

  • Jeffrey Gaffney, Nancy Marley(Authors)
  • 2017(Publication Date)
  • Elsevier

    (Publisher)

  G ) also known as Gibbs energy or the Gibbs function. The term “free” was used to mean that it represents the energy available (or free) to do useful work. Gibbs free energy is defined as being equal to the enthalpy of a system less the entropy times the temperature of the system;

  G = H − TS

  and the change in Gibbs free energy for a system at constant temperature and pressure is;

  Δ G = Δ H − T Δ S

    (19)

  Gibbs free energy is the maximum work that may be performed by a system at a constant temperature and pressure.

  The change in the Gibbs free energy for a chemical reaction (ΔG rxn  = ΔH rxn  − T ΔS rxn ) determines whether the reaction is thermodynamically possible or not. If Δ G of the initial state (reactants) is greater than the Δ G of the final state (products), Δ G (rxn)  < 0 and the reaction will take place spontaneously. If Δ G of the initial state is greater than Δ G of the final state or Δ G (rxn)  > 0, the reaction will not take place unless energy is added to the system and it will not be spontaneous. But, since the Δ G for the reverse reaction is the same as the value for the forward reaction, but with an opposite sign;

  Δ

  G forward

  = − Δ

  G reverse

  the reverse reaction will be spontaneous. In addition, once the Gibbs free energy reaches its minimum possible value, Δ G (rxn)  = 0 and the state of chemical equilibrium is reached.

  In summary:

  •  

  If Δ G (rxn)  < 0, the forward reaction will be spontaneous.

  •  

  If Δ G (rxn)  > 0, the reverse reaction will be spontaneous.

  •  

  If Δ G (rxn)  = 0, the reaction is at equilibrium and there will be no change in the concentrations of reactants or products.

  According to Eq. (19) , the factors that affect the value of Δ G of a chemical reaction are: Δ H , Δ S , and the temperature. Assuming Δ H and Δ S are independent of temperature, the values of these three factors will determine the sign of Δ G °(rxn) and the spontaneous direction of the reaction. The five possible combinations among these three factors are listed in Table 8.5 . If Δ H is < 0 (exothermic reaction) and Δ S is > 0, Δ G (ΔH  − T ΔS ) will be < 0 and the forward reaction will be spontaneous at all temperatures. If Δ H is > 0 (endothermic reaction) and Δ S is < 0, Δ G will be > 0 and the reverse reaction will be spontaneous at all temperatures. Under conditions where Δ H and Δ S are either both positive or both negative, Δ G will be < 0 for a limited range of temperatures. If they are both positive, Δ G is < 0 only at high temperatures and if they are both negative, Δ G is < 0 only at low temperatures. For these cases, the exact temperatures where Δ G will be < 0 and the reaction spontaneous must be calculated from Eq. (19)

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  eBook - ePub

  Physicochemical and Environmental Plant Physiology

  • Park S. Nobel(Author)
  • 2020(Publication Date)
  • Academic Press

    (Publisher)

  Appendix IV

  Gibbs Free Energy and Chemical Potential

  The concept of chemical potential is introduced in Chapter 2 (Section 2.2) and used throughout the rest of the book. In order to not overburden the text with mathematical details, certain points are stated without proof. Here we will derive an expression for the chemical potential, justify the form of the pressure term in the chemical potential, and also provide insight into how the expression for the Gibbs free energy arises.

  IV.A. Entropy and Equilibrium

  A suitable point of departure is to reconsider the condition for equilibrium. The most general statement we can make concerning the attainment of equilibrium by a system is that it occurs when the entropy of the system plus its surroundings is at a maximum. Unfortunately, entropy has proved to be an elusive concept to master and a difficult quantity to measure. Moreover, reference to the surroundings—the “rest of the universe” in the somewhat grandiloquent language of physics—is a nuisance. Consequently, thermodynamicists sought a function that would help describe equilibrium but would depend only on readily measurable parameters of the system under consideration. As we will see, the Gibbs free energy is such a function for most applications in biology.

  The concept of entropy (S ) is really part of our day-to-day observations. We know that an isolated system will spontaneously change in certain ways—a system proceeds toward a state that is more random, or less ordered, than the initial one. For instance, neutral solutes will diffuse toward regions where they are less concentrated (Fig. 1-5 ). In so doing, the system lowers its capacity for further spontaneous change. For all such processes, ΔS is positive, whereas ΔS becomes zero and S achieves a maximum at equilibrium. Equilibrium means that no more spontaneous changes will take place; entropy is therefore an index for the capacity for spontaneous change. It would be more convenient in some ways if entropy had been originally defined with the opposite sign. In fact, some authors introduce the quantity negentropy , which equals − S and reaches a minimum at equilibrium. In any case, we must ultimately use a precise mathematical definition for entropy, such as dS  = dQ /T , where dQ refers to the heat gain or loss in some reversible reaction taking place at temperature T

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  eBook - ePub

  AP&reg; Chemistry All Access Book + Online + Mobile

  • Kevin Reel, Derrick C. Wood, Scott A. Best(Authors)
  • 2014(Publication Date)
  • Research & Education Association

    (Publisher)

  Gibbs free energy (G) . Free energy is the energy available to do work, and takes the enthalpy and entropy of a reaction into account. If ΔG is negative, the reaction will be spontaneous; positive ΔG values mean that the reaction is nonspontaneous; and when ΔG = 0, the system is at equilibrium—meaning there is no preference. The Gibbs free energy value is related to the enthalpy and entropy according to the Gibbs-Helmholtz equation:

  Alternatively, the Gibbs free energy value can be calculated from free energy of formation values (ΔGf °) acquired under standard conditions through the summation equation:

  EXAMPLE:

  Using the following values, determine whether or not the burning of sugar (C12 H22 O11 ) will be a spontaneous process.

  SOLUTION: Because the units are not matching up, the ΔS° should be converted to kJ/mol. The Gibbs free energy is calculated using the Gibbs-Helmholtz equation, using the temperature of 298 K because the data is for standard conditions.

  Because the ΔG° is negative, this reaction is spontaneous .

  TEST TIP Make sure the units are matching up when plugging into the Gibbs equation, which will likely require you to convert the temperature into Kelvin and the ΔS° in kJ/mol K.

  Predicting Reaction Spontaneity

  On the AP Chemistry exam, you may be asked to predict the spontaneity of a reaction based solely on qualitative determinations. You should familiarize yourself with Table 10.1 , which describes the possible scenarios for enthalpy, entropy, and free energy based on the signs of ΔH, ΔS, and ΔG and the equation: ΔG = ΔH – T ΔS

  Table 10.1. Reaction Spontaneity: Possible Scenarios for Enthalpy, Entropy, and Free Energy Table 10.2. Thermo Signs and Symbols Summary

  Sign and Symbol	Meaning
  –ΔH	Exothermic; heat given off
  +ΔH	Endothermic; heat absorbed
  –ΔS	Decrease entropy; more organized
  +ΔS	Increase entropy; more random/disordered
  –ΔG	Spontaneous
  +ΔG	Nonspontaneous

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  eBook - ePub

  Biomolecular Thermodynamics

  From Theory to Application

  • Douglas Barrick(Author)
  • 2017(Publication Date)
  • CRC Press

    (Publisher)

  In addition to connecting potentials to physical quantities such as temperature and pressure, these differential relationships provide a way to resolve the contributions of individual chemical species to overall thermodynamics quantities. Central to this chemical dissection is the use of “partial molar quantities,” which are obtained by differentiation with respect to mole number. These partial molar quantities are intensive analogs of quantities such as energy, volume, and heat capacity, and provide a fundamental expression chemical reactivity. Of particular importance is the partial molar Gibbs free energy, referred to as the “chemical potential.”

  In Chapter 4 , we developed entropy as a thermodynamic potential to describe the direction of spontaneous change. The entropy acts as a thermodynamic potential as long as a system is isolated, that is, when there is no work, no heat flow, and no material exchange between system and the surroundings. While this is a useful way to think about the thermodynamics of the universe (where, by definition, there is no surroundings with which to interact), systems studied in the laboratory are not isolated from their surroundings (Figure 5.1A ).

  Figure 5.1 Laboratory and biological systems at constant pressure and temperature. (A) A typical laboratory sample containing a solution of large and small molecules in various states of conformation, assembly, and reaction. The sample is open to atmospheric pressure, so it can expand and contract while maintaining constant p, and has a resistive heater and/or heat sink that can maintain constant sample temperature. The distribution of various molecular species can be measured using devices such as light sources and detectors. (B) Living biological systems. Left, a bacterial cell; middle, eukaryotic cells in a culture dish; right, animals and a plant. In all three cases, temperature and pressure are usually constant (or vary slowly compared to processes of interest). In addition, material (and in one case, light) is exchanged among these living systems and their surroundings.

  Typically, laboratory systems are held at constant temperature and pressure (partly because such conditions are easy to achieve, requiring no thermal or mechanical insulation), which allows heat to flow and work to be done as a result of from volume change. Even when temperature (and sometimes pressure† ) is used as an experimental variable, the system under study is typically allowed to equilibrate with its surroundings at a series of different temperatures. Thus, variable temperature experiments are treated as a collection of measurements at fixed temperatures. Likewise, biological systems (cells, tissues, and organisms, Figure 5.1B

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  eBook - ePub

  BIOS Instant Notes in Physical Chemistry

  • Gavin Whittaker, Andy Mount, Matthew Heal(Authors)
  • 2000(Publication Date)
  • Taylor & Francis

    (Publisher)

  However, there are limitations to the practical scope of thermodynamics which should be borne in mind. Consideration of the energetics of a reaction is only one part of the story. Although hydrogen and oxygen will react to release a great deal of energy under the correct conditions, both gases can coexist indefinitely without reaction. Thermodynamics determines the potential for chemical change, not the rate of chemical change—that is the domain of chemical kinetics (see Topics F1 to F6). Furthermore, because it is such a common (and confusing) misconception that the potential for change depends upon the release of energy, it should also be noted that it is not energy, but entropy which is the final arbiter of chemical change (see Topic B5). Thermodynamics considers the relationship between the system —the reaction, process or organism under study—and the surroundings —the rest of the universe. It is often sufficient to regard the immediate vicinity of the system (such as a water bath, or at worst, the laboratory) as the surroundings. Several possible arrangements may exist between the system and the surroundings (Fig. 1). In an open system, matter and energy may be interchanged between the system and the surroundings. In a closed system, energy may be exchanged between the surroundings and the system, but the amount of matter in the system remains constant. In an isolated system, neither matter nor energy may be exchanged with the surroundings. A system which is held at constant temperature is referred to as isothermal, whilst an adiabatic system is one in which energy may be transferred as work, but not as heat, i.e. it is thermally insulated from its surroundings. Chemical and biological studies are primarily concerned with closed isothermal systems, since most processes take place at constant temperature, and it is almost always possible to design experiments which prevent loss of matter from the system under study. Fig

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  eBook - ePub

  Careers in Chemical and Biomolecular Engineering

  • Victor Edwards, Suzanne Shelley(Authors)
  • 2018(Publication Date)
  • CRC Press

    (Publisher)

  5 Basic Concepts: Equilibrium and Rate Processes

  Thermodynamics

  Fundamental definitions in thermodynamics

  Thermodynamics is a branch of physics that is concerned with temperature and heat, and their relation to energy and work in macroscopic systems (Van Ness and Abbott 2008). There are four laws of thermodynamics (discussed below) that apply to thermodynamic systems, such as heat engines or chemically reacting substances. There are numerous other equations that derive from those laws, and those equations allow users to predict the outcome of physical and chemical phenomena involving thermodynamic systems.

  Chemical thermodynamics is the study of the interrelation of energy with chemical reactions or with a physical change of state, within the confines of the laws of thermodynamics. Numerous chemical engineering unit operations and processes can be represented as thermodynamic systems for the purposes of analysis and design.

  Conceptually, in thermodynamics, a system may be an object, a quantity of matter, or a region of space that is selected for study and set apart (conceptually) from everything else; the “everything else” is referred to as the surroundings (Van Ness and Abbott 2008). The boundary of the system can be imagined as an envelope that encloses the system and separates it from its surroundings.

  A system can interact with its surroundings in several ways. If there is no interaction, the system is said to be isolated . A system that is not isolated may allow the exchange of energy and/or material across its boundary. A system that allows exchange of matter is said to be open . If energy can exchange between the system and the surroundings, but no matter can be exchanged, the system is said to be closed .

  Initially, changes in temperature or pressure may occur within an isolated system, even if there is no exchange of matter or energy with the surroundings. However, these changes eventually stop, and the system is said to be in a final static state of internal equilibrium (Figure 5.1

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  eBook - ePub

  Philosophy of Chemistry

  • Dov M. Gabbay, Paul Thagard, John Woods(Authors)
  • 2011(Publication Date)
  • North Holland

    (Publisher)

  Rukeyser 1964 , 262; emphasis added]

  Chemical equilibrium is usually understood to imply not only equilibrium under one set of conditions but also how it changes as external conditions are altered.

  The ‘certain functions’ mentioned above are enthalpy, the Helmholtz and Gibbs functions and chemical potential. The rationale for introducing Helmholtz and Gibbs functions is shown in Box 3 .

  Box 3

  Let us start with a combined statement of the first and second laws. From Eqs. 1 , 3 and 4 we have

  (13)

  From the above equation we see that energy is a function of entropy and volume. Hence the energy of a system at equilibrium is a surface in the U, V and S coordinate system. According to the above equation, energy increases with entropy when volume is fixed and decreases with volume when entropy is fixed. The following sketch of the surface shows that feature. The equilibrium surface is shown with gray shading. The non-equilibrium state is above the surface.

  With this figure as a model we can see the behavior of the system, (i) when it is isolated, (ii) when it is in contact with a heat bath and (iii) when it exchanges both heat and work with the surroundings.

  (i) According to the second law the entropy of an isolated system increases until it reaches equilibrium while its energy remains constant. This is indicated by arrow (i) between a non-equilibrium state and the equilibrium surface. Notice that a non-equilibrium state must be above the equilibrium surface; otherwise it could only reach equilibrium by decrease of entropy, contrary to the second law.

  (ii) Suppose now we keep entropy and volume constant by removing heat from the system gradually. In an equilibrium state the system will have no variance if both entropy and volume are constant. That restriction does not apply to a non-equilibrium state, which has a large number of degrees of freedom. Heat can be removed from a non-equilibrium system, while both energy and volume are kept constant, by immersing the system in a heat bath. Then the system has to reach equilibrium through loss of energy as indicated by the arrow marked (ii).

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  eBook - ePub

  Fundamentals of Chemical Reaction Engineering

  • Mark E. Davis, Robert J. Davis(Authors)
  • 2013(Publication Date)
  • Dover Publications

    (Publisher)

  APPENDIX A

  Review of ChemicalEquilibria

  A.1 | Basic Criteria for Chemical Equilibriumof Reacting Systems

  The basic criterion for equilibrium with a single reaction is:

  where ΔG is the Gibbs function, NCOMP is the number of components in the system,

  vi

  is the stoichiometric coefficient of species i , and i is the chemical potential of species i . The chemical potential is:

  where R g is the universal gas constant, is the standard chemical potential of species i in a reference state such that a i = 1, and a i is the activity of species i . The reference states are: (1) for gases (i.e., 0 = 1) (ideal gas, P = 1 atm) where is the fugacity, (2) for liquids, the pure liquid at T and one atmosphere, and (3) for solids, the pure solid at T and one atmosphere. If multiple reactions are occurring in a network, then Equation (A.1.1) can be extended to give:

  where NRXN is the number of independent reactions in the network.

  In general it is not true that the change in the standard Gibbs function, ΔG 0 , is zero. Thus,

  Therefore, or by using Equation (A.1.2): Now consider the general reaction:

  Application of Equation (A.1.6) to Equation (A.1.7) and recalling that ΔG = 0 at equilibrium gives:

  Thus, the equilibrium constant K a is defined as:

  Differentiation of Equation (A.1.8) with respect to T yields:

  Note that ΔG 0 = ΔH 0 − T ΔS 0 , where ΔH 0 and ΔS0 are the standard enthalpy and entropy, respectively, and differentiation of this expression with respect to T gives:

  Equating Equations (A. 1.10) and (A.1.l1) provides the functional form for the temperature dependence of the equilibrium constant:

  or after integration (assume ΔH 0 is independent of T ):

  Notice that when the reaction is exothermic (ΔH 0 is negative), K a increases with decreasing T

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