Chemistry
Free Energy of Formation
The free energy of formation is a measure of the stability of a compound relative to its elements in their standard states. It represents the change in free energy when a compound is formed from its constituent elements. A negative value indicates that the compound is more stable than its elements, while a positive value indicates the opposite.
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9 Key excerpts on "Free Energy of Formation"
eBook - PDF- Donald T. Haynie(Author)
- 2008(Publication Date)
- Cambridge University Press(Publisher)
Chapter 4 Gibbs free energy – theory A. Introduction This chapter discusses a thermodynamic relationship that provides a basis for explaining spontaneous chemical reactivity, chemical equilibrium, and the phase behavior of chemical compounds. The relationship involves a thermodynamic state function that enables prediction of the direction of a chemical reaction at constant tem-perature and pressure . The constraints of fixed T and p might seem annoyingly restrictive, because they are less general than the requirements of the Second Law, but in fact the gains made on imposing the constraints will outweigh the losses. How is that? One reason is at any given time an individual organism is practically at uniform pressure and temperature (but be sure to see the Exercises at the end of the chapter). Another is that constant temperature and pressure are the very conditions under which nearly all bench-top biochemistry experiments are done. Yet another is that, although the total entropy of the universe must increase in order for a process to be spontaneous, evaluation of the total entropy change requires mea-surement of both the entropy change of the system and the entropy change of the surroundings. Whereas 1 S system can often be found without too much difficulty, albeit only indirectly, 1 S surroundings can be hard to measure! How could one measure the entropy change of the rest of the universe? The subject of the present chapter provides a way around the difficulty. A particularly clear example of the inadequacy of 1 S system to predict the direction of spontaneous change is given by the behavior of water at its freezing point. Table 4.1 shows the thermo-dynamic properties of water for the liquid ! solid phase transition. The decrease in internal energy (which is practically identical to the enthalpy as long as the number of moles of gas doesn’t change; see Chapter 2 ) would suggest that water freezes spontaneously in the range 263–283 K.
eBook - PDF- Charles R. Russell(Author)
- 2013(Publication Date)
- Pergamon(Publisher)
In this way, consistent tables of heats of formation have been built up. These values of the heat of formation are particularly useful for calculating the energy change associated with other chemical reactions. A convenient procedure for determining the heat fo CHEMICAL ENERGY 143 reaction can be established by first writing the chemical equation for the reaction including a designation for the state of each material. Below each reactant and each product is entered the value of its heat of formation multiplied by the number of moles that are indicated in the balanced chemical equation (elements in their standard state are assigned the value of zero, as noted previously). Since the enthalpy change is defined as heat added to the system, an energy balance relative to the elements from which all the reactants and products were formed can be made by adding the enthalpy change ΔΗ° to the reactant side of the equation. This value can then be found by simple arithmetic. EXAMPLE 4-1. Calculate the heat of reaction of methyl alcohol with oxygen at 25 °C and 1 atm of pressure. Solution: The standard heats of formation are found in the tables and values for the reactants and products and are entered below the chemical equation with the values of the enthalpy change ΔΗ° treated as a heat addition on the reactant side. CH 3 OH(l)+^0 2 (g) = C0 2 (g)+2H 2 0(1) AH° + (-57.02) + 0 = ( - 94.05) + 2 ( - 68.32) AH° = -173.67 kg-cal/g-mole of methyl alcohol -173.67X1800 = _ 9 7 6 9 B t u / l b Therefore the combustion of methyl alcohol releases 9769 Btu per pound of fue under standard conditions. Many chemical reactions take place in solution, or one or more reactants or products may be in the form of a solution. Therefore, values are given of the heats of formation of materials either dis-solved in water at infinite dilution or at some specified concentra-tion.
- Peter V. Hobbs(Author)
- 2000(Publication Date)
- Cambridge University Press(Publisher)
By con-vention, the following are considered standard states: (1) for a solid, the 30 Chemical thermodynamics pure solid at 1 atm and 25°C; (2) for a liquid, the pure liquid at 1 atm pressure and 25°C; (3) for a gas, an ideal gas at 1 atm partial pressure and 25°C; and (4) for a solution, an ideal solution with a concentration of 1 mole of solute per liter of solution (i.e., 1M) at 25°C. The change in Gibbs free energy of a system, when reactants in their standard states are converted to products in their standard states, is called the molar standard free energy change (AG°) for the reaction. The superscript zero to the G indicates the standard state and the overbar indicates that the molar amounts of the reactants and products given by the numerical coefficients in the balanced chemical equation for the reaction are involved. For the forward reaction of the general chemical Reaction (1.5) AG ° = [g AG ? (G) + hAG° { (H) + . . . ] -[a AG ? (A) + b AG ? (B) +...] (2.34) where AG? (X), which is called the molar standard Gibbs Free Energy of Formation (or simply, the standard free energy offormation) of compound X, is the change in the Gibbs free energy when 1 mole of X is formed from its elements. By convention, the standard free energies of forma-tion of the elements in their most stable forms at 1 atm are taken to be zero. The temperature chosen for tabulating values of AG? (X) is usually 25°C. A selection of standard free energies of formation is given in Appendix V. It follows from the above definitions and Eq. (2.32) that if AG° for a reaction is negative, the reactants in their standard states will be con-verted spontaneously into the products in their standard states. If AG° is positive, the conversion will not be spontaneous, but the corresponding reverse reaction will be. However, even when AG° is positive, some products can form but in concentrations below that of their standard states.
eBook - PDF- Young, William Vining, Roberta Day, Beatrice Botch(Authors)
- 2017(Publication Date)
- Cengage Learning EMEA(Publisher)
For most compounds, uni2206 G f ° is negative. This means that under standard state conditions, compounds are generally more stable than the elements from which they are composed. That is, they are lower in free energy and could form spontaneously from their constituent elements. This should make sense, because only a few elements are found uncombined in nature. Another way to say this is that elements are generally higher in free energy than compounds, and energy is dis-sipated when they combine chemically under standard state conditions. Example Problem 20.3.2 Calculate standard free energy change using uni2206 G f ° values. Use standard free energies of formation to calculate the standard free energy change for the formation of carbon dioxide from carbon monoxide and oxygen gas at 25 °C . CO(g) 1 ½ O 2 (g) S CO 2 (g) Solution: You are asked to calculate uni2206 G ° rxn using uni2206 G f ° values. You are given the balanced chemical equation and uni2206 G f ° data for each substance. b Example Problem 20.3.1 (continued) Table 20.3.2 Selected Standard Free Energies of Formation for Pure Substances at 25 °C Substance uni2206 G f ° (kJ/mol) Substance uni2206 G f ° (kJ/mol) C(diamond) 2.9 Hg( / ) 0 C(graphite) 0 HCl(g) 2 95.3 CO(g) 2 137.2 HCl(aq) 2 131.2 CO 2 (g) 2 394.4 FeCl 2 (s) 2 302.3 CH 3 OH( / ) 2 166.3 Cu(s) 0 CH 3 CH 2 OH( / ) 2 174.8 H 2 O(g) 2 228.6 C 6 H 6 ( / ) 124.5 H 2 O( / ) 2 273.1 H 2 (g) 0 c Copyright 2018 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. WCN 02-300 Unit 20 Thermodynamics: Entropy and Free Energy 651 Use Equation 20.12 and uni2206 G f ° data to calculate the standard free energy change for this reaction.
eBook - PDFChemistry
Structure and Dynamics
- James N. Spencer, George M. Bodner, Lyman H. Rickard(Authors)
- 2011(Publication Date)
- Wiley(Publisher)
The name of this quantity recognizes the contributions of J. Willard Gibbs, a professor of mathematical physics at Yale from 1871 until the early 1900s, who some consider to be the greatest scientist produced by the United States. The Gibbs free energy of a system at any moment in time is defined as the enthalpy of the system minus the product of the temperature times the entropy of the system. The Gibbs free energy is therefore a state function because it is defined in terms of thermodynamic properties (enthalpy, entropy, and temperature) that are state functions. At a given temperature, the change in the Gibbs free energy of the sys- tem that occurs during a reaction is therefore equal to the change in the enthalpy of the system minus the product of the temperature times the change in entropy of the system. The beauty of the equation defining changes in the free energy of a system is its ability to determine the relative importance of the enthalpy and entropy terms for a particular reaction at a given temperature. The change in the free energy of the system that occurs during a reaction measures the balance between the two driving forces that determine whether a reaction is spontaneous. As we have seen, the enthalpy and entropy terms have different sign con- ventions. The enthalpy term is favorable when it is negative, whereas the entropy term is favorable when positive. ¢G = ¢H - T¢S G = H - TS The overall entropy of reaction is negative because the reaction transforms 4 moles of reactants into 2 moles of products. According to these calculations, ¢H° for the reaction is 92.2 kJ/mol rxn and ¢S° for the reaction is 198.8 J/mol rxn K. Enthalpy (¢H° 6 0) therefore drives the reaction toward the products, but entropy (¢S° 6 0) drives the reac- tion toward the reactants.
eBook - ePub- Alberto Gianinetti(Author)
- 2017(Publication Date)
- Bentham Science Publishers(Publisher)
This way even the changes in the chemical nature of a substance can be measured in terms of chemical potential, as if they were changes of a thermodynamic system, and then even chemical reactions wherein reactants transform into products can be measured in terms of their overall change in the chemical potential, so that their spontaneity can be established. In such instances, the chemical potential is typically dealt with in terms of the Gibbs free energy, which computes the change of the chemical potential consequent to a chemical transformation in the form of equivalent changes of enthalpy (release/uptake of thermal energy plus any work done by volume change) and entropy, based on tabulated standard-state thermodynamic data and equilibrium constants. What can be measured, however, is merely the change in chemical potential relative to the reaction, not the absolute values of chemical potential of the various species. This is because, in chemistry, by not considering the energetic equivalence of matter, and then by ignoring the subatomic state of the system, the chemical potential of any chemical species is necessarily considered only in relative terms. Anyway, the spontaneity of a reaction is directly dependent upon the change that occurs in the process, and not to initial and final values. Relative values of the chemical potentials of the various species can thus be calculated based on the assumption of some reference potential (to provide tabulated standard values that facilitate calculations of changes of the chemical potential in chemical reactions). Indeed, the values of the chemical potentials of the various substances are related to the chemical potentials of the elements they are composed of [ 42 ]. As long as we exclude transformations of elements, i.e. nuclear reactions, it is therefore useful to refer to the chemical potentials of the elements as reference chemical potentials
eBook - PDFChemistry
An Atoms First Approach
- Steven Zumdahl, Susan Zumdahl, Donald J. DeCoste, , Steven Zumdahl, Steven Zumdahl, Susan Zumdahl, Donald J. DeCoste(Authors)
- 2020(Publication Date)
- Cengage Learning EMEA(Publisher)
We saw in Section 16.4 that for a process at constant temperature and pressure, we can use the change in free en- ergy of the system to predict the sign of DS univ and thus the direction in which it is spontaneous. So far we have applied these ideas only to physical processes, such as changes of state and the formation of solutions. However, the main business of chem- istry is studying chemical reactions, and, therefore, we want to apply the second law to reactions. First, we will consider the entropy changes accompanying chemical reactions that occur under conditions of constant temperature and pressure. As for the other types of processes we have considered, the entropy changes in the surroundings are determined by the heat flow that occurs as the reaction takes place. However, the entropy changes in the system (the reactants and products of the reaction) are determined by positional probability. For example, in the ammonia synthesis reaction N 2 s gd 1 3H 2 s gd ¡ 2NH 3 s gd four reactant molecules become two product molecules, lowering the number of inde- pendent units in the system, which leads to less positional disorder. See Exercises 16.37 through 16.39 656 CHAPTER 16 Spontaneity, Entropy, and Free Energy Copyright 2021 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. N H Less entropy Greater entropy Fewer molecules mean fewer possible configurations. To help clarify this idea, con- sider a special container with a million compartments, each large enough to hold a hydrogen molecule. Thus there are a million ways one H 2 molecule can be placed in this container.
eBook - PDFStatistical Physics of Biomolecules
An Introduction
- Daniel M. Zuckerman(Author)
- 2010(Publication Date)
- CRC Press(Publisher)
Once the conditions are set, the pertinent free energy is all of the following: (1) It is the logarithm of that partition function obeying the conditions, multiplied by ( − k B T ) . (2) It quantifies the amount of work that can be done by the system under the condi-tions. (3) It tends to become minimized if the system is initially out of equilibrium, as we will see below. The notation for free energies uses the conditions (the parameters held constant) as “natural” variables. Therefore, each free energy should always be written in a way that make the corresponding conditions obvious. The free energies we have discussed are • F ( T , V , N ) = E − TS , the Helmholtz free energy • G ( T , P , N ) = F + P V , the Gibbs free energy • ( T , V , μ ) = F − N μ , the grand canonical potential Note that the total energy is the sum of kinetic and potential contributions—that is, E = KE + U . 174 Statistical Physics of Biomolecules: An Introduction 7.6.2 F REE E NERGIES A RE “S TATE F UNCTIONS ” As we have seen more than enough times, a free energy is defined from a partition function. In turn, the partition function simply integrates to some number once the natural variables—for example, T , V , N in Z ( T , V , N ) —are fixed. Thus, the natural variables define the free energy: once you specify the variables, the free energy is some number. A free energy is called a “state function” because it comes from a definite integral depending only on the equilibrium “state” of the system—that is, only on the natural variables. It does not depend on how that state was reached (maybe by a weird nonequilibrium process) because this doesn’t change the equilibrium integral. The notion of a state function is important in understanding free energy differ-ences generally, and especially in understanding “thermodynamic cycles,” which we shall study in the context of binding in Chapter 9.
eBook - ePub- Patrick E. McMahon, Rosemary McMahon, Bohdan Khomtchouk(Authors)
- 2019(Publication Date)
- CRC Press(Publisher)
Free energy incorporates the values for enthalpy (ΔH), entropy (ΔS), and temperature in Kelvins (T in K). The dependence on product/reactant concentration is included in the total entropy. The general form of the equation is:Δ G= Δ H−T Δ SThe requirement for a spontaneous process is ΔS(universe) = (+). Since temperature in Kelvin is always positive, a positive value for ΔS(universe) requires that the term (−TΔS(universe) ) = ΔG must be negative.A forward reaction is spontaneous if the free energy change (ΔG) for the direction as written is negative: ΔG = (−). This means that the free energy of the system decreases: the reaction (based on the definition of free energy) is energetically “downhill.” A spontaneous reaction need not proceed at a measurable rate; rate is a function of the path through which the reaction occurs and can be influenced but does not directly depend on the free energy change (a state function).A forward reaction is non-spontaneous if the free energy change (ΔG) is positive: ΔG = (+). This means that the free energy of the system increases: the reaction (based on the definition of free energy) is energetically “uphill.” A non-spontaneous reaction can still occur if energy is supplied to the reaction system from the surroundings. However, for this to occur, a path (sequence of bond-making and bond-breaking steps) must be available for energy input even when sufficient energy is provided.Free energy, based on the state functions of enthalpy and entropy, is also a state function
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