Free Energy Quiz

PDF page 885: One of the challenges of using the second law of thermodynamics to determine if a process is spontaneous is that it requires measurements of the entropy change for the system and the entropy change for the surroundings. An alternative approach involving a new thermodynamic property defined in terms of system properties only was introduced in the late nineteenth century by American mathematician Josiah Willard Gibbs. This new property is called the Gibbs free energy (G) (or simply the free energy), and it is defined in terms of a system’s enthalpy and entropy as the following:

PDF page 885: One of the challenges of using the second law of thermodynamics to determine if a process is spontaneous is that it requires measurements of the entropy change for the system and the entropy change for the surroundings. An alternative approach involving a new thermodynamic property defined in terms of system properties only was introduced in the late nineteenth century by American mathematician Josiah Willard Gibbs. This new property is called the Gibbs free energy (G) (or simply the free energy), and it is defined in terms of a system’s enthalpy and entropy as the following:

PDF page 886: G = H − TS Free energy is a state function, and at constant temperature and pressure, the free energy change (ΔG) may be expressed as the following: ΔG = ΔH − TΔS (For simplicity’s sake, the subscript “sys” will be omitted henceforth.) The relationship between this system property and the spontaneity of a process may be understood by recalling the previously derived second law expression: qsurr ΔS = ΔS + univ T The first law requires that qsurr = −qsys, and at constant pressure qsys = ΔH, so this expression may be rewritten as: ΔH ΔS = ΔS − univ T Multiplying both sides of this equation by −T, and rearranging yields the following: −TΔS = ΔH − TΔS univ Comparing this equation to the previous one for free energy change shows the following relation: ΔG = −TΔS univ The free energy change is therefore a reliable indicator of the spontaneity of a process, being directly related to the previously identified spontaneity indicator, ΔSuniv. Table 16.3 summarizes the relation between the spontaneity of a process and the arithmetic signs of these indicators. Relation between Process Spontaneity and Signs of Thermodynamic Properties ΔG < 0 spontaneous ΔSuniv > 0 ΔG > 0 nonspontaneous ΔSuniv < 0 ΔG = 0 at equilibrium ΔSuniv = 0

PDF page 886: G = H − TS Free energy is a state function, and at constant temperature and pressure, the free energy change (ΔG) may be expressed as the following: ΔG = ΔH − TΔS (For simplicity’s sake, the subscript “sys” will be omitted henceforth.) The relationship between this system property and the spontaneity of a process may be understood by recalling the previously derived second law expression: qsurr ΔS = ΔS + univ T The first law requires that qsurr = −qsys, and at constant pressure qsys = ΔH, so this expression may be rewritten as: ΔH ΔS = ΔS − univ T Multiplying both sides of this equation by −T, and rearranging yields the following: −TΔS = ΔH − TΔS univ Comparing this equation to the previous one for free energy change shows the following relation: ΔG = −TΔS univ The free energy change is therefore a reliable indicator of the spontaneity of a process, being directly related to the previously identified spontaneity indicator, ΔSuniv. Table 16.3 summarizes the relation between the spontaneity of a process and the arithmetic signs of these indicators. Relation between Process Spontaneity and Signs of Thermodynamic Properties ΔG < 0 spontaneous ΔSuniv > 0 ΔG > 0 nonspontaneous ΔSuniv < 0 ΔG = 0 at equilibrium ΔSuniv = 0

PDF page 886: G = H − TS Free energy is a state function, and at constant temperature and pressure, the free energy change (ΔG) may be expressed as the following: ΔG = ΔH − TΔS (For simplicity’s sake, the subscript “sys” will be omitted henceforth.) The relationship between this system property and the spontaneity of a process may be understood by recalling the previously derived second law expression: qsurr ΔS = ΔS + univ T The first law requires that qsurr = −qsys, and at constant pressure qsys = ΔH, so this expression may be rewritten as: ΔH ΔS = ΔS − univ T Multiplying both sides of this equation by −T, and rearranging yields the following: −TΔS = ΔH − TΔS univ Comparing this equation to the previous one for free energy change shows the following relation: ΔG = −TΔS univ The free energy change is therefore a reliable indicator of the spontaneity of a process, being directly related to the previously identified spontaneity indicator, ΔSuniv. Table 16.3 summarizes the relation between the spontaneity of a process and the arithmetic signs of these indicators. Relation between Process Spontaneity and Signs of Thermodynamic Properties ΔG < 0 spontaneous ΔSuniv > 0 ΔG > 0 nonspontaneous ΔSuniv < 0 ΔG = 0 at equilibrium ΔSuniv = 0

PDF page 886: G = H − TS Free energy is a state function, and at constant temperature and pressure, the free energy change (ΔG) may be expressed as the following: ΔG = ΔH − TΔS (For simplicity’s sake, the subscript “sys” will be omitted henceforth.) The relationship between this system property and the spontaneity of a process may be understood by recalling the previously derived second law expression: qsurr ΔS = ΔS + univ T The first law requires that qsurr = −qsys, and at constant pressure qsys = ΔH, so this expression may be rewritten as: ΔH ΔS = ΔS − univ T Multiplying both sides of this equation by −T, and rearranging yields the following: −TΔS = ΔH − TΔS univ Comparing this equation to the previous one for free energy change shows the following relation: ΔG = −TΔS univ The free energy change is therefore a reliable indicator of the spontaneity of a process, being directly related to the previously identified spontaneity indicator, ΔSuniv. Table 16.3 summarizes the relation between the spontaneity of a process and the arithmetic signs of these indicators. Relation between Process Spontaneity and Signs of Thermodynamic Properties ΔG < 0 spontaneous ΔSuniv > 0 ΔG > 0 nonspontaneous ΔSuniv < 0 ΔG = 0 at equilibrium ΔSuniv = 0

PDF page 886: G = H − TS Free energy is a state function, and at constant temperature and pressure, the free energy change (ΔG) may be expressed as the following: ΔG = ΔH − TΔS (For simplicity’s sake, the subscript “sys” will be omitted henceforth.) The relationship between this system property and the spontaneity of a process may be understood by recalling the previously derived second law expression: qsurr ΔS = ΔS + univ T The first law requires that qsurr = −qsys, and at constant pressure qsys = ΔH, so this expression may be rewritten as: ΔH ΔS = ΔS − univ T Multiplying both sides of this equation by −T, and rearranging yields the following: −TΔS = ΔH − TΔS univ Comparing this equation to the previous one for free energy change shows the following relation: ΔG = −TΔS univ The free energy change is therefore a reliable indicator of the spontaneity of a process, being directly related to the previously identified spontaneity indicator, ΔSuniv. Table 16.3 summarizes the relation between the spontaneity of a process and the arithmetic signs of these indicators. Relation between Process Spontaneity and Signs of Thermodynamic Properties ΔG < 0 spontaneous ΔSuniv > 0 ΔG > 0 nonspontaneous ΔSuniv < 0 ΔG = 0 at equilibrium ΔSuniv = 0

PDF page 898: Gibbs free energy (G) is a state function defined with regard to system quantities only and may be used to predict the spontaneity of a process. A negative value for ΔG indicates a spontaneous process; a positive ΔG indicates a nonspontaneous process; and a ΔG of zero indicates that the system is at equilibrium. A number of approaches to the computation of free energy changes are possible.

PDF page 898: Gibbs free energy (G) is a state function defined with regard to system quantities only and may be used to predict the spontaneity of a process. A negative value for ΔG indicates a spontaneous process; a positive ΔG indicates a nonspontaneous process; and a ΔG of zero indicates that the system is at equilibrium. A number of approaches to the computation of free energy changes are possible.

PDF page 886: G = H − TS Free energy is a state function, and at constant temperature and pressure, the free energy change (ΔG) may be expressed as the following: ΔG = ΔH − TΔS (For simplicity’s sake, the subscript “sys” will be omitted henceforth.) The relationship between this system property and the spontaneity of a process may be understood by recalling the previously derived second law expression: qsurr ΔS = ΔS + univ T The first law requires that qsurr = −qsys, and at constant pressure qsys = ΔH, so this expression may be rewritten as: ΔH ΔS = ΔS − univ T Multiplying both sides of this equation by −T, and rearranging yields the following: −TΔS = ΔH − TΔS univ Comparing this equation to the previous one for free energy change shows the following relation: ΔG = −TΔS univ The free energy change is therefore a reliable indicator of the spontaneity of a process, being directly related to the previously identified spontaneity indicator, ΔSuniv. Table 16.3 summarizes the relation between the spontaneity of a process and the arithmetic signs of these indicators. Relation between Process Spontaneity and Signs of Thermodynamic Properties ΔG < 0 spontaneous ΔSuniv > 0 ΔG > 0 nonspontaneous ΔSuniv < 0 ΔG = 0 at equilibrium ΔSuniv = 0

PDF page 886: In addition to indicating spontaneity, the free energy change also provides information regarding the amount of useful work (w) that may be accomplished by a spontaneous process. Although a rigorous treatment of this subject is beyond the scope of an introductory chemistry text, a brief discussion is helpful for gaining a better perspective on this important thermodynamic property. For this purpose, consider a spontaneous, exothermic process that involves a decrease in entropy. The free energy, as defined by ΔG = ΔH − TΔS may be interpreted as representing the difference between the energy produced by the process, ΔH, and the energy lost to the surroundings, TΔS. The difference between the energy produced and the energy lost is the energy available (or “free”) to do useful work by the process, ΔG. If the process somehow could be made to take place under conditions of thermodynamic reversibility, the amount of work that could be done would be maximal: ΔG = wmax However, as noted previously in this chapter, such conditions are not realistic. In addition, the technologies used to extract work from a spontaneous process (e.g., automobile engine, steam turbine) are never 100% efficient, and so the work done by these processes is always less than the theoretical maximum. Similar reasoning may be applied to a nonspontaneous process, for which the free energy change represents the minimum amount of work that must be done

PDF page 888: The standard free energy change for a reaction may also be calculated from standard free energy of formation ΔGf° values of the reactants and products involved in the reaction. The standard free energy of formation is the free energy change that accompanies the formation of one mole of a substance from its elements in their standard states. Similar to the standard enthalpy of formation, ΔG° is by definition zero for elemental substances under standard state f ° for a reaction from ΔG° values is the same as that demonstrated conditions. The approach used to calculate ΔG f previously for enthalpy and entropy changes. For the reaction mA + nB ⟶ xC + yD, the standard free energy change at room temperature may be calculated as

PDF page 888: The standard free energy change for a reaction may also be calculated from standard free energy of formation ΔGf° values of the reactants and products involved in the reaction. The standard free energy of formation is the free energy change that accompanies the formation of one mole of a substance from its elements in their standard states. Similar to the standard enthalpy of formation, ΔG° is by definition zero for elemental substances under standard state f ° for a reaction from ΔG° values is the same as that demonstrated conditions. The approach used to calculate ΔG f previously for enthalpy and entropy changes. For the reaction mA + nB ⟶ xC + yD, the standard free energy change at room temperature may be calculated as

PDF page 897: standard free energy of formation (ΔG° ) change in free energy accompanying the formation of one mole of f substance from its elements in their standard states

PDF page 887: Free energy is a state function, so its value depends only on the conditions of the initial and final states of the system. A convenient and common approach to the calculation of free energy changes for physical and chemical reactions is by use of widely available compilations of standard state thermodynamic data. One method involves the use of standard enthalpies and entropies to compute standard free energy changes, ΔG°, according to the following relation. ΔG° = ΔH° − TΔS°

PDF page 889: H O(l) → H O(g) ΔG ° = ΔG° gas − ΔG° liquid 2 2 f f This approach may also be used in cases where a nonspontaneous reaction is enabled by coupling it to a spontaneous reaction. For example, the production of elemental zinc from zinc sulfide is thermodynamically unfavorable, as indicated by a positive value for ΔG°: ZnS(s) → Zn(s) + S(s) ΔG° = 201.3 kJ 1 The industrial process for production of zinc from sulfidic ores involves coupling this decomposition reaction to the thermodynamically favorable oxidation of sulfur: S(s) + O (g) → SO (g) ΔG° = −300.1 kJ 2 2 2 The coupled reaction exhibits a negative free energy change and is spontaneous: ZnS(s) + O (g) → Zn(s) + SO (g)