Thermodynamics n Thermodynamics Enthalpy Entropy Free Energy The

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Thermodynamics n Thermodynamics: Enthalpy, Entropy, Free Energy The Direction of Chemical Reactions Ø The

Thermodynamics n Thermodynamics: Enthalpy, Entropy, Free Energy The Direction of Chemical Reactions Ø The First Law of Thermodynamics Conservation of Energy Ø Ø Ø 6/8/2021 Limitations of the First Law l The Sign of H and Spontaneous Change l Freedom of Motion and Disposal of Energy The Second Law of Thermodynamics l Predicting Spontaneous Change l Entropy and the Number of Microstates l Entropy and the Second Law The Third Law of thermodynamics l Standard Molar Entropies 1

Thermodynamics n n n 6/8/2021 Calculating the Change in Entropy of a Reaction Ø

Thermodynamics n n n 6/8/2021 Calculating the Change in Entropy of a Reaction Ø The Standard Entropy of Reaction Ø Entropy Changes in the Surroundings Ø Entropy Change and the Equilibrium State Ø Spontaneous Exothermic and Endothermic Reactions Entropy, Free Energy, and Work Ø Free Energy Change (∆G) and Reaction Spontaneity Ø Standard Free Energy Changes Ø G and Work Ø Temperature and Reaction Spontaneity Ø Coupling of Reactions Free Energy, Equilibrium, and Reaction Direction 2

Thermodynamics Enthalpy (∆H) Sum of Internal Energy (E) plus Product of Pressure & Volume

Thermodynamics Enthalpy (∆H) Sum of Internal Energy (E) plus Product of Pressure & Volume (Endothermic vs. Exothermic) ( Hrxn = Hf prod - Hf react) (Constant Pressure) Entropy (S) Measure of system order/disorder & the number of ways energy can be dispersed through the motion of its particles All real processes occur spontaneously in the direction that increases the Entropy of the universe (universe = system + surroundings) (At Equilibrium) Gibbs Free Energy (∆G) Difference between Enthalpy and the product of absolute temperature and the Entropy 6/8/2021 3

Thermodynamics n Thermodynamics - study of relationships between heat and other forms of energy

Thermodynamics n Thermodynamics - study of relationships between heat and other forms of energy in chemical reactions n The direction and extent of chemical reactions can be predicted through thermodynamics (i. e. , feasibility) n Chemical reactions are driven by heat (Enthalpy) and/or randomness (Entropy) n A measure of randomness (disorder) is Entropy (S) n An increase in disorder is spontaneous n Spontaneous reactions are moving toward equilibrium n Spontaneous reactions move in the direction where energy is lowered, and move to Q/K = 1 (equilibrium) 6/8/2021 4

Thermodynamics n Thermodynamics is used to determine spontaneity (a process which occurs by itself);

Thermodynamics n Thermodynamics is used to determine spontaneity (a process which occurs by itself); what natural forces determine the extent of a chemical reaction (i. e. , Kc)? n For a reaction to be useful it must be spontaneous (i. e. , goes to near completion, i. e. , far to the right) n 6/8/2021 Spontaneity of a reaction depends on: Ø Enthalpy - heat flow in chemical reactions Ø Entropy - measure of the order or randomness of a system (Entropy units - J/ o. K) l Entropy is a state function; S = Sfinal - Sinitial l Higher disorder equates to an increase in Entropy l Entropy has positional and thermal disorder 5

Thermodynamics First Law of Thermodynamics n The first law of Thermodynamics is a version

Thermodynamics First Law of Thermodynamics n The first law of Thermodynamics is a version of the law of Conservation of Energy, specialized for Thermodynamical systems n It is usually formulated by stating that the change in the Internal Energy ( E) of a closed system is equal to the amount of Heat (q) supplied to the system, minus the amount of Work (W = -P V) performed by the system on its surroundings n The law of conservation of energy can be stated The Energy of an Isolated System is Constant 6/8/2021 6

Thermodynamics n First Law of Thermodynamics Ø Conservation of Energy, E (or U in

Thermodynamics n First Law of Thermodynamics Ø Conservation of Energy, E (or U in some texts) Any change in the energy of the system must correspond to the interchange of “heat” (work) with an “External” surrounding Ø Total Internal Energy (E) - The sum of the kinetic and potential energies of the particles making up a substance Ø Kinetic Energy (Ek) - The energy associated with an object by virtue of its motion, Ek = ½mv 2 Ø Potential Energy (Ep) - The energy an object has by virtue of its position in a field of force, Ep = mgh 6/8/2021 (kg m 2/s 2) (joules) (kg m/s 2 m = kg m 2/s 2) 7

Thermodynamics Ø Work – The energy transferred is moved by a force, such as

Thermodynamics Ø Work – The energy transferred is moved by a force, such as the expansion of a gas in an open system under constant pressure Pressure = kg/(m s 2) Volume = m 3 Work (W) = kg/(m s 2) m 3 = kg m 2/s 2 = joules (J) Ø 6/8/2021 Internal Energy The Internal Energy of a system, E, is precisely defined as the heat at constant pressure (qp) plus the work (w) done by the system: 8

Thermodynamics n Enthalpy is defined as the internal energy plus the product of the

Thermodynamics n Enthalpy is defined as the internal energy plus the product of the pressure and volume – work n The change in Enthalpy is the change in internal energy plus the product of constant pressure and the change in Volume Recall n 6/8/2021 (At Constant Pressure) The change in Enthalpy equals the heat gained or lost (heat of reaction) at constant pressure – the entire change in “internal energy” ( E), minus any expansion “work” done by the system (P V) would have negative sign 9

Thermodynamics Ø E – total internal energy; the sum of kinetic and potential energies

Thermodynamics Ø E – total internal energy; the sum of kinetic and potential energies in the system Ø q – heat flow between system and surroundings (-q indicates that heat is lost to surroundings) 6/8/2021 Ø w – work (-w indicates work is lost to surroundings) Ø H – Enthalpy – extensive property dependent on quantity of substance and represents the heat energy tied up in the chemical bonds (heat of reaction) Ø Useful Units in Energy expressions l 1 J (joule) = 1 kg m 2/s 2 l 1 Pa (pascal) = 1 kg/m s 2 l 1 atm = 1. 01325 x 105 Pa l 1 atm = 760 torr = 760 mm Hg 10

Exchanges of Heat and Work with the Surroundings Pressure x. Volume Work = expansion

Exchanges of Heat and Work with the Surroundings Pressure x. Volume Work = expansion of volume due to forming a gas q>0 w>0 on system 6/8/2021 q<0 w<0 by system 11

Thermodynamics The 2 nd Law of Thermodynamics The total Entropy of a system and

Thermodynamics The 2 nd Law of Thermodynamics The total Entropy of a system and its surroundings always increases for a “Spontaneous” process n Entropy – A thermodynamic quantity related to the number of ways the energy of a system can be dispersed through the motions of its particles n Entropy is a state function; S = Sf - Si n Higher disorder equates to an increase in Entropy has positional and thermal disorder n The Entropy, S, is conserved for a reversible process n The disorder of the system and thermal surroundings must increase for a spontaneous process n A process occurs spontaneously in the direction that increases the Entropy of the universe 6/8/2021 12

Thermodynamics n A spontaneous change, whether a chemical or physical change, or just a

Thermodynamics n A spontaneous change, whether a chemical or physical change, or just a change in location is one that: Ø Occurs by itself under specified conditions Ø Occurs without a continuous input of energy from outside the system n In a non-spontaneous change, the surroundings must supply the system with a continuous input of energy n Under a given set of conditions, a spontaneous change in one direction is not spontaneous in the “other” direction A limitation of the 1 st Law of Thermodynamics n 6/8/2021 Spontaneous does not equate to “Instantaneous” 13

Thermodynamics n Limitations of the 1 st law of Thermodynamics Ø 6/8/2021 The 1

Thermodynamics n Limitations of the 1 st law of Thermodynamics Ø 6/8/2021 The 1 st Law accounts for the energy involved in a chemical process (reaction) l The internal energy (E) of a system, the sum of the kinetic and potential energy of all its particles, changes when heat (q) and/or work (w= -PV) are gained or lost by the system l Energy not part of the system is part of the surroundings 14

Thermodynamics 6/8/2021 l The surroundings (sur) and the system (sys) together constitute the “Universe

Thermodynamics 6/8/2021 l The surroundings (sur) and the system (sys) together constitute the “Universe (univ)” l Heat and/or work gained by system is lost by surroundings l The “total” energy of the Universe is constant 15

Thermodynamics n The first Law, however, does not account for the “direction” of the

Thermodynamics n The first Law, however, does not account for the “direction” of the change in energy Ex. The burning of gas in your car 6/8/2021 Ø Potential energy difference between chemical bonds in fuel mixture and those in exhaust is converted to kinetic energy to move the car Ø Some of the converted energy is released to the environmental surroundings as heat (q) Ø Energy (E) is converted from one form to another, but there is a “net” conservation of energy Ø 1 st law does not explain why the exhaust gas does not convert back into gasoline and oxygen Ø 1 st law does not account for the “direction” of a spontaneous change 16

Thermodynamics n Spontaneous Change and Change in Enthalpy ( H) Ø It was originally

Thermodynamics n Spontaneous Change and Change in Enthalpy ( H) Ø It was originally proposed (19 th Century) that the “sign” of the Enthalpy change ( H) – the heat lost or gained at constant pressure (qp) – was the criterion of spontaneity Ø Exothermic processes ( H < 0) were “spontaneous” Ø Endothermic processes ( H > 0) were “nonspontaneous” Ø Ex. Combustion (burning) of Methane in Oxygen is “Spontaneous” and “Exothermic” ( H < 0) When Methane burns in your furnace, heat is released 6/8/2021 17

Thermodynamics n The sign of the change in Enthalpy ( H), however, does not

Thermodynamics n The sign of the change in Enthalpy ( H), however, does not indicate spontaneity in all cases n An Exothermic process can occur spontaneously under certain conditions and the opposite Endothermic process can also occur spontaneously under other conditions Ex. Water freezes below 0 o. C and melts above 0 o. C Both changes are spontaneous Freezing is Exothermic Melting (& Evaporation) is Endothermic Most Water-Soluble Salts have a positive Hsoln yet they dissolve spontaneously The decomposition of N 2 O 5 is Endothermic and spontaneous 6/8/2021 18

Thermodynamics n 6/8/2021 Freedom of motion & energy dispersion Ø Endothermic processes result in

Thermodynamics n 6/8/2021 Freedom of motion & energy dispersion Ø Endothermic processes result in more particles (atoms, ions, molecules) with more freedom of motion – Entropy increases Ø During an Endothermic phase change, “fewer” moles of reactant produce “more” moles or product Ø The energy of the particles is dispersed over more quantized energy levels 19

Thermodynamics n Endothermic Spontaneous Process Less freedom of particle motion more freedom of motion

Thermodynamics n Endothermic Spontaneous Process Less freedom of particle motion more freedom of motion Localized energy of motion dispersed energy of motion Phase Change: Solid Liquid Gas Dissolving of Salt: Crystalline Solid + Liquid Ions in Solution Chemical Change: Crystalline Solids Gases + Ions in Solution n 6/8/2021 In thermodynamic terms, a change in the freedom of motion of particles in a system, that is, in the dispersal of their energy of motion, is a key factor determining the direction of a spontaneous process 20

Thermodynamics n n 6/8/2021 Quantized Energy Levels Ø Electronic Ø Kinetic - vibrational, rotational,

Thermodynamics n n 6/8/2021 Quantized Energy Levels Ø Electronic Ø Kinetic - vibrational, rotational, translational Microstate Ø A single quantized state at any instant Ø The total energy of the system is dispersed throughout the microstate Ø New microstates are created when system conditions change Ø At a given set of conditions, each microstate has the same total energy as any other Ø A given microstate is just as likely to occur as any other microstate 21

Thermodynamics n Microstates vs Entropy (Positional Disorder) Ø Boltzmann Equation where k – Boltzmann

Thermodynamics n Microstates vs Entropy (Positional Disorder) Ø Boltzmann Equation where k – Boltzmann Constant where R = Universal Gas Constant NA = Avogadro’s Number where W = No. of Microstates 6/8/2021 22

Thermodynamics 6/8/2021 Ø Compute Ssys Ø When n becomes NA , i. e. 1

Thermodynamics 6/8/2021 Ø Compute Ssys Ø When n becomes NA , i. e. 1 mole Ø The Boltzman constant “k = R/NA” has become “R” Ø A system with fewer microstates (smaller Wfinal) has lower Entropy (Lower S) Ø A system with more microstates (larger Wfinal) has higher Entropy (higher S) 23

Thermodynamics n 6/8/2021 Entropy change – Volume, Pressure, Concentration 24

Thermodynamics n 6/8/2021 Entropy change – Volume, Pressure, Concentration 24

Thermodynamics n Changes in Entropy Ø The change in Entropy of the system (

Thermodynamics n Changes in Entropy Ø The change in Entropy of the system ( Ssys) depends only on the difference between its final and initial values Ø ( Ssys) > 0 when its value increases during a change Ex. Sublimation of dry ice to gaseous CO 2 Ø ( Ssys) < 0 when its value decreases during a change Ex. Condensation of Water 6/8/2021 25

Thermodynamics n Entropy Changes based on Heat Changes Ø The 2 nd Law of

Thermodynamics n Entropy Changes based on Heat Changes Ø The 2 nd Law of Thermodynamics states that the change in Entropy for a gas expanding into a vacuum is related to the heat absorbed (qrev) and the temperature (T) at which the exchange occurs Qrev refers to a “Reversible” process where the expansion of the gas can be reversed by the application of pressure (work, PV) Ø The heat absorbed by the expanding gas increases the dispersal of energy in the system, increasing the Entropy Ø If the change in Entropy, Ssys, is greater than the heat absorbed divided the absolute temperature, the process occurs spontaneously Ø 6/8/2021 26

Thermodynamics n Determination of the Direction of a Spontaneous Process Second Law Restated All

Thermodynamics n Determination of the Direction of a Spontaneous Process Second Law Restated All real processes occur spontaneously in the direction that increases the Entropy of the universe (system + surroundings) 6/8/2021 Ø When changes in both the system and the surroundings occur, the universe must be considered Ø Some spontaneous processes end up with higher Entropy Ø Other spontaneous processes end up with lower Entropy 27

Thermodynamics 6/8/2021 Ø The Entropy change in the system or surroundings can be positive

Thermodynamics 6/8/2021 Ø The Entropy change in the system or surroundings can be positive or negative Ø For a spontaneous process, the “sum” of the Entropy changes must be positive Ø If the Entropy of the system decreases, the Entropy of the surroundings must increase, making the net increase to the universe positive 28

Thermodynamics The 3 rd Law of Thermodynamics n Entropy & Enthalpy are both “state”

Thermodynamics The 3 rd Law of Thermodynamics n Entropy & Enthalpy are both “state” functions n Absolute Enthalpies cannot be determined, only changes

Thermodynamics n Entropy values for substances are compared to “standard” states Ø Ø 6/8/2021

Thermodynamics n Entropy values for substances are compared to “standard” states Ø Ø 6/8/2021 Standard States l Gases – 1 atmosphere (atm) l Concentrations – Molarity (M) l Solids – Pure Substance Standard Molar Entropy l So (Units – J/mol K @ 298 o. K) l Values available in Reference Tables (Appendix “B”) 30

Thermodynamics n Predicting Relative So Values of a System Ø 6/8/2021 Temperature Changes l

Thermodynamics n Predicting Relative So Values of a System Ø 6/8/2021 Temperature Changes l So increases as temperature increases l Temperature increases as “heat” is absorbed (q > 0) l As temperature increases, the Kinetic Energies of gases, liquids, and solids increase and are dispersed over larger areas increasing number of microstates available, which increases Entropy 31

Thermodynamics § At any T > 0 o K, each particle moves about its

Thermodynamics § At any T > 0 o K, each particle moves about its lattice position § As temperature increases through the addition of “heat”, movement is greater § Total energy is increased giving particles greater freedom of movement § Energy is more dispersed § Entropy is increased 6/8/2021 32

Thermodynamics n 6/8/2021 Predicting Relative So Values of a System (Con’t) Ø Physical States

Thermodynamics n 6/8/2021 Predicting Relative So Values of a System (Con’t) Ø Physical States and Phase Changes l So increases for a substance as it changes from a solid to a liquid to a gas l Heat must be absorbed (q>0) for a change in phase to occur l Increase in Entropy from liquid to gas is much larger than from solid to liquid Svapo >> Sfuso 33

Thermodynamics n Predicting Relative So Values of a System (Con’t) Ø Dissolving a solid

Thermodynamics n Predicting Relative So Values of a System (Con’t) Ø Dissolving a solid or liquid l Entropy of a dissolved solid or liquid is greater than the Entropy of the “pure” solute l As the crystals breakdown, the ions have increased freedom of movement l Particle energy is more dispersed into more “microstates” Entropy is increased 6/8/2021 l Entropy increase is “greater” for ionic solutes than “molecular” solutes – more particles are produced l The slight increase in Entropy for “molecular” solutes in solution arises from the separation of molecules from one another when mixed with the solvent 34

Thermodynamics n Predicting Relative So Values of a System (Con’t) Ø Dissolving a Gas

Thermodynamics n Predicting Relative So Values of a System (Con’t) Ø Dissolving a Gas l Gases have considerable freedom of motion and highly dispersed energy in the gaseous state l Dissolving a gas in a solvent results in diminished freedom of motion Entropy is “Decreased” Ø Mixing (dissolving) a gas in another gas l Molecules separate and mix increasing microstates and dispersion of energy Entropy “Increases” 6/8/2021 35

Thermodynamics n Predicting Relative So Values of a System (Con’t) Ø Atomic Size l

Thermodynamics n Predicting Relative So Values of a System (Con’t) Ø Atomic Size l 6/8/2021 Multiple substances in a given phase will have different Entropies based on Atomic Size and Molecular Complexity Down a “Periodic” group energy levels become “closer” together as the atoms get “Heavier” No. of microstates and molar Entropy increase 36

Thermodynamics n Predicting Relative So Values of a System (Con’t) Ø Molecular Complexity l

Thermodynamics n Predicting Relative So Values of a System (Con’t) Ø Molecular Complexity l Allotropes – Elements that occur in different forms have higher Entropy in the form that allows more freedom of motion Ex. Diamond vs Graphite Diamond bonds extend the 3 dimensions, allowing limited movement – lower Entropy Graphite bonds extend only within twodimensional sheets, which move relatively easy to each other – higher Entropy 6/8/2021 37

Thermodynamics n Predicting Relative So Values of a System (Con’t) Ø Molecular Complexity (Con’t)

Thermodynamics n Predicting Relative So Values of a System (Con’t) Ø Molecular Complexity (Con’t) l 6/8/2021 Compounds Entropy increases as the number of atoms (or ions) in a formula unit of a molecule increases The trend is based on types of movement and the number of microstates possible NO (Nitrous Oxide) in the chart below can vibrate only toward and away from each other The 3 atoms of the NO 2 molecule have more virbrational motions 38

Thermodynamics n Predicting Relative So Values of a System (Con’t) Ø Molecular Complexity (Con’t)

Thermodynamics n Predicting Relative So Values of a System (Con’t) Ø Molecular Complexity (Con’t) l 6/8/2021 Compounds of large molecules A long organic hydrocarbon chain can rotate and vibrate in more ways than a short chain Entropy increase with “Chain Length” A ring compound with the same molecular formula as a corresponding chain compound has lower Entropy because a ring structure inhibits freedom of motion cyclopentane (C 5 H 10) vs pentene (C 5 H 10) Scyclopentane < Spentene 39

Thermodynamics n Predicting Relative So Values of a System (Con’t) Ø Physical State vs

Thermodynamics n Predicting Relative So Values of a System (Con’t) Ø Physical State vs Molecular Complexity When gases are compared to liquids: The effect of physical state (g, l, s) usually dominates that of molecular complexity, i. e. , the No. atoms in a formula unit or chain length 6/8/2021 40

Thermodynamics n Calculating Change in Entropy Ø 6/8/2021 Gases l The sign of the

Thermodynamics n Calculating Change in Entropy Ø 6/8/2021 Gases l The sign of the Standard Entropy of Reaction ( Sorxn) of a reaction involving gases can often be predicted when the reaction involves a change in the number of moles that occurs and all the reactants and products are in their “standard” states l Gases have great freedom of motion and high molar Entropies If the number of moles of gas increases, Sorxn is usually positive If the number of moles of gas decreases, Sorxn is usually negative 41

Thermodynamics n 6/8/2021 Entropy Changes in the Surroundings Ø 2 nd Law – For

Thermodynamics n 6/8/2021 Entropy Changes in the Surroundings Ø 2 nd Law – For a spontaneous process, a decrease in Entropy in the system, Ssys, can only occur if there is an increase in Entropy in the surroundings, Ssys, Ø Essential role of the surroundings is to either add heat to the system or remove heat from the system – surroundings act as a “Heat Sink” Ø Surroundings are generally considered so large that its temperature essentially remains constant even though its Entropy will change through the loss or gain of heat 42

Thermodynamics n Surroundings participate in two (2) types of Enthalpy changes Ø Ø 6/8/2021

Thermodynamics n Surroundings participate in two (2) types of Enthalpy changes Ø Ø 6/8/2021 Exothermic Change l Heat lost by system is gained by surroundings l Increased freedom of motion from temperature increase in surroundings leads to Entropy increase Endothermic Change l Heat gained by system is lost by surroundings l Heat lost reduces freedom of motion in surroundings, energy dispersal is less, and Entropy decreases 43

Thermodynamics n 6/8/2021 Temperature of the Surroundings Ø At lower temperatures l Little random

Thermodynamics n 6/8/2021 Temperature of the Surroundings Ø At lower temperatures l Little random motion l Little energy l Fewer energy levels l Fewer microstates l Transfer of heat from system has larger effect on how much energy is dispersed Ø At Higher Temperatures l Surroundings already have relatively large quantity of energy dispersal l More energy levels l More available microstates l Transfer of heat from system has much smaller effect on the total dispersion of energy 44

Thermodynamics n 6/8/2021 Temperature of the Surroundings Ø The change in Entropy of the

Thermodynamics n 6/8/2021 Temperature of the Surroundings Ø The change in Entropy of the surroundings is “greater” when heat is added at lower temperatures Ø Recall 2 nd Law – The change in Entropy of the surroundings is directly related to an “opposite” change in the heat (q) of the system and “inversely” related to the temperature at which the heat is transferred Ø Recall that for a process at “Constant Pressure”, the heat (qp) = H 45

Thermodynamics n 6/8/2021 Entropy Change and the Equilibrium State Ø For a process “spontaneously”

Thermodynamics n 6/8/2021 Entropy Change and the Equilibrium State Ø For a process “spontaneously” approaching equilibrium, the change in Entropy is positive Ø At equilibrium, there is no net change in the flow or energy to either the system or the surroundings Ø Any change in Entropy in the system is exactly balanced by an opposite Entropy change in the surroundings 46

Thermodynamics n 6/8/2021 Summary – Spontaneous Exothermic & Endothermic Reactions Ø Exothermic Reaction (

Thermodynamics n 6/8/2021 Summary – Spontaneous Exothermic & Endothermic Reactions Ø Exothermic Reaction ( Hsys < 0) l Heat, released from system, is absorbed by surroundings l Increased freedom of motion and energy dispersal in surroundings ( Ssurr > 0) Ø Ex. Exothermic where Entropy change: ( Ssys) > 0 47

Thermodynamics n Summary – Spontaneous Exothermic & Endothermic Reactions (Con’t) Ø 6/8/2021 Exothermic Reaction

Thermodynamics n Summary – Spontaneous Exothermic & Endothermic Reactions (Con’t) Ø 6/8/2021 Exothermic Reaction ( Hsys < 0) l Ex. Exothermic where Entropy change ( Ssys) < 0 l Entropy in surroundings must increase even more ( Ssurr > > 0) to make the total S positive 48

Thermodynamics n 6/8/2021 Summary – Spontaneous Exothermic & Endothermic Reactions (Con’t) Ø Endothermic Reaction

Thermodynamics n 6/8/2021 Summary – Spontaneous Exothermic & Endothermic Reactions (Con’t) Ø Endothermic Reaction ( Hsys > 0) l Heat lost by surroundings decreases the molecular freedom of motion and dispersal of energy l Entropy of surroundings decreases ( Ssurr) < 0 l Only way an Endothermic reaction can occur spontaneously is if ( Ssys) > 0 and large enough to outweigh the negative Ssurr Ø Ex. Solution Process for many ionic compounds l Heat is absorbed to form solution l Entropy of surroundings decreases l However, when crystalline solids become freemoving ions, the Entropy increase in the system is quite large ( Ssys) > > 0 l Ssys increase far outweighs negative Ssurr 49

Thermodynamics n Entropy, Free Energy and Work Ø Gibbs Free Energy (G) l Using

Thermodynamics n Entropy, Free Energy and Work Ø Gibbs Free Energy (G) l Using Hsys & Ssurr , it can be predicted whether a reaction will be “Spontaneous” at a particular temperature l J. Willard Gibbs developed a single criterion for spontaneity 6/8/2021 The Gibbs “Free Energy” (G) is a function that combines the system’s Enthalpy (H) and Entropy (S) 50

Thermodynamics n Gibbs Free Energy Change and Reaction Spontaneity The Free Energy Change (

Thermodynamics n Gibbs Free Energy Change and Reaction Spontaneity The Free Energy Change ( G) is a measure of the spontaneity of a process and of the useful energy available from it 6/8/2021 51

Thermodynamics n Gibbs Free Energy Change and Reaction Spontaneity Ø The sign of G

Thermodynamics n Gibbs Free Energy Change and Reaction Spontaneity Ø The sign of G tells if a reaction is spontaneous Ø From the 2 nd Law of Thermodynamics Ø 6/8/2021 l Suniv > 0 for spontaneous reaction l Suniv < 0 for nonspontaneous reaction l Suniv = 0 for process in “Equilibrium” Absolute Temperature (K) is “always positive” l G < 0 for a spontaneous process l G > 0 for a nonspontaneous process l G = 0 for a process in equilibrium 52

Thermodynamics n Standard Free Energy of Formation ( Gfo) n Gfo is the free

Thermodynamics n Standard Free Energy of Formation ( Gfo) n Gfo is the free energy change that occurs when 1 mole of compound is made from its “elements” and all of the components are in their “standard” states n Gfo values have properties similar to Hfo values 6/8/2021 Ø Gfo of an element in its standard form is “zero” Ø An equation coefficient (m or n) multiplies Gfo by that number Ø Reversing a reaction changes the sign of Gfo Ø Gfo values are obtained from tables 53

Thermodynamics n G and the Work (w) a System Can Do Ø For a

Thermodynamics n G and the Work (w) a System Can Do Ø For a Spontaneous process ( G < 0) at constant Temperature (T) and Pressure (P), G is the “Maximum” of useful work obtainable from the system as the process takes place For a Nonspontaneous process ( G > 0) at constant T & P, G is the “Minimum” work that must be done to the system to make the process take place Ø In any process, neither the “maximum” or the “minimum” work is achieved because some “Heat” is lost Ø A reaction at equilibrium, which includes phase changes ( G = 0), can no longer do “any work” Ø 6/8/2021 54

Thermodynamics n 6/8/2021 The Effect of Temperature on Reaction Spontaneity Ø When the signs

Thermodynamics n 6/8/2021 The Effect of Temperature on Reaction Spontaneity Ø When the signs of H & S are the same, some reactions that are non-spontaneous at one temperature become spontaneous at another, and vice versa Ø The temperature at which a reaction becomes spontaneous is the temperature at which a “Positive” G switches to a “Negative” G Ø This occurs because of the changing magnitude of the -T S term Ø This cross-over temperature (reaction at equilibrium) occurs when G = 0 Ø Thus: 55

Thermodynamics n The Effect of Temperature on Reaction Spontaneity Ø Reactions Independent of Temperature

Thermodynamics n The Effect of Temperature on Reaction Spontaneity Ø Reactions Independent of Temperature l Spontaneous Reaction at all Temperatures H < 0 (Exothermic) S > 0 - T S is always negative G is always “negative” l Nonspontaneous Reaction at all Temperatures H > 0 (Endothermic) Both oppose spontaneity - T S is positive G is always positive 6/8/2021 S < 0 56

Thermondynamics Ø Temperature Dependent Reactions When H & S have the same sign, the

Thermondynamics Ø Temperature Dependent Reactions When H & S have the same sign, the relative magnitudes of the –T S and H terms determine the sign of G l 6/8/2021 Reaction is spontaneous at high Temperatures H > 0 S > 0 S favors spontaneity (-T S) < 0) H does not favor spontaneity Spontaneity will occur only when -T S (generally high temperature) is large enough to make G negative 57

Thermodynamics Ø Temperature Dependent Reactions (Con’t) When H & S have the same sign,

Thermodynamics Ø Temperature Dependent Reactions (Con’t) When H & S have the same sign, the relative magnitudes of the (– T S) and H terms determine the sign of G l 6/8/2021 Reaction is spontaneous at lower Temperatures H < 0 S < 0 H favors spontaneity S does not favor spontaneity (- T S) > 0) G will only be negative when -T S is smaller the H term, usually at a lower temperature 58

Thermodynamics n 6/8/2021 Summary – Reaction Spontaneity and the Sign of ∆H ∆S -T∆S

Thermodynamics n 6/8/2021 Summary – Reaction Spontaneity and the Sign of ∆H ∆S -T∆S ∆G Description — + — — Spontaneous at all Temperatures + — + + Nonspontaneous at all Temperatures + + — Spontaneous at Higher Temperature Nonspontaneous at Lower Temperatures — — + + — Spontaneous at Lower Temperatures Nonspontaneous at Higher Temperatures 59

Thermodynamics n Free Energy, Equilibrium, and Reaction Direction Ø Ø Ø 6/8/2021 From Chapter

Thermodynamics n Free Energy, Equilibrium, and Reaction Direction Ø Ø Ø 6/8/2021 From Chapter 17 l Q < K (Q/K < 1) – reaction proceeds “Right” l Q > K (Q/K > 1) – reaction proceeds “Left” l Q = K (Q/K = 1) – Reaction has reached “Equilibrium” Energy & Spontaneity l Exothermic ( H < 0) – reaction proceeds “Right” l Endothermic ( H > 0) – reaction proceeds “Left” Free Energy & Spontaneity l G < 0 for a spontaneous process l G > 0 for a nonspontaneous process l G = 0 for a process in equilibrium 60

Thermodynamics n Relationship between Q/K and G Ø If Q/K < 1, then ln(Q/K)

Thermodynamics n Relationship between Q/K and G Ø If Q/K < 1, then ln(Q/K) < 0 and if G < 0 Then: Reaction is Exothermic and spontaneous Ø If Q/K > 1, then ln(Q/K) > 0 and if G > 0 Then: Reaction is Endothermic and nonspontaneous Ø If Q/K = 1, then ln(Q/K) = 0 and if G = 0 Then: Reaction has reached equilibrium 6/8/2021 Ø In each case the signs of ln(Q/K) and G are the same for a given reaction direction Ø Gibbs noted that ln(Q/K) and G are proportional to each other and are related (made equal) by the proportionality constant “RT” 61

Thermodynamics n Recall: Q represents the concentrations (or Pressures) of a systems components at

Thermodynamics n Recall: Q represents the concentrations (or Pressures) of a systems components at any time during the reaction, whereas, K represents the concentrations when the reaction has reached “equilibrium” n G Depends on how the Q ratio of the concentrations differs from the equilibrium ratio, K n Expressing G when “Q” is at standard state conditions 6/8/2021 Ø All concentrations are = 1 M (pressures = 1 atm) Ø Q=1 Ø Standard Free Energy ( Go) can be computed from the Equilibrium constant (K) Ø Logarithmic relationship means a “small” change in Go has a large effect on the value of K 62

Thermodynamics n For expressing the free energy for nonstandard initial conditions Ø 6/8/2021 Substitute

Thermodynamics n For expressing the free energy for nonstandard initial conditions Ø 6/8/2021 Substitute Go equation into G equation 63