THE SECOND LAW OF THERMODYNAMICS. Professor Benjamin G. Levine CEM 182H Lecture 5

THE SECOND LAW OF THERMODYNAMICS Professor Benjamin G. Levine CEM 182H Lecture 5

Chemical Equilibrium N 2 + 3 H 2 2 NH 3 Chemical reactions go in both directions Systems started from any initial state will approach an equilibrium state In this equilibrium state the rates of the forward and backward reaction are equal to one another Thermodynamics helps us predict this state

Thermodynamics Is the macroscopic science of how energy changes from one form to another Tells you the direction of changes in a wide range of scientific systems What is the equilibrium state of a chemical system? How do living things obtain, store, and use energy? How did the universe begin and how will it end? How would we design a more efficient engine?

Thermodynamics Limitations Thermodynamics tells you the direction of change, not the rate Thermodynamics can t explain how microscopic properties lead to macroscopic ones

The System A system is the part of the universe that we are interested in You as the scientist choose the system!

The Surroundings The surroundings are the remainder of the universe The surroundings may exchange energy and matter with the system The system and its surroundings together are called the thermodynamic universe System Surroundings

Describing the System Boundary When you are faced with a thermodynamic problem, you must be able to identify what can and what can t cross the boundary between the system and the surroundings System Surroundings

Describing the System Boundary An open system can exchange matter with it s surroundings A closed system can not exchange matter with it s surroundings (The walls of a closed system are said to be impermeable) System Surroundings

Describing the System Boundary An isolated system cannot exchange energy or matter with it s surroundings System Surroundings

Describing the System Boundary Rigid walls prevent any mechanical deformation (e.g. compression) from being done on the system by the surroundings (or vice versa) Non-rigid walls allow such deformation System Surroundings

Describing the System Boundary Adiabatic walls allow no thermal energy to pass between the system and surroundings Diathermal walls allow thermal energy to pass the system boundary System Surroundings

State Functions The macroscopic properties of a thermodynamic system (such as pressure, volume, temperature) are called state functions (also thermodynamic variables, state variables) State functions describing the system can be classified as intensive or extensive Intensive variables are independent of the size of the system Extensive variables depend linearly on the size of the system

Thermodynamic States A thermodynamic state is a macroscopic condition of the system in which the thermodynamic variable can be held at fixed values (independent of time) by defining an appropriate boundary and surroundings. System Surroundings

About Thermodynamic States The thermodynamic state completely defines the state functions of the system Not all possible states of a system are thermodynamics states

Thermodynamic States PV = nrt Constant P=100 atm Constant V=100 L Constant n=1 mol Constant T=100 K The equation of state defines all possible thermodynamic states of a system

About Thermodynamic States The thermodynamic state completely defines the state functions of the system Not all possible states of a system are thermodynamics states COLD HOT

Thermodynamic Processes A thermodynamic process changes the thermodynamic state of a system. Examples Compressing a gas from 1 L to 0.5 L Boiling water Reacting N 2 and H 2 to form NH 3 Cooling of an overheated car engine Fission of uranium in a nuclear reactor

Thermodynamic Processes Thermodynamic processes are defined by their starting and ending points Starting point T = 273 K V = 1 L n = 1 mole Ending point T = 273 K V = 2 L n = 1 mole

Irreversible Processes Irreversible processes are thermodynamic processes via states that are not thermodynamics states It is impossible to return the universe to its initial state after an irreversible process

Reversible Processes If we change the system slowly enough, it never leaves a thermodynamics state Such a process is called reversible It is possible to return the universe to its initial state after an reversible process

Reversible Processes A truly reversible process would take infinite time However, reversible processes offer an ideal model for irreversible ones, and let us understand the limits placed on real irreversible ones

Reversible Processes There are an infinite number of reversible paths between two thermodynamic states Temperature Initial State Final State Pressure

Describing Thermodynamic Processes X = X X final initial Temperature Initial State Pressure Final State These changes in state functions do not depend on the path! P = P P final T = T T final V = V V final U = U U final initial initial initial initial

How does energy move between the system and its surroundings? Heat Work Heat transfer in Heat transfer out System Work done on system Surroundings Work done by system

Work Lifting the ball increases it s gravitational potential energy You have done work on the ball w = Fd Work (units of energy) force distance

Pressure Volume Work w = Fd = F ( h h ) ext f i = P A( h h ) ext f i area of piston A P ext = P ( Ah Ah ) ext f i = P ( V V ) ext f i = P V ext h f final height

A Note About the Sign By convention work done on the system is positive work done by the system is negative w > 0 w < 0 System Work done on system Surroundings Work done by system

Where does the energy come from/go? Kinetic energy of molecules Potential energy Chemical bonds Intermolecular forces The total of the above energies is called the internal energy, U The internal energy is a state function

Definition of Work Work is a means of changing the internal energy of the system by mechanical (electrical, etc.) interaction

Definition of Heat Heat is a means of changing the internal energy of the system without mechanical interaction

The Sign of Heat By convention Heat flowing into the system is positive Heat flowing out of the system is negative q > 0 q< 0 Heat flowing into system System Surroundings Heat flowing out of system

The First Law of Thermodynamics U = w + q

The First Law of Thermodynamics There exists a state function called internal energy whose changes are independent of path, although the values of q and w individually depend on the path of the process.

Heat Capacity Summary Specific heat capacity q = Mc T s Molar heat capacity q = nc T m Heat capacity q = C T

Heat Capacity under Different Conditions Constant P Constant V Gas Gas Gas does PV work on the surroundings Gas does not do PV work on the surroundings

Heat Capacity under Different Conditions The molar heat capacity at constant pressure is represented by c p The molar heat capacity at constant volume is represented by c v The heat capacity of a gas at constant pressure is higher than that of the same gas at constant volume The difference is generally negligible for solids and liquids

Bomb Calorimetry U = q V Chemical Reaction Calorimetric Fluid Insulation

Bomb Calorimetry U = q V Bomb calorimetry is convenient because the heat corresponds directly to the change in internal energy Bomb calorimetry is not convenient because keeping a chemical reaction at constant volume is difficult

Heat Transfer at Constant Pressure H = U + PV H = q P

Heat and Work Depend on Path 1 mole of Helium 2 atm A Heat at constant P C Pressure Cool at constant V Cool at constant V 1 atm D Heat at constant P B 10 L 30 L Volume

First Law Summary So Far There is a state variable called internal energy whose change is independent of path U = w + q Changes in internal energy occur when energy passes across the system boundary either as work or heat

Polyatomic vs. Monatomic Gases Gas C p (J mol -1 K -1 ) He 20.79 ( 5/2 * R ) Ne 20.79 Ar 20.79 H 2 28.81 O 2 29.36 F 2 31.30 H 2 O 33.54 (all c p determined at 298 K and 1 atm) These deviations from 5/2 * R persist even in the ideal gas limit (low density)

Polyatomic vs. Monatomic Gases Kinetic theory of gases assumes that gas molecules are point particles with no internal structure The only internal energy in this picture is the translational kinetic energy of the molecules y x z

Polyatomic vs. Monatomic Gases Directions in which a molecule can move are called degrees of freedom Polyatomic molecules have additional degrees of freedom y x z

Degrees of freedom in a diatomic molecule Translational x, y, z y z x

Degrees of freedom in a diatomic molecule Translational x, y, z Rotational rotate around x or z axis y x z

Degrees of freedom in a diatomic molecule Translational x, y, z Rotational rotate around x or z axis Vibration - stretching

Degrees of freedom in polyatomic molecules Translational

Degrees of freedom in polyatomic molecules Translational Rotational y x z

Degrees of freedom in polyatomic molecules Translational Rotational Vibrational Symmetric Stretching

Counting Degrees of Freedom Total 3N Translational All molecules have 3 translational degrees of freedom Rotational Linear molecules (including diatomics) have 2 rotational degrees of freedom Nonlinear molecules have 3 rotational degrees of freedom All remaining degrees of freedom are vibrational. Where N is the number of atoms: Linear molecule: (3N 5) Nonlinear molecule: (3N 6)

Equipartition of Energy In our treatment of the ideal gas we found that the average kinetic energy in each translational degree of freedom is E kin The principle of equipartition of energy suggests that all degrees of freedom will average this same kinetic energy = 1 2 k T B

Potential Energy of Vibrational Modes We can approximate chemical bonds to behave like springs: 1 Epotential = 2 k( RAB Re ) The average potential energy is equal to the average kinetic energy E potential = 1 2 k T B 2

Equipartition of Energy The average molar internal energy per Translational degree of freedom 1 RT 2 Rotational degree of freedom 1 RT 2 Vibrational degree of freedom RT

Equipartition of Energy The contribution to the molar heat capacity, c v Translational degree of freedom 1 R 2 Rotational degree of freedom 1 R 2 Vibrational degree of freedom R

Estimation of Molar Heat Capacity of Gases Gas Calculated c p Measure c p @ 298 K H 2 37.41 28.81 N 2 37.41 29.12 O 2 37.41 29.36 F 2 37.41 31.30 Cl 2 37.41 33.91 Br 2 37.41 36.02 CO 37.41 29.12

Heat Capacities of Solids The law of Dulong and Petit states that at high temperature (room temperature included) the heat capacity of solids is 3R No translational modes for atoms, 3 vibrational modes

Thermochemistry Some chemical reactions give off energy, others absorb energy We can think of chemical reactions as thermodynamic processes, where the reactants are thermodynamic states Thus can define changes in state functions for chemical reactions

Reaction Enthalpy For a given reaction we can define a change in enthalpy called the reaction enthalpy which corresponds to the heat absorbed by the system when the reaction is performed at constant pressure Like with other thermodynamic processes, the reaction enthalpy can be measured by calorimetry

Reaction Enthalpy CO (g) + ½ O 2 (g) CO 2 (g) ΔH = -283.0 kj The reaction above gives off 283.0 kj of energy per mole of CO (and ½ mole of O 2 ) reacted

Reaction Enthalpy 2 CO (g) + O 2 (g) 2 CO 2 (g) ΔH = -566.0 kj The reaction above gives off 566.0 kj of energy per 2 moles of CO (and mole of O 2 ) reacted (because enthalpy is an extensive variable)

Reaction Enthalpy CO 2 (g) CO (g) + ½ O 2 (g) ΔH = 283.0 kj The reaction above absorbs 283.0 kj of energy per mole of CO 2 reacted

Exothermic and Endothermic Reactions A exothermic reaction at constant T and P gives off heat to it s surroundings (ΔH < 0) A endothermic reaction at constant T and P absorbs heat from it s surroundings (ΔH > 0)

Hess s Law Hess s Law If two or more chemical equations can be added to give another chemical equation, the corresponding enthalpies of reaction must be added.

Reactions at Constant Volume U = H ( PV ) ( PV ) = n RT gas

Enthalpy of Phase Changes The enthalpy of physical changes, such as phase changes, can be analyzed in the same way Molar enthalpy of fusion: H 2 O (s) H 2 O (l) ΔH fus = 6.007 kj / mol Molar enthalpy of vaporization: H 2 O (l) H 2 O (g) ΔH vap = 40.66 kj / mol

Standard State Enthalpies There is no unambiguous way to define absolute enthalpies (or internal energies) of a substance Instead, we only talk about changes in these quantities We can define the enthalpy of a substance relative to a standard states of those substances

Standard State Enthalpies We arbitrarily set the enthalpies of the standard states of pure elements to zero The standard enthalpy (ΔHº) of a reaction is defined as the change in enthalpy of a reaction assuming all reactants and products are in their standard states

Standard State Enthalpies The standard enthalpy of formation (ΔH f º) of a substance is defined as the change in enthalpy to one mole of that substance in its standard state from the elements in their standard states H 2 (g) + ½ O 2 (g) H 2 O (l) ΔHº = -285.83 kj ΔH f º = -285.83 kj / mol

Computing Standard Enthalpies We can compute the standard enthalpies of any reaction if we know the standard enthalpies of formation of the reactants and products The standard enthalpies of formations of many substances are tabulated (e.g. Appendix D of your textbook) products reactant i f j f i j = H n H ( i) n H ( j) Stoiciometric coefficients

Bond Enthalpies Averaging bond enthalpies provides us a means to estimate heats of formation Atom Molar enthalpy of atomization (kj/mol) Bond Enthalpies (kj/mol) H- C- C= O- H 218.0 436 413 463 C 716.7 413 348 615 351 N 472.7 391 292 615 O 249.2 463 351 728 139 S 278.8 339 259 477 F 79.0 563 441 185

Summary of Thermochemistry Chemical reactions can be treated as thermodynamic processes The enthalpy of reaction quantifies the heat passed to the system during a chemical reaction at constant temperature and pressure Enthalpies of reaction can be calculated from standard enthalpies of formation, which describe the formation of compounds from standard states of elements Average bond enthalpies can be used to estimate heats of formation

Reversible Processes in Ideal Gases It s not always possible to calculate the changes in thermodynamic variables for a particular irreversible process Reversible processes offer an idealized model of real, irreversible ones

Reversible Processes in Ideal Gases Types of reversible processes: Isochoric constant volume Isobaric constant pressure Isothermal constant temperature Adiabatic no heat

Summary of Ideal Gas Processes Isochoric V = 0, P V = 0 Isobaric P = 0 Isothermal reversible T = 0, U = 0, w = q Adiabatic reversible q = 0, U = w

Reversible Isothermal Process w = nrt ln V 2 V 1 q = nrt ln V 2 V 1

Reversible Adiabatic Process

What we know about thermodynamics so far We can define a state variable, internal energy, the change in which is equal to the heat and work done on the system We can calculate the heat and work done on the system in various specific situations

What we don t know about thermodynamics so far How to predict what happens and what doesn t happen How to predict what direction change will occur

How do we proceed? The second law of thermodynamics tells us which processes occur spontaneously and which don t A new state function, the entropy, will be defined Processes in which the change in entropy of the universe is negative are not spontaneous A new state function, the Gibbs free energy, will make it easier for us to determine which processes occur spontaneously

Spontaneous processes Cold Windowsill

Spontaneous processes Hot Pie Cold Windowsill

Spontaneous processes Cooler Pie Cold Windowsill Higher temperature object spontaneously cool when in contact with lower temp. ones

Spontaneous processes

Spontaneous processes Gas expands to fill it s container

Spontaneous processes

Spontaneous processes Sugar spontaneously dissolves in water

Spontaneous processes

Spontaneous processes Oil spontaneously separates from water

Spontaneous processes C 3 H 8 + 5 O 2 3 CO 2 + 4 H 2 O

Spontaneous processes C 3 H 8 + 5 O 2 3 CO 2 + 4 H 2 O 3 CO 2 + 4 H 2 O C 3 H 8 + 5 O 2 Propane spontaneously combusts, but does not spontaneously form from CO 2 and H 2 O

Spontaneous processes

Spontaneous processes Egg spontaneously break, but do not spontaneously come back together

Notes about spontaneous processes To say a process is spontaneous is not the same as saying that it happens fast Diamond spontaneously becomes graphite at 1 atm To say a process is not spontaneous is not the same as saying that it is impossible to perform this process by adding energy into the system Reheating the pie Boiling the water off of the sugar Continuously stirring oil and water Reconstructing the egg

Entropy Entropy is a state function that helps us understand which processes are spontaneous and which aren t Entropy is often described as a measure of disorder, but this definition can be very misleading Others (including the text and myself) describe it as a measure of the range of possible molecular motions

Microscopic interpretation of entropy

Microscopic interpretation of entropy 1

Microscopic interpretation of entropy 1 What is the probability of the gas molecule being on the left side? ½

Microscopic interpretation of entropy 1 2 What is the probability of both gas molecules being on the left side?

Microscopic interpretation of entropy 2 1 What is the probability of both gas molecules being on the left side?

Microscopic interpretation of entropy 2 2 1 1 1 1 2 What is the probability of both gas molecules being on the left side? 2

Microscopic interpretation of entropy 2 2 1 1 1 1 2 What is the probability of both gas molecules being on the left side? ½ * ½ = ¼ 2

Microscopic interpretation of entropy 1 3 2 1 2 3 1 3 2 3 2 1 1 2 3 2 1 3 3 1 2 1 2 What is the probability of all gas molecules being on the left side? 3

Microscopic interpretation of entropy 1 3 2 1 2 3 1 3 2 3 2 1 1 2 3 2 1 3 3 1 2 1 2 What is the probability of all gas molecules being on the left side? ½ * ½ * ½ = ( ½ ) 3 = 1/8 3

Microscopic interpretation of entropy 1 3 2 1 2 3 1 3 2 3 2 1 1 2 3 2 1 3 3 1 2 1 2 3 What is the probability of having an approximately have of molecules on each side? 3/4

Microscopic interpretation of entropy What is the probability of all gas molecules being on the left side if we have a mole of gas?

Microscopic interpretation of entropy ( 1 ) What is the probability of all gas molecules being on the left side if we have a mole of gas? 6.022*10 23 = ( 10 ) 2 180,000,000,000,000,000,000,000 1

Clicker question! Consider four ideal gas molecules in a container with two sides. What is the probability of having all molecules on the left? What is the probability of having 2 gas particles on each side? 1 2 3 4

Clicker question! Consider four ideal gas molecules in a container with two sides. What 1 is 2 the probability of having all molecules on the left? What 3 is the 3 4 probability 4 of having 2 gas particles on each side? A) 1/2 B) 1/4 C) 3/8 D) 1/16 1 2 1 2 2 1 3 3 4 4 2 1 1 2 3 3 4 4 6 / 16 = 3/8

Microscopic interpretation of entropy There is nothing in the laws of mechanics that prevent the gas particles from all being on the same side at the same time This configuration is just exceedingly improbable if there is a large number of particles Spontaneity arises (in part) from this statistical motion of large numbers of particles Smaller systems exhibit large statistical fluctuations

Measuring the range of possible motions We will count the possible microscopic states, or microstates, accessible to the system For classical systems, a microstate is a particular set of values for the positions and momenta of each particle in the system

Counting microstates of a monatomic ideal gas at constant U

Entropy of phase transitions Entropy of evaporation Liquid Gas

Entropy of phase transitions Entropy of evaporation is positive Liquid Gas

Entropy of phase transitions Entropy of evaporation is positive Entropy of melting Solid Liquid

Entropy of phase transitions Entropy of evaporation is positive Entropy of melting is positive Solid Liquid

Clicker question! Do you think the change in entropy for this chemical reaction is positive, negative, or zero? S 8 (g) 8 S (g) A) Positive B) Negative C) Zero

Macroscopic description of entropy The heat engine Hot Bath Heat Engine Work Cold Bath Heat

Statements of the second law Kelvin There is no device that can transform heat withdrawn from a reservoir completely into work with no other effect. Clausius There is no device that can transfer heat from a colder to a warmer reservoir without net expenditure of work.

Carnot Cycle Carnot Heat Engine

Carnot Cycle Cylander Carnot Heat Engine

Carnot Cycle Cylander Piston Carnot Heat Engine

Carnot Cycle Carnot Heat Engine Cylander Piston 1 mol ideal gas

Carnot Cycle Carnot Heat Engine Cylander Piston 1 mol ideal gas Constant temperature baths T h T c

Carnot Cycle Carnot Heat Engine T h T c

Carnot Cycle Carnot Heat Engine Pressure Volume T h T c

Carnot Cycle 1 (P 1, V 1 ) Carnot Heat Engine Pressure Volume T h T c

Carnot Cycle 1 (P 1, V 1 ) Carnot Heat Engine 2 (P 2, V 2 ) Pressure Volume T h T c

Carnot Cycle 1 (P 1, V 1 ) Carnot Heat Engine 2 (P 2, V 2 ) Pressure 3 (P 3, V 3 ) Volume T h T c

Carnot Cycle 1 (P 1, V 1 ) Carnot Heat Engine Pressure 4 (P 4, V 4 ) Volume 2 (P 2, V 2 ) 3 (P 3, V 3 ) T h T c

Carnot Cycle 1 (P 1, V 1 ) Carnot Heat Engine 2 (P 2, V 2 ) Pressure 4 (P 4, V 4 ) 3 (P 3, V 3 ) Volume T h T c

Efficiency of a Carnot Engine

Can an engine be more efficient than the reversible Carnot engine? Let s assume the existence of an engine more efficient than the reversible Carnot engine called the super engine

Carnot Cycle in Reverse Each step in the Carnot cycle is reversible, therefore the whole cycle can be operated in reverse An engine operating in reverse is called a heat pump Hot Bath Heat Engine Heat Cold Bath Work

Can an engine be more efficient than the reversible Carnot engine? Hot Bath -q rev,h Carnot Engine w rev q rev,c Cold Bath

Can an engine be more efficient than the reversible Carnot engine? Hot Bath -q rev,h q super,h Carnot Engine w rev -w super Super Engine q rev,c -q super,c Cold Bath

Can an engine be more efficient than the reversible Carnot engine? Hot Bath -q rev,h q super,h Carnot Engine w rev = -w super Super Engine q rev,c Cold Bath -q super,c

Can an engine be more efficient than the reversible Carnot engine? Clausius: It is impossible to construct a device that will transfer heat from a cold reservoir to a hot reservoir in a continuous cycle with no net expenditure of work. Thus, if we believe the second law, no engine can be more efficient than the reversible one, and all reversible engines operating between the same two temperatures must have the same efficiency!

More discussion of efficiency of thermodynamics cycles

More discussion of efficiency of thermodynamics cycles Pressure Volume

More discussion of efficiency of thermodynamics cycles Isothermal Pressure Adiabatic Volume

More discussion of efficiency of thermodynamics cycles Isothermal i q i, rev T = i 0 Pressure Adiabatic Sum over isothermal paths (q = 0 for adiabatic paths) Volume

More discussion of efficiency of thermodynamics cycles Isothermal 1 T dq rev = 0 Pressure Adiabatic Integral over closed cycle Volume

More discussion of efficiency of thermodynamics cycles B A 1 dq T rev Pressure B A Volume

More discussion of efficiency of thermodynamics cycles B A 1 A 1 dqrev + dq B rev = T T 0 Pressure B A Volume

More discussion of efficiency of thermodynamics cycles B A 1 A 1 dqrev + dq B rev = T T 0 Pressure B A Volume Integral is always the same regardless of path

Macroscopic definition of entropy S = final initial 1 dq T rev Change in entropy

Summary of entropy Microscopically, entropy increases with the number of microstates accessible to the system S = k B ln Ω Macroscopically, entropy relates to the heat given off by a reversible process S = final initial 1 dq T rev

Entropy Changes in Reversible Processes

Clicker questions! Consider two samples of ideal gas in an identical initial state. One is heated from T 1 to T 2 at constant pressure, the other at constant volume. Which increases in entropy by a greater amount? A) Constant P sample B) Constant V sample

S of Surroundings At constant pressure and temperature q surr = H sys S = surr H T surr sys

What does entropy tell us? = S tot S = S + S tot sys surr If then a process is reversible > S tot 0 0 If then a process is irreversible and spontaneous < S tot 0 If then a process is not spontaneous

Examples

Summary of Entropy and the Second Law In a reversible process the total entropy of a system plus its surroundings is unchanged. In an irreversible process the total entropy of a system plus its surroundings must increase. A process for which S < 0 is not spontaneous.

Defining standard-state entropies So far we have only discussed changes in entropy for thermodynamics processes Like enthalpy, it would be convenient to define standard-state entropies that can be tabulated The third law of thermodynamics helps us define such a reference

The Nernst Heat Theorem An empirical observation: In any thermodynamic process involving only pure phases in their equilibrium states, the entropy change approaches zero as the temperature approaches 0 K.

Third Law of Thermodynamics The entropy of any pure substance (element or compound) in its equilibrium state approaches zero at the absolute zero of temperature

Absolute entropies The entropy at a given temperature can be defined by reference to T = 0 K c T T P ST = n dt 0 Absolute entropy

Absolute entropies The entropy at a given temperature can be defined by reference to T = 0 K T cp ST = n dt + S(phase changes) 0 T Absolute entropy

Standard-state entropies The absolute entropy at T = 298.15 K is the standard-state entropy 298.15 c P S = n dt + S(phase changes) 0 T Standard-state entropy

Standard entropies of reaction

A state variable to determine spontaneity The change in the entropy of the universe tells us whether a process is spontaneous: If S tot = 0 then a process is reversible If S tot > 0 then a process is irreversible < 0 S tot If then a process is not spontaneous It would be convenient to have a state variable describing the system only that would tell us whether a process is spontaneous

The Gibbs Free Energy

Gibbs Free Energy and Phase Transitions

Gibbs Free Energy of Formation C (s, graphite) + O 2 (g) CO 2 (g) Standard States G = H T S = 393.51 J mol f f 1

Gibbs Free Energies and Chemical Reactions

Practice Thermo Problem 3 O 2 (g) 2 O 3 (g) What is the standard enthalpy of this reaction? What is the standard entropy of this reaction? What is the standard Gibbs free energy of this reaction? Assuming ideal gas behavior, and ignoring quantum effects, what are H, S, and G of this reaction at 50º C and 1 atm? H f º (25 Cº) kj mol -1 Sº (25 Cº) J mol -1 K -1 O 2 0 205.03 O 3 142.7 238.82 c p (O 2 ) = 9/2 R c p (O 3 ) = 7 R

Summary of Gibbs Free Energy The Gibbs free energy is used to predict the spontaneity of processes at constant T and P G = H TS The sign of the Gibbs free energy of the system is opposite the sign of the total entropy of the universe A negative change in Gibbs free energy indicates a spontaneous process Zero change in Gibbs free energy indicates a reversible process