ThermodynamicsThermodynamics

The universe is in a state of constant change, the only invariant is Energy

Consider ….Consider ….

2

Gravity causes molecules of water move turbine blades

turbines move coils of wire in magnetic fields

moving magnetic fields move electrons

moving electrons drive chemical reactions in a battery

chemical reactions power your phone creating light and sound

Consider ….Consider …. In this example gravity is responsible for a

working smartphone Gravity does work on the blades The turning blades do work on electrons Electrons do work in chemical reactions Chemical reactions do work on a speaker and power

LEDs in the screen, power radios etc

The ability of something to do work on something else is transferred from gravity to water to electrons to chemical reactions to moving magnetics and moving air and light from the screen

In this example gravity is responsible for a working smartphone Gravity does work on the blades The turning blades do work on electrons Electrons do work in chemical reactions Chemical reactions do work on a speaker and power

LEDs in the screen, power radios etc

The ability of something to do work on something else is transferred from gravity to water to electrons to chemical reactions to moving magnetics and moving air and light from the screen

3

Consider ….Consider ….

4

Gravity causes hydrogen atoms fuse to make Helium and a little bit of mass is converted into light and heat etc

Photons are absorbed by chlorophyll and used to power photosynthesis

We extract the oil

make biofuel

ignite the biofuel and excess energy released gives the molecules to power to move pistons

Consider ….Consider …. In this example Gravity causes fusion reactions in

the sun are responsible for a working car Mass is converted to light light moves electrons Electrons do work in chemical reactions to create sugars

oils etc Oils react with oxygen to create fast moving CO2 and H2O Molecules push pistons and drive the car

The ability of something to do work on something else is transferred from the sun to chlorophyll to electrons to chemical reactions to moving molecules and moving pistons and moving wheels

In this example Gravity causes fusion reactions in the sun are responsible for a working car Mass is converted to light light moves electrons Electrons do work in chemical reactions to create sugars

oils etc Oils react with oxygen to create fast moving CO2 and H2O Molecules push pistons and drive the car

The ability of something to do work on something else is transferred from the sun to chlorophyll to electrons to chemical reactions to moving molecules and moving pistons and moving wheels

5

Energy: the capacity to do work

Energy: the capacity to do work

In each step in the previous examples a capacity to do work is transferred from one thing to another, this is called energy

Gravitational energy is transferred into kinetic energy, into electrical energy, chemical energy, sound and light energy etc

All dynamic processes in the universe are due to the flow of energy

Thermodynamics is the study of heat flow and the laws that govern it

Since we want to understand chemical transformation we need to understand energy transformation

In each step in the previous examples a capacity to do work is transferred from one thing to another, this is called energy

Gravitational energy is transferred into kinetic energy, into electrical energy, chemical energy, sound and light energy etc

All dynamic processes in the universe are due to the flow of energy

Thermodynamics is the study of heat flow and the laws that govern it

Since we want to understand chemical transformation we need to understand energy transformation 6

EnergyEnergy

Energy is a universal invariant It can change from one form to another but cannot be

created or destroyed

It is measured in Joules (J)

There is potential energy (energy that something has because of where and what it is) and kinetic energy (the energy is has because of how fast it is moving)

The lower the potential energy the more stable something is. Potential energy can be negative

When some process happens, generally it is to lower the potential energy

The study of energy helps us to predict whether a process is spontaneous or not

Energy is a universal invariant It can change from one form to another but cannot be

created or destroyed

It is measured in Joules (J)

There is potential energy (energy that something has because of where and what it is) and kinetic energy (the energy is has because of how fast it is moving)

The lower the potential energy the more stable something is. Potential energy can be negative

When some process happens, generally it is to lower the potential energy

The study of energy helps us to predict whether a process is spontaneous or not

7

What is Thermodynamics?What is Thermodynamics?

Thermodynamics is a branch of physics concerned with energy flow. Historically it had an emphasis on heat, temperature and their relation to energy and work.

Study of energy changes accompanying chemical and physical changes to a system

Defines systems using a few macroscopic (measurable) variables, such as internal energy, entropy, temperature and pressure

Statistical treatment of microstates (atom positions and velocities) to obtain macrostates

In chemistry, thermodynamics predicts if reactions occur, how the equilibrium constant changes with temperature

Thermodynamics is a branch of physics concerned with energy flow. Historically it had an emphasis on heat, temperature and their relation to energy and work.

Study of energy changes accompanying chemical and physical changes to a system

Defines systems using a few macroscopic (measurable) variables, such as internal energy, entropy, temperature and pressure

Statistical treatment of microstates (atom positions and velocities) to obtain macrostates

In chemistry, thermodynamics predicts if reactions occur, how the equilibrium constant changes with temperature

8

9

First Law of ThermodynamicsFirst Law of Thermodynamics

you can’t get something for nothing

First Law of Thermodynamics: Energy cannot be Created or Destroyed the total energy of the universe cannot change though you can transfer it from one place to another

ΔEuniv = 0 = ΔEsys + ΔEsurr (1)

you can’t get something for nothing

First Law of Thermodynamics: Energy cannot be Created or Destroyed the total energy of the universe cannot change though you can transfer it from one place to another

ΔEuniv = 0 = ΔEsys + ΔEsurr (1)

10

First Law of ThermodynamicsConservation of Energy

For an exothermic reaction, “lost” heat from the system goes into the surroundings

two ways energy “lost” from a system, converted to heat, q used to do work, w

Energy conservation requires that the internal energy E change in the system equal the heat released (q) + work done (w)

ΔE = q + w (2)ΔE = ΔH + PΔV (3)

E is the total energy of everything in the system (the kinetic and potential energy of the atoms)

ΔE (ΔU)is a state function internal energy change independent of how this change

occurs

The first law and time reversal

The first law and time reversal

The first law tells us that only processes where there is no net change in the total energy are allowed (energy is conserved)

The first law tells us that only processes where there is no net change in the total energy are allowed (energy is conserved)

11

The first law and spontaneityThe first law and spontaneity

In all observed phenomena the total energy is always the same

The energy at t, E(t) is equal to the energy at time time t+dt,

E(t) = E(t+dt) So if that is the case why do we always see some

processes only going one way?

In all observed phenomena the total energy is always the same

The energy at t, E(t) is equal to the energy at time time t+dt,

E(t) = E(t+dt) So if that is the case why do we always see some

processes only going one way?

12

✓

✗

The first law and spontaneityThe first law and spontaneity

Clearly the first law isn’t the end of the story regarding energy and what happens in processes

Clearly the first law isn’t the end of the story regarding energy and what happens in processes

13

✓

✗

16

Factors Affecting Whether a Reaction Is Spontaneous

It turns out that there are two factors that determine the thermodynamic favorability are the enthalpy H and the entropy S.

The enthalpy is a comparison of the bond energy of the reactants to the products. bond energy = amount needed to break a bond. statistical model of collective behavior ΔH

The entropy factors relates to the randomness/orderliness of a system ΔS

The enthalpy factor is generally more important than the entropy factor

Let’s look at these

It turns out that there are two factors that determine the thermodynamic favorability are the enthalpy H and the entropy S.

The enthalpy is a comparison of the bond energy of the reactants to the products. bond energy = amount needed to break a bond. statistical model of collective behavior ΔH

The entropy factors relates to the randomness/orderliness of a system ΔS

The enthalpy factor is generally more important than the entropy factor

Let’s look at these

Enthalpy related to the internal energy E, the energy change measured at

constant P is ΔH = ΔΔgenerally kJ/mol)

ΔHrxn is related to the breaking and forming of chemical bonds. Stronger bonds = more stable molecules

if products more stable than reactants, energy released exothermic ΔH = negative

if reactants more stable than products, energy absorbed endothermic ΔH = positive

The enthalpy is favorable for exothermic reactions and unfavorable for endothermic reactions.

Hess’ Law

related to the internal energy E, the energy change measured at constant P is ΔH = ΔΔgenerally kJ/mol)

ΔHrxn is related to the breaking and forming of chemical bonds. Stronger bonds = more stable molecules

if products more stable than reactants, energy released exothermic ΔH = negative

if reactants more stable than products, energy absorbed endothermic ΔH = positive

The enthalpy is favorable for exothermic reactions and unfavorable for endothermic reactions.

Hess’ Law

Spontaneity: Enthalpy Driven ProcessesSpontaneity: Enthalpy Driven Processes

• In many cases, the direction of spontaneity can be determined by comparing the potential energy of the system at the start and the end

• Cellulose and O2 have a bigger potential energy than the equivalent amount of carbon dioxide and water

• The transformation lowers the overall potential energy, C-O and H-O bonds are more stable than C-C and C-H bonds

• exothermic reactions are spontaneous

• The extra energy leaves as heat

• All transformations have accompanying energy changes.

• Can we tell which transformations will occur spontaneously by studying the energy change?

Spontaneity: Entropy Driven ProcessesSpontaneity: Entropy Driven Processes

• But some processes are spontaneous but not exothermic!

• These are entropy driven processes

21

Entropy S

Entropy, S, is a thermodynamic function that increases as the number of equivalent ways of arranging the atoms/molecules (positions and velocities) in a system to give the appropriate V, U and T increases S generally J/(K.mol)

S = k ln W = Q/T (6)

k = Boltzmann Constant = 1.38 x 10-23 J/K W is the number of energetically equivalent ways

accessible, unitless (measure of our lack of knowledge about the system)

Entropy is the energy dispersal per unit temperature

Random systems require less energy than ordered systems

Measure of the unavailability of a system to do work

22

WW

Energetically Equivalent States for the Expansion of a Gas

Energetically Equivalent States for the Expansion of a Gas

23

Macrostates → MicrostatesMacrostates → Microstates

This macrostate can be achieved throughseveral different arrangements of the particles

This macrostate can be achieved throughseveral different arrangements of the particles

These microstates all have the same

macrostate

So there are 6 different particle arrangements that result in the same

macrostate

These microstates all have the same

macrostate

So there are 6 different particle arrangements that result in the same

macrostate

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Macrostates and ProbabilityMacrostates and Probability

There is only one possible arrangement that gives State A and one that gives

State B

There is only one possible arrangement that gives State A and one that gives

State B

There are 6 possible arrangements that give State C

There are 6 possible arrangements that give State C

Therefore State C has higher entropy than either State A or State B

Therefore State C has higher entropy than either State A or State B

The macrostate with the highest entropy also has the greatest dispersal of energyThe macrostate with the highest entropy also has the greatest dispersal of energy

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Changes in Entropy, ΔSChanges in Entropy, ΔS

entropy change is favorable when the result is a more random system. ΔS is positive

Some changes that increase the entropy are: reactions whose products are in a more disordered state.

(solid > liquid > gas) reactions which have larger numbers of product molecules

than reactant molecules. increase in temperature solids dissociating into ions upon dissolving

entropy change is favorable when the result is a more random system. ΔS is positive

Some changes that increase the entropy are: reactions whose products are in a more disordered state.

(solid > liquid > gas) reactions which have larger numbers of product molecules

than reactant molecules. increase in temperature solids dissociating into ions upon dissolving

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Increases in EntropyIncreases in Entropy

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The 2nd Law of Thermodynamics: Spontaneity

"Energy spontaneously disperses from being localized to becoming spread out if it is not hindered from doing so.”

The total entropy change of the universe must be positive for a process to be spontaneous for reversible process ΔSuniv = 0,

for irreversible (spontaneous) process ΔSuniv > 0

ΔSuniv = ΔSsys + ΔSsurr (7)

if the entropy of the system decreases, then the entropy of the surroundings must increase by a larger amount when ΔSsys is negative, ΔSsurr is positive

the increase in ΔSsurr often comes from the heat released in an exothermic reaction

"Energy spontaneously disperses from being localized to becoming spread out if it is not hindered from doing so.”

The total entropy change of the universe must be positive for a process to be spontaneous for reversible process ΔSuniv = 0,

for irreversible (spontaneous) process ΔSuniv > 0

ΔSuniv = ΔSsys + ΔSsurr (7)

if the entropy of the system decreases, then the entropy of the surroundings must increase by a larger amount when ΔSsys is negative, ΔSsurr is positive

the increase in ΔSsurr often comes from the heat released in an exothermic reaction

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Temperature Dependence of ΔSsurrTemperature Dependence of ΔSsurr

when a system process is exothermic, it adds heat to the surroundings, increasing the entropy of the surroundings

when a system process is endothermic, it takes heat from the surroundings, decreasing the entropy of the surroundings

the amount the entropy of the surroundings changes depends on the temperature it is at originally

the higher the original temperature, the less effect addition or removal of heat has

when a system process is exothermic, it adds heat to the surroundings, increasing the entropy of the surroundings

when a system process is endothermic, it takes heat from the surroundings, decreasing the entropy of the surroundings

the amount the entropy of the surroundings changes depends on the temperature it is at originally

the higher the original temperature, the less effect addition or removal of heat has

29

Gibbs Free Energy, ΔG

For a spontaneous process ΔSuniv > 0

maximum amount of energy from the system available to do work on the surroundings at constant temperature T

(9)

when ΔG < 0, there is a decrease in free energy of the system that is released into the surroundings; therefore a process will be spontaneous when ΔG is negative

For a spontaneous process ΔSuniv > 0

maximum amount of energy from the system available to do work on the surroundings at constant temperature T

(9)

when ΔG < 0, there is a decrease in free energy of the system that is released into the surroundings; therefore a process will be spontaneous when ΔG is negative

30

Thermodynamics and SpontaneityFree Energy

spontaneity is determined by comparing the free energy G of the system before the reaction with the free energy of the system after reaction, it includes both the enthalpy and entropy change of a process

ΔG = ΔH – T∙ΔS (9)

if the system after reaction has less free energy than before the reaction, the reaction is thermodynamically favorable

spontaneity ≠ fast or slow

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Gibbs Free Energy, ΔG

process will be spontaneous when ΔG is negative

ΔG will be negative when ΔH is negative and ΔS is positive

exothermic and more random ΔH is negative and large and ΔS is negative but small ΔH is positive but small and ΔS is positive and large

or high temperature

ΔG will be positive when ΔH is + and ΔS is − never spontaneous at any temperature

when ΔG = 0 the reaction is at equilibrium

32

ΔG, ΔH, and ΔSΔG, ΔH, and ΔS

Chemical Potential EnergyChemical Potential Energy

The chemical potential – is a form of free energy used for chemical reactions, in spontaneous reactions the chemical potential decreases

34

Thermodynamics vs. KineticsThermodynamics vs. Kinetics

• Kinetics describes how fast things change• Thermodynamics is concerned if they will change and if so

what changes we will see in internal energy, temperature, pressure etc

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Example: Diamond → GraphiteExample: Diamond → Graphite

Graphite is more stable than diamond, so the conversion of diamond into graphite is spontaneous – but don’t worry, it’s so slow that your ring won’t turn into pencil lead in your lifetime (or through many of your generations).

Graphite is more stable than diamond, so the conversion of diamond into graphite is spontaneous – but don’t worry, it’s so slow that your ring won’t turn into pencil lead in your lifetime (or through many of your generations).

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Reversibility of ProcessReversibility of Process

any spontaneous process is irreversible it will proceed in only one direction

a reversible process will proceed back and forth between the two end conditions equilibrium results in no change in free energy

if a process is spontaneous in one direction, it must be nonspontaneous in the opposite direction

any spontaneous process is irreversible it will proceed in only one direction

a reversible process will proceed back and forth between the two end conditions equilibrium results in no change in free energy

if a process is spontaneous in one direction, it must be nonspontaneous in the opposite direction

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Entropy Change and State ChangeEntropy Change and State Change

Phase changes, melting boiling etc these are endothermic changes driven by entropy concerns not enthalpy concerns

38

Entropy Change in State ChangeEntropy Change in State Change

when materials change state, the number of macrostates it can have changes as well for entropy: solid < liquid < gas because the degrees of freedom of motion

increases solid → liquid → gas

when materials change state, the number of macrostates it can have changes as well for entropy: solid < liquid < gas because the degrees of freedom of motion

increases solid → liquid → gas

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Heat Flow, Entropy, and the 2nd LawHeat Flow, Entropy, and the 2nd Law

Heat must flow from water to ice in order for the entropy of the universe to increase

But why that way round? The 1st law is not violated if more ice was formed?

Flowing hot to cold we increase energy randomization.

Heat flowing into the hot concentrated energy so S decreases

Heat must flow from water to ice in order for the entropy of the universe to increase

But why that way round? The 1st law is not violated if more ice was formed?

Flowing hot to cold we increase energy randomization.

Heat flowing into the hot concentrated energy so S decreases

The reaction C3H8(g) + 5 O2(g) 3 CO2(g) + 4 H2O(g) has ΔHrxn = -2044 kJ at 25°C.

Calculate the entropy change of the surroundings.

The reaction C3H8(g) + 5 O2(g) 3 CO2(g) + 4 H2O(g) has ΔHrxn = -2044 kJ at 25°C.

Calculate the entropy change of the surroundings.

combustion is largely exothermic, so the entropy of the surrounding should increase significantly

ΔHsystem = -2044 kJ, T = 298 K

ΔSsurroundings, J/K

Check:

Solution:

Concept Plan:

Relationships:

Given:

Find:

ΔST, ΔH

41

Free Energy Change and SpontaneityFree Energy Change and Spontaneity

The reaction CCl4(g) C(s, graphite) + 2 Cl2(g) has ΔH = +95.7 kJ and ΔS = +142.2 J/K at 25°C. Calculate ΔG and determine if it is spontaneous.

The reaction CCl4(g) C(s, graphite) + 2 Cl2(g) has ΔH = +95.7 kJ and ΔS = +142.2 J/K at 25°C. Calculate ΔG and determine if it is spontaneous.

Since ΔG is +, the reaction is not spontaneous at this temperature. To make it spontaneous, we need to

increase the temperature.

ΔH = +95.7 kJ, ΔS = 142.2 J/K, T = 298 K

ΔG, kJ

Answer:

Solution:

Concept Plan:

Relationships:

Given:

Find:

ΔGT, ΔH, ΔS

The reaction CCl4(g) C(s, graphite) + 2 Cl2(g) has ΔH = +95.7 kJ and ΔS = +142.2 J/K.

Calculate the minimum temperature it will be spontaneous.

The reaction CCl4(g) C(s, graphite) + 2 Cl2(g) has ΔH = +95.7 kJ and ΔS = +142.2 J/K.

Calculate the minimum temperature it will be spontaneous.

The temperature must be higher than 673K for the reaction to be spontaneous

ΔH = +95.7 kJ, ΔS = 142.2 J/K, ΔG < 0

Answer:

Solution:

Concept Plan:

Relationships:

Given:

Find:

TΔG, ΔH, ΔS

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The 3rd Law of ThermodynamicsAbsolute Entropy

The 3rd Law of ThermodynamicsAbsolute Entropy

the absolute entropy of a substance is the amount of energy it has due to dispersion of energy through its particles

the 3rd Law states that for a perfect crystal at absolute zero, the absolute entropy = 0 J/mol∙K

therefore, every substance that is not a perfect crystal at absolute zero has some energy from entropy

therefore, the absolute entropy of substances is always +

the absolute entropy of a substance is the amount of energy it has due to dispersion of energy through its particles

the 3rd Law states that for a perfect crystal at absolute zero, the absolute entropy = 0 J/mol∙K

therefore, every substance that is not a perfect crystal at absolute zero has some energy from entropy

therefore, the absolute entropy of substances is always +

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Standard EntropiesStandard Entropies

S°

Extensive (depends on the system size)

entropies for 1 mole at 298 K for a particular state, a particular allotrope, particular molecular complexity, a particular molar mass, and a particular degree of dissolution

S°

Extensive (depends on the system size)

entropies for 1 mole at 298 K for a particular state, a particular allotrope, particular molecular complexity, a particular molar mass, and a particular degree of dissolution

47

Relative Standard EntropiesStates

Relative Standard EntropiesStates

the gas state has a larger entropy than the liquid state at a particular temperature

the liquid state has a larger entropy than the solid state at a particular temperature

the gas state has a larger entropy than the liquid state at a particular temperature

the liquid state has a larger entropy than the solid state at a particular temperature

SubstanceS°,

(J/mol∙K)

H2O (l) 70.0

H2O (g) 188.8

48

Relative Standard EntropiesMolar Mass

Relative Standard EntropiesMolar Mass

the larger the molar mass, the larger the entropy

available energy states more closely spaced, allowing more dispersal of energy through the states

the larger the molar mass, the larger the entropy

available energy states more closely spaced, allowing more dispersal of energy through the states

49

Relative Standard EntropiesAllotropes

Relative Standard EntropiesAllotropes

the less constrained the structure of an allotrope is, the larger its entropy

the less constrained the structure of an allotrope is, the larger its entropy

50

Relative Standard EntropiesMolecular Complexity

Relative Standard EntropiesMolecular Complexity

larger, more complex molecules generally have larger entropy

more available energy states, allowing more dispersal of energy through the states

larger, more complex molecules generally have larger entropy

more available energy states, allowing more dispersal of energy through the states

SubstanceMolarMass

S°, (J/mol∙K)

Ar (g) 39.948 154.8

NO (g) 30.006 210.8

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Relative Standard EntropiesDissolution

Relative Standard EntropiesDissolution

dissolved solids generally have larger entropy

distributing particles throughout the mixture

dissolved solids generally have larger entropy

distributing particles throughout the mixture

SubstanceS°,

(J/mol∙K)

KClO3(s) 143.1

KClO3(aq) 265.7

Calculate ΔS for the reaction4 NH3(g) + 5 O2(g) 4 NO(g) + 6 H2O(l)

Calculate ΔS for the reaction4 NH3(g) + 5 O2(g) 4 NO(g) + 6 H2O(l)

ΔS is +, as you would expect for a reaction with more gas product molecules than reactant molecules

standard entropies look up in appendix to textbook or googleΔS, J/K

Check:

Solution:

Concept Plan:

Relationships:

Given:Find:

ΔSSoNH3, So

O2, SoNO, So

H2O,

Substance S, J/mol/K

NH3(g) 192.8

O2(g) 205.2

NO(g) 210.8

H2O(g) 188.8

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Calculating ΔGoCalculating ΔGo

at 25oC:ΔGo

reaction = ΣnGof(products) - ΣnGo

f(reactants)

at temperatures other than 25oC:

assuming the change in ΔHoreaction and ΔSo

reaction is negligible

ΔGoreaction = ΔHo

reaction – TΔSoreaction

at 25oC:ΔGo

reaction = ΣnGof(products) - ΣnGo

f(reactants)

at temperatures other than 25oC:

assuming the change in ΔHoreaction and ΔSo

reaction is negligible

ΔGoreaction = ΔHo

reaction – TΔSoreaction

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Calculate ΔGo at 25oC for the reactionCH4(g) + 8 O2(g) CO2(g) + 2 H2O(g) + 4

O3(g)

Calculate ΔGo at 25oC for the reactionCH4(g) + 8 O2(g) CO2(g) + 2 H2O(g) + 4

O3(g)

standard free energies of formation from Appendix of textbook or google ΔGo, kJ

Solution:

Concept Plan:

Relationships:

Given:Find:

ΔGoΔGof of prod & react

Substance ΔGof, kJ/mol

CH4(g) -50.5

O2(g) 0.0

CO2(g) -394.4

H2O(g) -228.6

O3(g) 163.2

The reaction SO2(g) + ½ O2(g) SO3(g) has ΔHo = -98.9 kJ and ΔSo = -94.0 J/K at 25°C.

Calculate ΔGo at 125oC and determine if it is spontaneous.

The reaction SO2(g) + ½ O2(g) SO3(g) has ΔHo = -98.9 kJ and ΔSo = -94.0 J/K at 25°C.

Calculate ΔGo at 125oC and determine if it is spontaneous.

Since ΔG is -, the reaction is spontaneous at this temperature, though less so than at 25oC

ΔHo = -98.9 kJ, ΔSo = -94.0 J/K, T = 398 K

ΔGo, kJ

Answer:

Solution:

Concept Plan:

Relationships:

Given:

Find:

ΔGoT, ΔHo, ΔSo

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ΔG RelationshipsΔG Relationships

if a reaction can be expressed as a series of reactions, the sum of the ΔG values of the individual reaction is the ΔG of the total reaction ΔG is a state function

if a reaction is reversed, the sign of its ΔG value reverses

if the amounts of materials is multiplied by a factor, the value of the ΔG is multiplied by the same factor the value of ΔG of a reaction is extensive

if a reaction can be expressed as a series of reactions, the sum of the ΔG values of the individual reaction is the ΔG of the total reaction ΔG is a state function

if a reaction is reversed, the sign of its ΔG value reverses

if the amounts of materials is multiplied by a factor, the value of the ΔG is multiplied by the same factor the value of ΔG of a reaction is extensive

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Free Energy and Reversible ReactionsFree Energy and Reversible Reactions

the change in free energy is a theoretical limit as to the amount of work that can be done

if the reaction achieves its theoretical limit, it is a reversible reaction

the change in free energy is a theoretical limit as to the amount of work that can be done

if the reaction achieves its theoretical limit, it is a reversible reaction

59

Real ReactionsReal Reactions

in a real reaction, some of the free energy is “lost” as heat if not most

therefore, real reactions are irreversible

in a real reaction, some of the free energy is “lost” as heat if not most

therefore, real reactions are irreversible

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ΔG under Nonstandard ConditionsΔG under Nonstandard Conditions

ΔG = ΔGo only when the reactants and products are in their standard states

• there normal state at that temperature

• partial pressure of gas = 1 atm

• concentration = 1 M

under nonstandard conditions, ΔG = ΔGo + RTlnQ

• Q is the reaction quotient

at equilibrium ΔG = 0

• ΔGo = ─RTlnK

ΔG = ΔGo only when the reactants and products are in their standard states

• there normal state at that temperature

• partial pressure of gas = 1 atm

• concentration = 1 M

under nonstandard conditions, ΔG = ΔGo + RTlnQ

• Q is the reaction quotient

at equilibrium ΔG = 0

• ΔGo = ─RTlnK

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62

Example - ΔG

Calculate ΔG at 427°C for the reaction below if the PN2 = 33.0 atm, PH2= 99.0 atm, and PNH3= 2.0 atm

N2(g) + 3 H2(g) 2 NH3(g)

Q = PNH3

2

PN21 x PH2

3

(2.0 atm)2

(33.0 atm)1 (99.0)3= = 1.2 x 10-7

ΔG = ΔG° + RTlnQ

ΔG = +46400 J + (8.314 J/K)(700 K)(ln 1.2 x 10-7)

ΔG = -46300 J = -46 kJ

ΔH° = [ 2(-46.19)] - [0 +3( 0)] = -92.38 kJ = -92380 J

ΔS° = [2 (192.5)] - [(191.50) + 3(130.58)] = -198.2 J/K

ΔG° = -92380 J - (700 K)(-198.2 J/K)

ΔG° = +46400 J

63

64

Example - K

Estimate the equilibrium constant and position of equilibrium for the following reaction at 427°C

N2(g) + 3 H2(g) 2 NH3(g)

ΔG° = -RT lnK

+46400 J = -(8.314 J/K)(700 K) lnK

lnK = -7.97

K = e-7.97 = 3.45 x 10-4

since K is << 1, the position of equilibrium favors reactantssince K is << 1, the position of equilibrium favors reactants

ΔH° = [ 2(-46.19)] - [0 +3( 0)] = -92.38 kJ = -92380 J

ΔS° = [2 (192.5)] - [(191.50) + 3(130.58)] = -198.2 J/K

ΔG° = -92380 J - (700 K)(-198.2 J/K)

ΔG° = +46400 J

65

Temperature Dependence of KTemperature Dependence of K

for an exothermic reaction, increasing the temperature decreases the value of the equilibrium constant

for an endothermic reaction, increasing the temperature increases the value of the equilibrium constant

for an exothermic reaction, increasing the temperature decreases the value of the equilibrium constant

for an endothermic reaction, increasing the temperature increases the value of the equilibrium constant