chapter 17 thermodynamics: spontaneity, entropy, and free energy general chemistry: an integrated...

Chapter 17Thermodynamics: Spontaneity,

Entropy, and Free Energy

General Chemistry: An Integrated Approach

Hill, Petrucci, 4th Edition

Mark P. HeitzState University of New York at Brockport

© 2005, Prentice Hall, Inc.

Chapter 17: Thermodynamics 2

• Thermodynamics examines the relationship between heat and work.

• Spontaneity is the notion of whether or not a process can take place unassisted.

• Entropy is a mathematical concept describing the distribution of energy within a system.

• Free energy is a thermodynamic function that relates enthalpy and entropy to spontaneity, and can also be related to equilibrium constants.

Introduction

Chapter SeventeenGeneral Chemistry 4th edition, Hill, Petrucci, McCreary, Perry

Prentice Hall © 2005Hall © 2005

3

• With a knowledge of thermodynamics and by making a few calculations before embarking on a new venture, scientists and engineers can save themselves a great deal of time, money, and frustration.– “To the manufacturing chemist thermodynamics gives information

concerning the stability of his substances, the yield which he may hope to attain, the methods of avoiding undesirable substances, the optimum range of temperature and pressure, the proper choice of solvent.…” - from the introduction to Thermodynamics and the Free Energy of Chemical Substances by G. N. Lewis and M. Randall

• Thermodynamics tells us what processes are possible.– (Kinetics tells us whether the process is practical.)

Why Study Thermodynamics?



4

• A spontaneous process is one that can occur in a system left to itself; no action from outside the system is necessary to bring it about.

• A nonspontaneous process is one that cannot take place in a system left to itself.

• If a process is spontaneous, the reverse process is nonspontaneous, and vice versa.

• Example: gasoline combines spontaneously with oxygen.

• However, “spontaneous” signifies nothing about how fast a process occurs.

• A mixture of gasoline and oxygen may remain unreacted for years, or may ignite instantly with a spark.

Spontaneous Change



5

• Thermodynamics determines the equilibrium state of a system.

• Thermodynamics is used to predict the proportions of products and reactants at equilibrium.

• Kinetics determines the pathway by which equilibrium is reached.

• A high activation energy can effectively block a reaction that is thermodynamically favored.

• Example: combustion reactions are thermodynamically favored, but (fortunately for life on Earth!) most such reactions also have a high activation energy.

Spontaneous Change (cont’d)



6

• Early chemists proposed that spontaneous chemical reactions should occur in the direction of decreasing energy.

• It is true that many exothermic processes are spontaneous and that many endothermic reactions are nonspontaneous.

• However, enthalpy change is not a sufficient criterion for predicting spontaneous change …




7


Water falling (higher to lower potential energy) is

a spontaneous process.

H2 and O2 combine spontaneously to form water

(exothermic) BUT …… liquid water vaporizes

spontaneously at room temperature; an

endothermic process.

Conclusion: enthalpy alone is not a sufficient criterion for prediction of spontaneity.



8

The Concept of Entropy

When the valve is opened … … the gases mix spontaneously.

• There is no significant enthalpy change.

• Intermolecular forces are negligible.

• So … why do the gases mix?


The Concept of EntropyConsider mixing two gases: this occurs spontaneously, and the gases form a homogeneous mixture.

The driving force is a thermodynamic quantity called entropy, a mathematical concept that is difficult to portray visually

EOS

There is essentially no enthalpy change involved, so why is the process spontaneous?


Entropy The total energy of a system remains unchanged in the mixing of the gases but the number of possibilities for the distribution of that energy increases

This spreading of the energy and increase of entropy correspond to a greater physical disorder at the microscopic level

EOS


EntropyThere are two natural tendencies behind spontaneous processes: the tendency to achieve a lower energy state and the tendency toward a more disordered state

EOS


Increase in Entropy in theVaporization of Water

Evaporation is spontaneous because of the increase in entropy.



13

• The spreading of the energy among states, and increase of entropy, often correspond to a greater physical disorder at the microscopic level (however, entropy is not “disorder”).

• There are two driving forces behind spontaneous processes: the tendency to achieve a lower energy state (enthalpy change) and the tendency for energy to be distributed among states (entropy).

• In many cases, however, the two factors work in opposition. One may increase and the other decrease or vice versa. In these cases, we must determine which factor predominates.

The Concept of Entropy



14

• The difference in entropy (S) between two states is the entropy change (S).

• The greater the number of configurations of the microscopic particles (atoms, ions, molecules) among the energy levels in a particular state of a system, the greater is the entropy of the system.

• Entropy generally increases when:– Solids melt to form liquids.– Solids or liquids vaporize to form gases.– Solids or liquids dissolve in a solvent to form

nonelectrolyte solutions.– A chemical reaction produces an increase in the

number of molecules of gases.– A substance is heated.

Assessing Entropy Change



15

Example 17.2Predict whether each of the following leads to an increase or decrease in the entropy of a system. If in doubt, explain why.

(a) The synthesis of ammonia:N2(g) + 3 H2(g) 2 NH3(g)

(b) Preparation of a sucrose solution:

C12H22O11(s) C12H22O11(aq)

(c) Evaporation to dryness of a solution of urea, CO(NH2)2, in water:

CO(NH2)2(aq) CO(NH2)2(s)

H2O(l)


Entropy (S)

Entropy (S) is a state function: it is path independent

Sfinal – Sinit = S

EOS

S = qrev/T

The greater the number of configurations of the microscopic particles (atoms, ions, molecules) among the energy levels in a particular state of a system, the greater the entropy of the system



17

• Sometimes it is necessary to obtain quantitative values of entropy changes.

S = qrxn/T• where qrxn is reversible heat, a state function.

Entropy Change

A reversible process can be reversed by a very small

change, as in the expansion of this gas. A reversible

process is never more than a tiny step from equilibrium.

The expansion can be reversed by allowing the sand to return, one grain at a

time.


Standard Molar EntropiesThe standard molar entropy, So, is the entropy of one mole of a substance in its standard state.

S = vpSo(products) – vrSo(reactants)

EOS

According to the Third Law of Thermodynamics, the entropy of a pure, perfect crystal can be taken to be zero at 0 K


Standard Molar EntropiesIn general, the more atoms in its molecules, the greater is the entropy of a substance

EOS

Entropy is a function of temperature


The Second Lawof Thermodynamics

The Second Law of Thermodynamics establishes that all spontaneous or natural processes increase the entropy of the universe

Stotal = Suniverse = Ssystem + Ssurroundings

EOS

In a process, if entropy increases in both the system and the surroundings, the process is surely spontaneous



21

• What is the significance of: –TΔSuniv = ΔHsys – TΔSsys ?

• The entropy change of the universe—our criterion for spontaneity—has now been defined entirely in terms of the system.

• The quantity –TΔSuniv is called the free energy change (G).

• For a process at constant temperature and pressure:

Gsys = Hsys – TSsys

Free Energy and Free Energy Change



22

• If G < 0 (negative), a process is spontaneous.

• If G > 0 (positive), a process is nonspontaneous.

• If G = 0, neither the forward nor the reverse process is favored; there is no net change, and the process is at equilibrium.

Free Energy and Free Energy Change



23

Case 3 illustrated

ΔH is (+) and is more-or-less constant with T.

Since ΔS is (+), the slope TΔS is also (+).

At low T, the size of TΔS is small, and ΔH

(+) predominates.

At high T, the size of TΔS is large, and –TΔS

predominates.


Example 17.5 A Conceptual Example

Molecules exist from 0 K to a few thousand kelvins. At elevated temperatures, they dissociate into atoms. Use the relationship between enthalpy and entropy to explain why this is to be expected.

Analysis and ConclusionsTo cause a molecule to dissociate into its atoms, we must supply the molecule with enough energy to induce such vigorous vibrations that its atoms fly apart, an endothermic process (∆H > 0). To assess the entropy change, we first note that a molecule has a greater number of available energy levels than does any one of its constituent atoms taken alone. However, because two or more atoms are produced for every molecule dissociated, we find a greater number of available energy levels in a system of individual atoms than if the same atoms are united into molecules (∆S > 0). The key factor, then, is the temperature, T. At low temperatures, ∆H is the determining factor, dissociation into atoms is a nonspontaneous process, and therefore molecules are generally stable with respect to uncombined atoms. However, no matter how large the value of ∆H, eventually a temperature is reached at which the magnitude of T∆S exceeds that of ∆H. Then ∆G is negative, and the dissociation becomes a spontaneous process. For all known molecules, this high temperature limit is no more than a few thousand kelvins.


Standard Free Energy Change

The standard free energy change, Go, of a reaction is the free energy change when reactants and products are in their standard states

e.g., O2 is a gas, Br2 is liquid, etc. ...

Go = Ho – TSo

EOS

Be mindful of units; H is usually in kJ and S is in J K–1


Standard Free Energy Change

The standard free energy of formation, Gof, is

the free energy change that occurs in the formation of 1 mol of a substance in its standard state from the reference forms of its elements in their standard states

EOS

Go = vp Gof(products) – vr Go

f(reactants)


Free Energy Changeand Equilibrium

At equilibrium, G = 0. Therefore, at the equilibrium temperature, the free energy change expression becomes

H = TS and S = H/T

EOS

Entropy and enthalpy of vaporization can be related to normal boiling point


Vaporization Energies

Trouton’s rule implies that about the same amount of disorder is generated in the passage of one mole of substance from liquid to vapor when comparisons are made at the normal boiling point

EOS

S°vapn = H°vapn/Tbp 87 J mol–1 K–1



29

Illustrating Trouton’s Rule

The three substances have different entropies and different boiling

points, but S of vaporization is about the same for all three.



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Raoult’s Law Revisited

Entropy of vaporization of the solvent is about the same in each case,

which means …

A pure solvent has a lower entropy than a solution containing

the solvent.

… higher entropy for the vapor from the

solution than from the pure solvent.

Entropy of a vapor increases if the vapor expands into a

larger volume—lower vapor pressure.


Relationship of Go and Keq

G = 0 is a criterion for equilibrium at a single temperature, the one temperature at which the equilibrium state has all reactants and products in their standard states

G and Go are related through the reaction quotient, Q

G = Go + RT ln Q

Under the conditions of G = 0 and Q = Keq, the equation above becomes

EOS

Go = RT ln Keq


The Equilibrium Constant, Keq

Activities are the dimensionless quantities needed in the equilibrium constant expression Keq

For pure solid and liquid phases: activity, a, = 1

For gases: Assume ideal gas behavior, and replace the activity by the numerical value of the gas partial pressure in atm.

EOS

For solutes in aqueous solution: Assume intermolecular or interionic attractions are negligible and replace solute activity by the numerical value of the solute molarity


The Significance of the Sign and Magnitude of Go

Go is a large, negative quantity and equilibrium is very far to the right (towards products)

Gprod << Greac

EOS



Go is a large, positive quantity and equilibrium is very far to the left (towards reactants)

Gprod >> Greac

EOS



the equilibrium lies more toward the center of the reaction profile

Gprod Greac

EOS


The Dependence ofGo and Keq on Temperature

To obtain equilibrium constants at different temperatures, it will be assumed that H and S do not change much with temperature

EOS

the 25 oC values of Ho and So along with the desired temperature are substituted

Go = Ho – TSo


The Dependence ofGo and Keq on Temperature

To obtain Keq at the desired temperature, the following equation is used …

EOS

This is the van’t Hoff equation

2eq

1 1 2

1 1ln lnoK HK

K R T T


Equilibrium with VaporHo for either sublimation or vaporization is used depending on the other component

EOS

This is the Clausius–Clapeyron equation

211

2 11ln

TTR

H

P

Povap

Partial pressures are exchanged for K’s


Temperature Dependence of Keq

EOS


Summary of Concepts

• A spontaneous change is one that occurs by itself without outside intervention

• The third law of thermodynamics states that the entropy of a pure, perfect crystal at 0 K can be taken to be zero

• The direction of spontaneous change is that in which total entropy increases

EOS

• The free energy change, G, is equal to –TS, and it applies just to the system itself


Summary (cont’d)

• The standard free energy change, Go, can be calculated by substituting standard enthalpies and entropies of reaction and a Kelvin temperature into the Gibbs equation, or, by combining standard free energies of formation

EOS

• The condition of equilibrium is one for which G = 0


Summary (cont’d)

• The value of Go is in itself often sufficient to determine how a reaction will proceed

• Values of Gof, Ho

f, and S are generally tabulated for 25 oC. To obtain values of Keq at other temperatures, the van’t Hoff equation must be used

EOS

• The Clausius–Clapeyron equation connects solid/vapor or liquid/vapor equilibria to varying temperature

chapter 17 thermodynamics: spontaneity, entropy, and free energy general chemistry: an integrated...

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