Chemical Thermodynamics: Chemical Thermodynamics: Entropy, Free Energy and Entropy, Free Energy and

EquilibriumEquilibriumChapter 18Chapter 18

18.1-18.618.1-18.6

Chemical ThermodynamicsChemical Thermodynamics

Science of interconversion of energyScience of interconversion of energy Heat into other forms of energyHeat into other forms of energy Amount of heat gained/released from a systemAmount of heat gained/released from a system Spontaneity of a reactionSpontaneity of a reaction Gibbs free energy functionGibbs free energy function Relationship between Gibbs Free Energy and Relationship between Gibbs Free Energy and

chemical equilibrium chemical equilibrium

Spontaneous ProcessesSpontaneous Processes

Main objectiveMain objective Spontaneous Reaction- Spontaneous Reaction- a reaction does occur a reaction does occur

under specific conditionsunder specific conditions Non-spontaneous Reaction-Non-spontaneous Reaction- a reaction does a reaction does

not occur under specific conditionsnot occur under specific conditions

Spontaneous ProcessesSpontaneous Processes

A waterfall runs downhill A lump of sugar dissolves in a cup of coffee At 1 atm, water freezes below 0ºC and ice

melts above 0ºC Heat flows from a hotter object to a colder

object Iron exposed to oxygen and water forms rust

Spontaneous ProcessesSpontaneous Processes

Spontaneous ProcessesSpontaneous Processes

Does a decrease in enthalpy mean a reaction proceeds spontaneously?

Spontaneous reactions

CH4 (g) + 2O2 (g) CO2 (g) + 2H2O (l) H0 = -890.4 kJ

H+ (aq) + OH- (aq) H2O (l) H0 = -56.2 kJ

H2O (s) H2O (l) H0 = 6.01 kJ

NH4NO3 (s) NH4+(aq) + NO3

- (aq) H0 = 25 kJH2O

EntropyEntropy

To predict spontaneity we need:To predict spontaneity we need: Change in enthalpyChange in enthalpy EntropyEntropy Entropy- Entropy- a measure of the randomness or disorder a measure of the randomness or disorder

of a system.of a system. ↑ ↑ Disorder = ↑ EntropyDisorder = ↑ Entropy

EntropyEntropy

New Deck OrderNew Deck Order Shuffled Deck OrderShuffled Deck Order ProbabilityProbability Ordered stateOrdered state Disordered StateDisordered State

Microstates and EntropyMicrostates and Entropy

Microstates and EntropyMicrostates and Entropy

Boltzmann, 1868Boltzmann, 1868 S = S = kk ln W ln W

kk = 1.38 x 10 = 1.38 x 10-23-23 J/K J/K ↑ ↑ W = ↑ EntropyW = ↑ Entropy

∆ ∆ S = SS = Sff – S – Sii

∆ ∆ S = S = kk ln ln WWff

WWii

Wf > Wi then S > 0

Wf < Wi then S < 0

Entropy and DisorderEntropy and Disorder

If the change from initial to final results in an increase in randomness

Sf > Si S > 0

For any substance, the solid state is more ordered than the liquid state and the liquid state is more ordered than gas state

Ssolid < Sliquid << Sgas

Entropy and DisorderEntropy and Disorder

Entropy and DisorderEntropy and Disorder

How does the entropy of a system change for each of the following processes?

(a) Forming sucrose crystals from a supersaturated solution

Randomness decreases Entropy decreases (S < 0)

(b) Heating hydrogen gas from 600C to 800C

Randomness increases Entropy increases (S > 0)

Entropy and DisorderEntropy and Disorder

Standard EntropyStandard Entropy

The standard entropy of reaction (S0 ) is the entropy change for a reaction carried out at 1 atm and 250C.

rxn

The Second Law of The Second Law of ThermodynamicsThermodynamics

The entropy of the universe increases in a The entropy of the universe increases in a spontaneous process and remains unchanged spontaneous process and remains unchanged in an equilibrium process. in an equilibrium process. Importance?Importance?

Spontaneous process: Suniv = Ssys + Ssurr > 0

Equilibrium process: Suniv = Ssys + Ssurr = 0

Entropy Changes in the SystemEntropy Changes in the System

To calculate To calculate ΔΔSSunivuniv, we need both , we need both ΔΔSSsyssys ΔΔSSsurrsurr

ΔΔSSsyssys

aA + bB cC + dD

S0rxn nS0(products)= mS0(reactants)-

Entropy Changes in the SystemEntropy Changes in the System

Entropy Changes in the SystemEntropy Changes in the System

When gases are produced (or consumed)

• If a reaction produces more gas molecules than it consumes, S0 > 0.

• If the total number of gas molecules diminishes, S0 < 0.

• If there is no net change in the total number of gas molecules, then S0 may be positive or negative BUT S0 will be a small number.

Entropy Changes in the SystemEntropy Changes in the System

Entropy Changes in the Entropy Changes in the SurroundingsSurroundings

Entropy Changes in the Entropy Changes in the SurroundingsSurroundings

ΔΔSSsurrsurr = = --ΔΔHHsyssys TT

Using the information from Example 18.2, determine whether or not the Using the information from Example 18.2, determine whether or not the reaction is spontaneous.reaction is spontaneous.

NN22(g) + 3H(g) + 3H22(g) (g) → → 2 NH2 NH33(g)(g) ΔΔHºHºrxnrxn = -92.6 kJ/mol = -92.6 kJ/mol

ΔΔSSsyssys = -199 J/K ∙ mol = -199 J/K ∙ mol

ΔΔSSsurrsurr = = -(-92.6 x 1000) J/mol-(-92.6 x 1000) J/mol 298 K298 K

ΔΔSSsurrsurr = 311 J/mol = 311 J/mol

ΔΔSSunivuniv = = ΔΔSSsyssys + + ΔΔSSsurrsurr

ΔΔSSunivuniv = -199 J/K ∙ mol + 311 J/mol = -199 J/K ∙ mol + 311 J/mol

ΔΔSSUNIVUNIV = 112 J/K ∙ mol = 112 J/K ∙ mol

The Third Law of Thermodynamics The Third Law of Thermodynamics and Absolute Entropyand Absolute Entropy

Third Law of Third Law of Thermodynamics-Thermodynamics- the the entropy of a perfect entropy of a perfect crystalline substance is crystalline substance is zero at the absolute zero zero at the absolute zero of temperature.of temperature.

Gibbs Free EnergyGibbs Free Energy

Predicts the direction of a spontaneous Predicts the direction of a spontaneous reaction.reaction.

Uses properties of the system to calculate. Uses properties of the system to calculate. For a constant pressure-temperature process:For a constant pressure-temperature process:

G = Hsys -TSsys

G < 0 The reaction is spontaneous in the forward direction.

G > 0 The reaction is nonspontaneous as written. The reaction is spontaneous in the reverse direction.G = 0 The reaction is at equilibrium.

Standard Free-Energy ChangesStandard Free-Energy Changes

The standard free-energy of reaction (G0 ) is the free-energy change for a reaction when it occurs under standard-state conditions.

rxn

Standard free energy of formation (G0) is the free-energy change that occurs when 1 mole of the compound is formed from its elements in their standard states.

f

G0rxn nG0 (products)f= mG0 (reactants)f-

Standard Free-Energy ChangesStandard Free-Energy Changes

Factors Affecting Factors Affecting ΔΔGG

Free Energy and Chemical Free Energy and Chemical EquilibriumEquilibrium

G = G0 + RT lnQ

R is the gas constant (8.314 J/K•mol)

T is the absolute temperature (K)

Q is the reaction quotient

At Equilibrium

G = 0 Q = K

0 = G0 + RT lnK

G0 = RT lnK

Free Energy and Chemical Free Energy and Chemical EquilibriumEquilibrium

Free Energy and Chemical Free Energy and Chemical EquilibriumEquilibrium

Free Energy and Chemical Free Energy and Chemical EquilibriumEquilibrium

Thermodynamics of a Rubber BandThermodynamics of a Rubber Band