Entropy and Free Entropy and Free EnergyEnergy

Chapter 19

Laws of ThermodynamicsLaws of Thermodynamics

• First Law–Energy is conserved in chemical processes• neither created nor destroyed• converted from one form into another

• Second Law–For any spontaneous process, the entropy of

the universe increases• the real criterion for spontaneity • changes in randomness of the universe is +

Some definitions…Some definitions…

Free energy- the energy that is available to do work.

Entropy- a measure of the disorder of a system.

Enthalpy-at constant pressure, it is the heat evolved or absorbed in the reaction.

Spontaneous ReactionNon-spontaneous ReactionLaw of Disorder-processes move in the

direction of maximum disorder or randomness

Entropy “Rules” Entropy “Rules” (see p 729 for examples)(see p 729 for examples)

1. Entropy of a gas is greater than that of a liquid or a solid.

2. Entropy increases when a substance is divided into parts.

3. Entropy tends to increase in chemical reactions in which the total number of product molecules is greater than the total number of reactant molecules.

4. Entropy tends to increase when temperature increases.

Reaction SpontaneityReaction Spontaneity

The size and direction of heat (enthalpy) changes and entropy changes together determine whether a reaction is spontaneous.

How How ΔΔH and H and ΔΔS Affect Reaction Spontaneity S Affect Reaction Spontaneity

ΔH ΔS Spontaneous?

Decreases(exothermic)

Increases (more disorder in products than in reactants)

Yes

Increases(endothermic)

Increases ΔS > ΔH

Decreases(exothermic)

Decreases (less disorder in products than in reactants)

ΔH > ΔS

Increases(endothermic)

Decreases No

Some background on the standard Some background on the standard conditions for entropy…conditions for entropy…

Units for S: J/KUsually given as J/K x mol because we are

interested in a specific substance.S° signifies entropy at standard conditions

(101.3 kPa and 25°C).Theoretical entropy of a perfect crystal at

0 K is zero.

Entropy CalculationsEntropy Calculations

Standard Entropy change (ΔS°) can be calculated using:

ΔS°(reaction) = ΔS°(products)- ΔS° (reactants)

Practice Problem:Practice Problem:

Calculate the standard entropy change (ΔS°) that occurs when 1 mol H2O(g) at 25°C and 101.3 kPa condenses to 1 mol H2O(l) at the same temperature.

H2O(g) S° = 188.7 J/KxmolH2O(l) S° = 69.94 J/KxmolΔS°=69.94 – 188.7 = -118.8 J/KxmolThe negative sign indicates that

entropy decreases.

Free Energy CalculationsFree Energy Calculations

Josiah Gibbs formulated the Gibbs free Energy change (ΔG) equation.

It is the maximum amount of energy that can be coupled to another process to do useful work. The change in Gibbs free energy is related to the change in entropy (ΔS) and the change in enthalpy (ΔH) of the system by the following equation:

ΔG = ΔH – TΔS(T=temperature in Kelvin)

ΔΔGG

If –ΔG, reaction is spontaneous in forward direction

If +ΔG, reaction is non-spontaneous in forward direction but spontaneous in reverse direction. Work must be supplied from surroundings to make it occur.

If ΔG=0, reaction is at equilibriumAll spontaneous processes release free

energy.In a spontaneous reaction ΔG is negative

because the system loses free energy.

C2H5OH(l) + 3O2(g) 2CO2(g) + 3H2O(g) + 1235 kJ

• What is the sign of H?• What is the sign of S?• Plug signs into: ΔG = ΔH – TΔS

• Prediction???

• spontaneous

Qualitative Prediction of Qualitative Prediction of SpontaneitySpontaneity

ΔG = ΔG° + RT ln Q(where R=8.314 J/mol K)At equilibrium ΔG=0 and Q=K, therefore:ΔG°=-RT ln K and K= e-ΔG°/RT (find

these formulas on your AP cheat sheet)Turn to page 740 and try practice exercise

19.12

Free Energy and KeqFree Energy and Keq

G is the energy change by a system G is the energy change by a system going from initial conditions to going from initial conditions to equilibriumequilibrium

G negative reaction proceeds right to equilibrium

G positive reaction proceedsleft to equilibrium

G = 0 at equilibrium

But…But…

Infinite number of combinations of variables◦conc, T, P, etc.

Reference values based on standard conditions◦gases at 1 atm◦solids and liquids – most stable form at 1 atm and 298 K

◦solutions at 1 M

Standard EnthalpyStandard Enthalpy

Tabulated

Hof

standard

formation

Horxn

Horxn = npHo

f (products) - nrHof (reactants)

Standard EntropyStandard Entropy

Tabulated

Sostandard

Sorxn

Sorxn = npSo (products) - nrSo

(reactants)

S of a pure crystal at 0 K = 0Third Law of Thermodynamics

Standard Free EnergyStandard Free Energyone methodone method

Tabulated

Gof

Gorxn

Gorxn = npGo

f (products) - nrGof (reactants)

formation

Standard Free EnergyStandard Free Energyanother methodanother method

Gorxn Areaction A

Gorxn B

Gorxn C

Gorxn

reaction B

reaction C

reaction of interest

SUM

SUM

Standard Free EnergyStandard Free Energyyet another methodyet another method

Gorxn Ho

rxn - T Sorxn=

Standard Free EnergyStandard Free EnergyALL THREE METHODSALL THREE METHODS

Standard states of all reactants and products

1 M ; 1 atm

Equilibrium

Gorxn

Free Energy related to Free Energy related to Standard Free EnergyStandard Free Energy

Grxn = Gorxn + RT lnQ