1

Week 15 CHEM 1310 - Sections L and M 1

Entropy & Physical Changes

Entropy is dependent on temperature

S = kB ln Ω ∆ S = qrev / T

1 2

1 2

2

1

2

1

ln at constant Pressure

ln at constant Volume

T T p

T T V

TS nC

T

TS nC

T

Æ

Æ

Ê ˆD = Á ˜

Ë ¯

Ê ˆD = Á ˜

Ë ¯

Show explanation on board:

Week 15 CHEM 1310 - Sections L and M 2

Entropy & Physical Changes

Entropy changes are also associated withchanges in phase

fusrevHq

ST T

DD = =

Calculate the change in entropy that occurs when asample containing 1.00 mol of ice is heated from

–20°C to +20°C at 1 atm pressure.

The molar heat capacities of H2O(s) and H2O(l) are38.1 JK-1mol-1 and 75.3 J K-1mol-1 respectively and the

enthalpy of fusion (melting) is 6.01 kJ mol-1 at 0°C.

Show on board

Week 15 CHEM 1310 - Sections L and M 3

• Use calorimetry

• Measure cp vs T

• Deduce molar absoluteentropy – J K-1 mol-1

• If phase change occursfrom 0 T, then add ΔSof phase transition

Δ Svap = Δ Hvap

Tb

Example

Measuring Entropy

2

Week 15 CHEM 1310 - Sections L and M 4

Sº increases are you read down a Group.Sº is similar across a Period.

Ssolid < S liquid < SgasKnow this!

Standard Molar Entropies

Week 15 CHEM 1310 - Sections L and M 5

Δ Sreaction = Sproducts - Sreactants

ΔSrxn° = ΣS°products – ΣS°reactants

a A + b B → c C + d D

Standard molar entropy valuesS° in units JK-1mol-1

Entropy of a Reaction

Week 15 CHEM 1310 - Sections L and M 6

• 1st Law of Thermodynamics– In any process, the total energy of the universe remains

unchanged: energy is conserved

• 2nd Law of Thermodynamics– S, the entropy of a universe, must increase– Δ Suniv = (Δ Ssys + Δ Ssurroundings) > 0

Laws of Thermodynamics

ΔSuniv > 0 Spontaneous

ΔSuniv = 0 Equilibrium

ΔSuniv < 0 Non-spontaneous

3

Week 15 CHEM 1310 - Sections L and M 7

Entropy & Spontaneity

Week 15 CHEM 1310 - Sections L and M 8

Gibbs’ Free Energy

How are Enthalpy and Entropy related?G = H - T•S

G has several names1. Gibbs function2. Gibbs free energy3. Free Enthalpy

For the change in the Gibbs Energy of system, atconstant Temperature and Pressure

ΔGsys = ΔHsys - T·ΔSsys

Week 15 CHEM 1310 - Sections L and M 9

Recall the 2nd Law of ThermodynamicsΔSuniverse > 0 (spontaneous process)

ΔSuniverse = ΔSsystem + ΔSsurroundings

Thus, ΔSsystem + ΔSsurroundings > 0

Gibbs’ Free Energy

4

Week 15 CHEM 1310 - Sections L and M 10

ΔSsys - ΔHsys

T> 0

Recall the 1st Law of Thermodynamics

ΔHsurroundings = - ΔHsys

ΔSsystem + ΔSsurroundings > 0

ΔHsurroundingsΔSsurroundings =

Energy is conserved!

T=

- ΔHsystem

TThus…

Gibbs’ Free Energy

Week 15 CHEM 1310 - Sections L and M 11

Gibbs’ Free Energy ExpressionΔGsys = ΔHsys – Tsys ΔSsys

ΔSsys - ΔHsys

T> 0

Multiply by T: TΔSsys - ΔHsys > 0

Multiply by -1: ΔHsys - TΔSsys < 0

Gibbs’ Free Energy

Week 15 CHEM 1310 - Sections L and M 12

Gibbs’ Free Energy ExpressionΔGsys = ΔHsys – Tsys ΔSsys

If ΔGsys < 0, then rxn is spontaneousIf ΔGsys = 0, then rxn is at equilibrium

If ΔGsys > 0, then rxn is non-spontaneous

For constant T and P!Therefore, both Δ S and Δ G are indicative of reaction spontaneity.

Gibbs’ Free Energy

5

Week 15 CHEM 1310 - Sections L and M 13

ΔGreaction = Gproducts - Greactants

ΔG°rxn = Δ H°rxn – T Δ S°rxn

a A + b B → c C + d D

ΔG°f = Δ H°f – T Δ S°f

Standard GibbsEnergy of Reaction:

Standard Molar GibbsEnergy of Formation:

ΔG°rxn = cΔG°f, for C + dΔG°f, for D - aΔG°f, for A- bΔG°f, for B

Appendix D

Gibbs’ Energy Expressions

Week 15 CHEM 1310 - Sections L and M 14

Gibbs’ Energy and Temp

Week 15 CHEM 1310 - Sections L and M 15

Δ H is negativeΔ S is positiveΔ G is negative

ΔG°rxn = Δ H°rxn – T Δ S°rxn

SpontaneousReaction

Temp & Gibbs’ Free Energy

6

Week 15 CHEM 1310 - Sections L and M 16

Δ H is positiveΔ S is negativeΔ G is positive

ΔG°rxn = Δ H°rxn – T Δ S°rxn

Non-spontaneousReaction

Temp & Gibbs’ Free Energy

Week 15 CHEM 1310 - Sections L and M 17

Δ H is positiveΔ S is positiveΔ G is negative,when T is big!

ΔG°rxn = Δ H°rxn – T Δ S°rxn

SpontaneousReaction

Temp & Gibbs’ Free Energy

Week 15 CHEM 1310 - Sections L and M 18

Δ H is negativeΔ S is negativeΔ G is negative,when T is small!

ΔG°rxn = Δ H°rxn – T Δ S°rxn

SpontaneousReaction

Temp & Gibbs’ Free Energy