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School of Chemistry and Biochemistry - Entropy &...
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1 Week 15 CHEM 1310 - Sections L and M 1 Entropy & Physical Changes Entropy is dependent on temperature S = k B ln Ω ∆ S = q rev / T 1 2 1 2 2 1 2 1 ln at constant Pressure ln at constant Volume T T p T T V T S nC T T S nC T Æ Æ Ê ˆ D = Á ˜ Ë ¯ Ê ˆ D = Á ˜ Ë ¯ Show explanation on board: Week 15 CHEM 1310 - Sections L and M 2 Entropy & Physical Changes Entropy changes are also associated with changes in phase fus rev H q S T T D D = = Calculate the change in entropy that occurs when a sample containing 1.00 mol of ice is heated from –20°C to +20°C at 1 atm pressure. The molar heat capacities of H 2 O(s) and H 2 O(l) are 38.1 JK -1 mol -1 and 75.3 J K -1 mol -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 c p vs T • Deduce molar absolute entropy – J K -1 mol -1 • If phase change occurs from 0 T, then add Δ S of phase transition ΔS vap = ΔH vap T b Example Measuring Entropy
Transcript of School of Chemistry and Biochemistry - Entropy &...
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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
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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
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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
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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
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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
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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
