chem 163b second midterm reviewchen.chemistry.ucsc.edu/163breview02tas.pdf · 2017. 3. 7. · chem...
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CHEM 163B THERMODYNAMICS
MIDTERM #2 REVIEWJia Lu (Gabby) jelu@ucsc.eduOffice Hour: Monday 3:00-4:00pm @ PSB 145Gabe Mednick gmednick@ucsc.eduOffice Hour: Wednesday 1:00-2:00pm @ PSB 145
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KEY CONCEPTS
• The Second Law of Thermodynamics and Carnot Engine• The Third Law of Thermodynamics and absolute entropy• Clausius inequality• Maxwell’s relation• Gibbs-Helmholtz Equation• Chemical potential and chemical reaction
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SECOND LAW OF THERMODYNAMICS
It is impossible for a system to undergo a cyclic process whose sole effects are the flow of heat into the system from a heat reservoir and the performance of an equal amount of work by the system on the surroundings.
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CARNOT CYCLE• A combination of 4 reversible processes
• Two isothermal processes• Two adiabatic processes
• Applies to ALL reversible cycles
1
| |1
< 100%
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ENTROPY (S)
• Definition of entropy• S= lnΩ• ∆ ≡
• State function – predicts the direction of natural / spontaneous change• ∮ ∮
• Entropy increases (∆ ) for a spontaneous (irreversible process) change in an isolated system
• For reversible processes, ∆ ∆ ∆• For adiabatic processes, q 0 → ∆
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ENTROPY DEPENDENCE ON P &V
Constant Pressure
• , → ,• For any system
∆ , κ• For ideal gas
∆ , ln
Constant Volume
• , → ,• For any system
∆ ,
• For ideal gas
∆ , ln
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THIRD LAW OF THERMODYNAMICS
The entropy of a pure, perfectly crystalline substance (element or compound) is zero at zero Kelvin.
0 , ′∆ ,
′∆ ,
′
1 0Absolute entropy (in general):•• ↑ as size of molecule increases (↑ DOF)• weakly bound > strongly bound• increases with increasing molar mass
During phase transition
Zero Kelvin can Never be reached
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CLAUSIUS INEQUALITY
• From the First Law: • For reversible processes: • Since U is state function,
•• For spontaneous processes
• 0 and 0 (expansion)• 0 and 0 (compression)
• 0• 0 or / > : irreversible processes
= : reversible processes
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SPONTANEITY
• Entropy• For an isolated system, ∆
• Helmholtz free energy• Maximum work done on the surroundings• For constant T & V, ∆
• Gibbs free energy• Maximum non-expansion work done on the surroundings• For constant T & P, ∆
Can solely focus on system alone
Need to take into account of surroundings
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CHEMICAL MIXTURE(SIMPLE MIXING)
• For real gases and liquids, ∆ 0• For immiscible situations: ∆ 0, ∆ ∆ ∆ 0
• Repulsive interaction• For miscible situations: ∆ 0, ∆ ∆
• Weak repulsive interaction
• For ideal gases, ∆ 0• Ideal gases do not interact with each other• ∆ 0 →• ∆ ∆ 0
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DERIVATION OF MAXWELL’S EQUATION
• Knowing:• U = q + w• H = U + PV• A = U - TS• G = H - TS
• Show:•
•
•
•
Hint:
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GIBBS-HELMHOLTZ EQUATION
Show ∆
∆
Processinvolvingtwodifferenttemperatures:∆ ∆
∆ ∆∆
1 1
∆
1
∆
1
∆1
1
∆
1At constant P, assuming H
does not depend on T
• Basic mathematic rules•
• If ,• 1 ·
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CHEMICAL POTENTIAL
• ≡, ,
• Partial molar Gibbs free energy
• Chemical potential at any states• ° °• ° standard state chemical potential (pure substance, P = 1 bar)
• In multi-components mixtures• ° ∑ °
Standard state pressure = 1 barNormal state pressure = 1 atm
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FOR A CHEMICAL REACTION
• ∆ ° ∑ ° ∑ °
• ∆ ° ∑ ,° ∑ ,°
• ∆ ∆ °
•∏ ,∏ ,
Activities (α, unit-less) for:• Gasses
• ° • Solutions
•
• Pure solid or liquid• 1
At equilibrium, NOT °
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EQUILIBRIUM CONSTANT (
• At equilibrium,•
• ∆°
• Variations (Le Chatelier’s Principle):• Differential: ∆
°
• Integration: ln ∆°
If • For endothermic reactions
• ∆ ° 0 → ln 0
• Forward reaction spontaneous• →
• For exothermic reactions• ∆ ° 0 → ln 0
• ←
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