The Chaos Connection Slides The Chaos Connection
Thermodynamic Favorability, Entropy, & Gibbs Free Energy
AP Chemistry | Unit 9: Thermodynamics
Today's Mission
Connect thermodynamic favorability (spontaneity) to entropy and enthalpy.
Analyze how local entropy decreases are "paid for" by surroundings.
Derive the Gibbs Free Energy equation from the 2nd Law of Thermodynamics.
Warm-Up: The Dressing Dilemma
5 Minutes
"Why do oil and vinegar separate after you shake them?"
Discussion Points:
Is it Energy driving them apart?
Is it Entropy (disorder) driving them apart?
Which state is more "organized"?
Video Analysis
Embedded media
Focusing on:
"Negative Entropy Changes"
Watch how the narrator explains why cleaning a room doesn't actually violate the 2nd Law.
"Entropy can decrease in some ways... so long as it increases in others."
The Total Toll
Second Law of Thermodynamics
\[ \Delta S_{univ} = \Delta S_{sys} + \Delta S_{surr} > 0 \]
The System
The specific chemical reaction or phase change we are watching.
The Surroundings
Everything else. Usually where heat is dumped (exothermic) or taken from (endothermic).
The Bridge to Gibbs
To predict if a reaction is "favored" (spontaneous), we don't want to measure the Surroundings every time.
Pro-Tip from Physics:
\[ \Delta S_{surr} = -\frac{\Delta H_{sys}}{T} \]
Activity Instructions
1 Grab the "Gibbs Connection" worksheet.
2 Follow the steps to combine the equations.
3 Derive the famous \(\Delta G\) equation!
3-2-1 Reflection
3
Rules
List 3 rules for predicting if entropy increases in a reaction.
2
Examples
Provide 2 examples of phase changes and their \(\Delta S\) sign.
1
Question
Pose 1 question about the "Heat Death" of the universe.
Gibbs Connection Worksheet Gibbs Connection
AP Chemistry: Unit 9 Activity
Name:
Date:
The Goal: We know the 2nd Law states \(\Delta S_{univ} > 0\) for a spontaneous process. However, measuring the surroundings is difficult. In this activity, you will derive a way to predict spontaneity using only properties of the system.
Part 1: The Derivation
1. Start with the Second Law of Thermodynamics. Write the expression for the total entropy change of the universe:
2. We can't easily measure the surroundings. But we know that for a process at constant pressure and temperature:
\[ \Delta S_{surr} = -\frac{\Delta H_{sys}}{T} \]
Substitute this expression for \(\Delta S_{surr}\) into your equation from Step 1:
3. To simplify, multiply the entire equation by \(-T\):
4. Scientists define the term Gibbs Free Energy (\(\Delta G\)) as \(-T\Delta S_{univ}\). Write the final equation relating \(\Delta G\), \(\Delta H_{sys}\), and \(\Delta S_{sys}\):
Key Insight: If \(\Delta S_{univ}\) must be positive for a process to be spontaneous, then \(\Delta G\) (which is \(-T\Delta S_{univ}\)) must be for a process to be spontaneous.
Part 2: Temperature Dependency
Fill in the table below to predict under what temperature conditions a reaction is thermodynamically favored.
\(\Delta H\) \(\Delta S\) Predicting \(\Delta G\) (Spontaneity) Negative (-) Positive (+) Positive (+) Negative (-) Negative (-) Negative (-) Positive (+) Positive (+)
Part 3: Spontaneity Practice
Scenario: Decomposition of Nitrogen Dioxide
\(2 NO_2 (g) \rightarrow 2 NO (g) + O_2 (g)\)
\(\Delta H = +114.4 \text{ kJ/mol} \quad \Delta S = +146.4 \text{ J/mol}\cdot\text{K}\)
A) Is this reaction favored at "standard" conditions (298 K)? Show your calculation.
B) Calculate the "Crossover Temperature" (where the reaction becomes spontaneous).
Thermo Tool Reference Guide ThermoTool v2.0
ADVANCED SPONTANEITY PREDICTOR
Quick-Logic Matrix: \(\Delta G = \Delta H - T\Delta S\)
Q1 Favored at all T
\( \Delta H = (-) \)
\( \Delta S = (+) \)
Enthalpy driven & Entropy driven
Q2 Never Favored
\( \Delta H = (+) \)
\( \Delta S = (-) \)
"Non-Spontaneous" at any temperature
Q3 Favored at High T
\( \Delta H = (+) \)
\( \Delta S = (+) \)
Entropy must overcome Enthalpy
Q4 Favored at Low T
\( \Delta H = (-) \)
\( \Delta S = (-) \)
Enthalpy must overcome Entropy
Critical Constants & Conversion
Standard Temp 298.15 K
Gas Constant (R) 8.314 J/mol·K
UNIT ALERT: Check kJ vs J!
Divide \(\Delta S\) (J) by 1000 before using in \(\Delta G\) equation with \(\Delta H\) (kJ).
Finding the Equilibrium point
\[ T_{crossover} = \frac{\Delta H}{\Delta S} \]
This is the temperature where \(\Delta G = 0\) (The tipping point)
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GIBBS
ENTROPY
CROSS
SOLVE
