Chapter 16 Gen Chem 2

Learning Objectives
- Distinguish between spontaneous and nonspontaneous processes.
- Describe the dispersal of matter and energy that accompanies certain spontaneous processes.
Overview of Spontaneous Processes
- Processes have a natural tendency to occur in one direction under specified conditions.
- Example: Water flows downhill (spontaneous) vs. uphill requires intervention (nonspontaneous).
- Rust (iron corrosion) happens spontaneously; reforming iron requires energy input (nonspontaneous).
Definitions
- Spontaneous Process: A process that occurs naturally under certain conditions (e.g., ice melting at room temperature).
- Nonspontaneous Process: A process that requires continuous energy input from external sources (e.g., freezing water).
Speed and Spontaneity
- The spontaneity of a process is independent of the speed at which it occurs.
- Example: Radioactive decay is spontaneous but happens at varying rates.
- Technetium-99m: half-life of 6 hours (rapid decay).
- Uranium-238: half-life of over 4 billion years (very slow decay).
Thermodynamic Stability
- Diamonds are thermodynamically unstable but kinetically stable because they do not easily convert to graphite despite spontaneous tendency.
- Graphitization of diamond to graphite is spontaneous but slow at room temperature.

Example of Gas Expansion
- Two flasks, one with an ideal gas and one empty, connected by a valve.
- Opening the valve allows gas to expand uniformly, leading to greater dispersal. No work done (P = 0 in vacuum).
Heat Transfer Example
- When two objects at different temperatures (TX > TY) are in contact, heat flows from the hotter to the cooler object, resulting in a uniform thermal energy distribution.
Key Factor
- Spontaneity linked to changes in dispersal of matter or energy; aim for uniform distribution.

(a) Sublimation of Solid: Conversion of solid to gas increases dispersal due to larger volume.
(b) Condensation of Gas: Gas to liquid conversion decreases dispersal due to lesser volume.
(c) Diffusion of Food Coloring: Drop of dye in water leads to uniform color distribution.
Checkpoint Assignment
- Energy redistribution observed in thermal contact with a spoon and hot coffee; thermal energy shifts from coffee to spoon.

Learning Objectives
- Define entropy.
- Explain the relationship between entropy and the number of microstates.
- Predict the sign of the entropy change for various processes.
Historical Insight
- 1824: Nicolas Léonard Sadi Carnot identifies efficiency of steam heat engines.
- Rudolf Clausius links heat flow to temperature, formalizing a new thermodynamic property: Entropy (S).
- Entropy is expressed as:
  $S = k ext{ln}(W)$ where W is number of microstates and k is the Boltzmann constant (1.38 x $10^{-23}$ J/K).
Microstates and Entropy
- A microstate is a specific configuration of a system’s particles.
- More microstates yield higher entropy $(Wf > Wi ightarrow riangle S > 0)$ .
- Less microstates lead to lower entropy $(Wf < Wi ightarrow riangle S < 0)$ .

Entropy and Phases
- Solids: atoms/molecules primarily fixed, limited movement, smaller number of microstates.
- Liquids: greater freedom of movement, more microstates.
- Gases: huge volume occupancy and many possible configurations, maximum microstates.
Phase Transition Examples:
- Melting (solid to liquid, $riangle S > 0$ )
- Freezing (liquid to solid, $riangle S < 0$ )
- Vaporization (liquid to gas, $riangle S > 0$ )
- Condensation (gas to liquid, $riangle S < 0$ )

Temperature Increases
- Entropy increases with temperature due to broader kinetic energy distribution.
Impacts of Mass and Composition
- Heavier atoms/molecules have higher entropy.
- Mixtures have greater entropy than pure substances due to additional arrangements/possibilities.
Entropy Predictions
- Example Process: Dissolution of solid in liquid results in increased freedom/movement and disorder, leading to $riangle S > 0$ .

Learning Objectives
- State the second and third laws of thermodynamics.
- Calculate entropy changes for phase transitions and reactions under standard conditions.
Second Law of Thermodynamics
- Spontaneous processes yield increased entropy in the universe $( riangle S_{univ} > 0)$ .
- Nonspontaneous $( riangle S{univ} < 0)$ ; equilibrium $( riangle S{univ} = 0)$ .
Heat Transfers
- Heat from system to surroundings increases entropy of surroundings more than decreases of system.
- Entropy Change Examples:
- Identify heat flow direction and quantify.
Third Law of Thermodynamics
- Absolute zero (0 K) corresponds to zero entropy for perfect crystalline solids (one microstate.)

Learning Objectives
- Define Gibbs free energy (G) and its relation to spontaneity.
- Calculate free energy change using formation energies.
- Explain how temperature affects spontaneity.
- Relate standard free energy changes to equilibrium constants.
Gibbs Free Energy
- Relationship between enthalpy (H) and entropy (S):
  $riangle G = riangle H - T riangle S$
- Negative $riangle G$ indicates spontaneity; positive indicates nonspontaneity.
- This indicates direction toward equilibrium.
Calculating Free Energy
- Standard free energy changes $riangle G^ heta$ computed from standard enthalpy and entropy data (use tables for values).
Example Calculations
- Detail calculations for standard reactions and results in spontaneity predictions.

Entropy (S): Measure of dispersal of energy and matter within a system.
Gibbs Free Energy Change (G): State function for system enthalpy and entropy.
Spontaneous Process: Occurs without continuous energy input.
Nonspontaneous Process: Requires continuous energy input.
Standard Entropy (S°): Calculated entropy at standard conditions (1 bar, 298 K).
Standard Free Energy Change (ΔG°): Free energy change under standard states.

$S = k ext{ln}(W)$
Triangle S{univ} = riangle S{sys} + riangle S_{surr} $</li><li>$ riangle G = riangle H - T riangle S $$