13.5: Entropy Changes and Spontaneity

Learning Objectives

• Understand and explain the second and third laws of thermodynamics.
• Calculate entropy changes for phase transitions and chemical reactions under standard conditions.

Connecting Entropy and Heat to Spontaneity

• Entropy is a key property that can predict the spontaneity of a process.
• Processes with an increase in system entropy (S_sys > 0) are often spontaneous, but not always.
• Total Entropy (S_univ): Includes both the system and surroundings.
  • Formula: S_univ = S_sys + S_surr

Thermodynamic Models

1. Heat flows spontaneously from hot to cold:

   • S_sys = q_rev/T_sys
   • S_surr = q_rev/T_surr
   • Results in an increase in S_univ since T_sys > T_surr.

2. Heat flows from cold to hot:

   • Non-spontaneous, results in a decrease in S_univ.

3. Reversible Heat Flow (T_sys ≈ T_surr):

   • No net change in S_univ.

• Second Law of Thermodynamics: All spontaneous changes increase the entropy of the universe (S_univ > 0).

Entropy and Spontaneity

• For large surroundings, q_surr is a good approximation of q_rev.
• Spontaneity check:
  • Formula: S_univ = S_sys + q_surr/T

Example: Ice Melting

• Entropy Change: H2O(s) to H2O(l) is 22.1 J/K.
• Heat required: 6.00 kJ.
• At -10.0 °C: Non-spontaneous (S_univ < 0).
• At +10.0 °C: Spontaneous (S_univ > 0).

Exercise: Water Freezing

• Freezing is the reverse of melting.
• At -10.0 °C: Freezing is spontaneous, +0.7 J/K.
• At +10.0 °C: Freezing is non-spontaneous, -0.9 J/K.

Summary

• Second Law: Spontaneous processes increase the universe's entropy.
• Non-spontaneous processes have S_univ < 0.
• At equilibrium, S_univ = 0.

Key Equations

• S = S_298(products) - S_298(reactants)
• S = q_rev/T
• S_univ = S_sys + S_surr
• S_univ = S_sys + q_surr/T

Contributors and Attributions

• Content by Paul Flowers, Klaus Theopold, and Richard Langley.
• Licensed under CC BY OpenStax.

This summary provides a detailed understanding of entropy changes and their relation to spontaneity in thermodynamic processes.