2-25-25

Course Information

• Course Title: General Chemistry 1B 2025

• Instructor: Dr. A. J. Shaka

• Institution: University of California, Irvine

• Quarter: Winter Quarter 2025

• Course Code: 40120

Lecture Topics

• Lecture 13:

  • Enthalpy of Formation

  • Third Law Entropy

  • Free Energy

Enthalpy of Formation

• Definition:

  • The enthalpy of formation is the heat absorbed or released when making one mole of a compound from its elements in their standard states.

  • By convention, enthalpy of formation of any element is set to zero.

• Analogy:

  • Similar to how sea level is assigned a height of zero.

  • Without this convention, differences in height would have to be recorded for every location.

• Example:

  • For the reaction: [ N_2(g) + O_2(g) \rightarrow N_2O(g) ]

    • The enthalpy of formation, ( \Delta H_f^\circ ) for N2O is +82.05 kJ/mol.

    • Assumed conditions: 298.15 K and 1 atm pressure.

  • Note: This reaction may not occur under standard lab conditions.

• Warnings about Enthalpy Values:

  • Enthalpy values apply strictly to the written reaction.

  • If a reaction is multiplied by a number, multiply the ( \Delta H ) by that same number.

  • Enthalpy is described per mole of product formed; sometimes fractions are needed to balance reactions.

• Physical State Considerations:

  • Enthalpy of formation values vary depending on the physical state of the substance, e.g.:

    • Liquid water: ( H_2O(l) \Delta H_f^\circ = -285.8 , \text{kJ/mol} )

    • Water vapor: ( H_2O(g) \Delta H_f^\circ = -241.8 , \text{kJ/mol} )

Application: Practice Problem 29

• Scenario:

  • Decomposition of ammonia: [ 4NH_3(g) \rightarrow 2N_2(g) + 6H_2(g) ]

    • Ammonia’s formation reaction serves as a point for decomposition calculations.

• Methodology:

  • Find the standard enthalpy of formation of ammonia (given: ( \Delta H_f^\circ = -46 , \text{kJ/mol} )).

  • Convert forward reaction to enthalpy values for product formation reactions.

• Results:

  • Total calculated enthalpy change for the reaction: ( \Delta H = -812 , \text{kJ} )

Third Law of Thermodynamics

• Ludwig Boltzmann's Contribution:

  • Developed a statistical theory defined by the equation:[ S = k , ln W ]

  • Where ( k ) is Boltzmann’s constant, ( S ) is absolute entropy, and ( W ) is the number of possible microstates.

• Absolute Zero and Perfect Crystals:

  • At absolute zero (0 Kelvin), there is no thermal energy available for a perfect crystal, yielding:[ S = k , ln 1 = 0 ]

  • Thus, the entropy of a perfect crystal at absolute zero is defined as zero, which gives rise to the Third Law.

Free Energy and Spontaneous Changes

• Understanding ( \Delta G ):

  • At constant temperature, the surroundings can be treated as an infinite heat bath.

  • Heat exchange occurs while maintaining constant temperature.

• Spontaneity Criterion:

  • The criterion for spontaneity is given by ( \Delta S_{universe} \geq 0 ).

  • Connects system changes to thermodynamic potentials.

• Equating Enthalpy and Entropy Changes:

  • At constant pressure and temperature:[ \Delta G = \Delta H - T \Delta S \leq 0 ]

Entropy and Phase Changes

• Third Law Application:

  • Entropy can be directly calculated from the behavior of a perfect crystal at absolute zero, advancing further to relate heat added.

• Phase Change Considerations:

  • In phase transitions, entropy changes can be evaluated using: [ \Delta S = \frac{\Delta H_{Transition}}{T_{Transition}} ]

  • An example includes melting and boiling points as equilibria with ( \Delta G = 0 ).

• Example Problem 30:

  • Calculate changes in entropy for water heating from 50.0 °C to 150.0 °C using specific heat capacities and the enthalpy of vaporization.

  • Final result reflects a positive entropy change (( \Delta S = 248.96 , J/K )).

Irreversible Processes

• General Rule:

  • Any real process has ( \Delta S_{universe} > 0 ).

• Example:

  • Two copper blocks come to a common temperature demonstrating an increase in total entropy of the universe through heat transfer leading to equalized temperatures.

• Implication:

  • Entropy changes reflect the direction of spontaneous processes, emphasizing that irreversible processes remain non-reversible in nature.