Lecture 6: Thermodynamics and Gibbs Free Energy

Lecture Overview

  • Focus of Lecture 6:

    • More on Entropy and Gibbs Free Energy

    • Equilibrium Constant

    • Applications of the First Law of Thermodynamics and Thermochemistry

    • Instructor: Khashayar Ghandi (kghandi@uoguelph.ca)

Entropy and Spontaneity

  • Criterion for a Spontaneous Reaction Away from Equilibrium:

    • The entropy (B) of the system and surroundings must increase.

    • Definition of Gibbs Free Energy (G):
      G = H - TS

    • Key inequalities:

    • T riangle S > riangle H

    • riangle H - T riangle S < 0

    • Alternatively, can be expressed as:
      riangle H < T riangle S

Chemical Equilibrium

  • Definition: At chemical equilibrium, the concentrations and pressures of reactants and products do not change.

  • Equilibrium Constant:

    • The relationship of equilibrium concentrations

    • For gaseous reactions, expressed as partial pressures (K = K_p)

    • For liquid solutions, expressed in molarities (K = K_c).

  • Concentration and Activity:

    • Activity is a dimensionless quantity representing concentration or partial pressure relative to a unit concentration.

    • For a dissolved substance B:
      ext{Activity} = rac{c_B}{c ^{ ext{°}}} where $c^{ ext{°}} = 1 ext{ mol·L}^{-1}$.

    • For a gas G:
      ext{Activity} = rac{p_G}{p^{ ext{°}}}

Equilibrium Constant Expression - Example

  • Example Reactions:

    1. N2O4(g)
      ightleftharpoons 2NO_2(g)

    2. Zn(s) + 2H^+(aq)
      ightleftharpoons Zn^{2+}(aq) + H_2(g)

  • The expressions for the equilibrium constant K can be derived from the stoichiometric coefficients.

Gibbs Free Energy and Work

  • At a given temperature, the Gibbs Free Energy (G) calculation can be addressed via:

    • riangle G = riangle H - T riangle S

    • riangle G = w + P riangle V

    • Also, riangle G = w_{ ext{other}} at constant pressure leading to insights about chemical spontaneity.

  • Utility in Work:

    • Spontaneous reactions can perform useful work such as in gasoline combustion or battery reactions, utilized in vehicles.

    • Additionally, facilitate energy for non-spontaneous reactions, which is significant in biology.

Exergonic vs. Endergonic Processes

  • Definitions:

    • Exergonic Processes:

    • Characterized by a negative Gibbs free energy change ($ riangle G < 0$).

    • Endergonic Processes:

    • Characterized by a positive Gibbs free energy change ($ riangle G > 0$).

  • It is crucial for sustaining life to couple exergonic and endergonic reactions in cells.

Changes in Gibbs Free Energy under Equilibrium Conditions

  • If pressure changes near chemical equilibrium:

    • riangle G = V riangle P

    • The relationship can be detailed as:
      riangle Gf - riangle Gi = nRT rac{ riangle P}{P}
      G - G^{ ext{∘}} = nRT ext{ln} rac{P}{1}

    • Final form is:
      G = G^{ ext{∘}} + nRT ext{ln} P

    • Free Energy Change Formula:
      riangle G = riangle G^{ ext{∘}} + RT ext{ln} Q

  • At equilibrium, riangle G = 0 and Q = K, leading to:

    • riangle G^{ ext{∘}} = -RT ext{ln} K

Standard Gibbs Free Energies of Formation

  • Definition:

    • Change in Gibbs free energy when 1 mole of substance forms from its elements in standard states at 1 atm and a specified temperature (commonly 25°C).

  • Comparison with standard enthalpy of formation:

    • riangle Hf^{ ext{∘}} matches $ riangle Gf^{ ext{∘}}$ methodology.

Standard Entropies and Their Calculation

  • **Entropy Change for a Reaction:

    • Conditions leading to increased entropy include:**

    1. Reactions producing smaller molecules from a larger one (increase in count).

    2. Reactions that increase the number of moles of gas.

    3. Phase changes from solid to liquid/gas or liquid to gas.

  • Standard State for Entropy (S°):

    • Defined for pure substance as 1 atm pressure or a 1 M solution.

    • To compute riangle S^{ ext{°}}:

    • riangle S^{ ext{°}} = ext{Sum of } nS^{ ext{°}} ext{ (products)} - ext{Sum of } nS^{ ext{°}} ext{ (reactants)}

Standard Entropies Table (25°C)

  • Table 18.1 Examples of Standard Entropies:

    • Common values to note include:

    • $e^{-}$ (g): 20.87 J/(mol-K)

    • Br₂(g): 245.3 J/(mol-K)

    • NH3(g): 192.7 J/(mol-K)

    • Cl2(g): 223.0 J/(mol-K)

    • Ca(s): 41.59 J/(mol-K)

    • H2O(l): 69.95 J/(mol-K)

Practice Examples

  • Example 3: Calculation of heat required to heat a piece of 35.8 g zinc from 20.00°C to 28.00°C using its specific heat of 0.388 J/(g K).

  • Example 4: Estimation of enthalpy change using bond energies for the reaction:

    • Bonds Broken and Formed:

    • Bonds Broken: 1 C=C (602 kJ), 1 Cl—Cl (240 kJ) = 842 kJ

    • Bonds Formed: 1 C—C (346 kJ), 2 C—Cl (654 kJ) = 1000 kJ

    • Total Change: riangle H = 842 kJ - 1000 kJ = -158 kJ

  • Example 5: The combustion of nitromethane ext{CH}3 ext{NO}2 in oxygen leading to temperature measurements.

Additional Examples and Questions

  • Further explorations in energy transformations through chemical reactions noting experimental parameters, calculations, signs of enthalpy and entropy changes along with temperature effects.

  • Example analyses could include classical calorimetry and reaction energetics in practical applications, guided through structured problem-solving methods.