Chapter 17

Spontaneous Physical and Chemical Processes

  • Examples of Spontaneous Processes:

    • A waterfall runs downhill.

    • A lump of sugar dissolves in a cup of coffee.

    • At 1 atm, water freezes below 0°C and ice melts above 0°C.

    • Heat flows from a hotter object to a colder object.

    • A gas expands in an evacuated bulb.

    • Iron exposed to oxygen and water forms rust.

Spontaneity and Enthalpy

  • Understanding Spontaneity:

    • Queries if a decrease in enthalpy indicates spontaneous reactions.

    • Sample reaction:

    • ext{C}{2} ext{H}{2}(g) + 2 ext{O}{2}(g) ightarrow 2 ext{CO}{2}(g) + ext{H}_{2} ext{O}(l)

    • ext{Δ}H° = -890.4 ext{ kJ/mol} \ ext{H}{2} ext{O}(s) ightarrow ext{H}{2} ext{O}(l) \ ext{Δ}H° = +6.01 ext{ kJ/mol}

    • ext{NH}4 ext{NO}3(s)
      ightarrow ext{NH}4^+(aq) + ext{NO}3^-(aq) \ ext{Δ}H° = +25 ext{ kJ/mol}

Entropy

  • Definition of Entropy (S):

    • A measure of how spread out or dispersed the energy of a system is among the various ways that energy can exist within that system.

Change in Entropy

  • Mathematical Representation:

    • ΔS = Sf - Si

    • If the process results in an increase in energy dispersal, then ΔS > 0

    • Solid > Liquid > Gas:

      • S{ ext{solid}} < S{ ext{liquid}} < S_{ ext{gas}}

  • Microstates and Entropy:

    • W = ext{number of microstates} \ S = k ext{ln} W \

    • If Wf > Wi , then ΔS > 0

    • If Wf < Wi , then ΔS < 0

Processes That Lead to Increased Entropy

  • Any physical change that increases the number of microstates leads to a positive change in entropy (e.g., phase changes such as evaporation).

Examples of Spontaneous Reactions

  • Examples with changes in Entropy:

    • ext{Br}2(l) ightarrow ext{Br}2(g) \ ΔS > 0

    • ext{I}2(s) ightarrow ext{I}2(g) \ ΔS > 0

State Functions

  • Definition:

    • Properties determined by the state of the system, independent of how the condition was achieved (e.g., energy, enthalpy, pressure, volume, temperature, entropy).

  • Example: Potential energy of two hikers at different paths remains the same if they reach the same elevation.

Standard Entropy Values


  • Table of Standard Entropy Values at 25°C:

    Substance

    S° (J/K mol)


    H2O(l)

    69.9


    H2O(g)

    188.7


    Br2(l)

    152.3


    Br2(g)

    245.3


    I2(s)

    116.7


    I2(g)

    260.3


    C(diamond)

    2.4


    C(graphite)

    5.69


    CH4(methane)

    186.2


    C2H6(ethane)

    229.5


    He(g)

    126.1


    Ne(g)

    146.2

    Example Calculations of Entropy Changes

    Example 17.1

    • Predicting Entropy Change Direction:

      1. Freezing Ethanol:

      • Phase change results in rigid structure, thus ΔS < 0

      1. Evaporating Bromine:

      • Increases microstates; ΔS > 0

      1. Dissolving Glucose in Water:

      • Increased dispersal of matter; ΔS > 0

      1. Cooling Nitrogen from 80°C to 20°C:

      • Decrease in molecular motion; ΔS < 0

    Thermodynamic Laws

    • First Law of Thermodynamics:

      • Energy conversion principle: Energy can be converted from one form to another, but cannot be created or destroyed.

    • Second Law of Thermodynamics:

      • Entropy Dynamics:

      • The entropy of the universe increases in spontaneous processes.

      • ΔS{univ} = ΔS{sys} + ΔS_{surr} > 0 for spontaneous processes.

      • In equilibrium processes, ΔS_{univ} = 0

    Standard Entropy Change for Reactions

    • Definition of Standard Entropy of Reaction (ΔS°₍rxn₎):

      • Entropy change under standard conditions (1 atm, 25°C). [ ΔS° = ΣS{products} - ΣS{reactants} ]

    Example of Standard Entropy Change Calculations

    Example 17.2

    • Calculating Standard Entropy Changes:

      1. For the reaction: [ ext{CaCO}3(s) ightarrow ext{CaO}(s) + ext{CO}2(g) ]

        • Use standard entropy values:

        • ΔS°{rxn} = S{CaO} + S{CO2} - S{CaCO3}

        • Example calculation yields 160.5 ext{ J/K mol} increase in entropy.

      2. Other reactions:

      • Similar calculations can be made for other reactions listed (N2 + H2 → NH3).

    Gas Production Impact on Entropy

    • Gas Production and Entropy Sign:

      • Producing more gas molecules: ΔS° > 0

      • Consuming gas molecules: ΔS° < 0

      • No net change in gas molecules may yield small ΔS° values.

    Strategies for Predicting Signs of Entropy Change

    Example 17.3

    • Predicting Sign of Entropy Change:

      1. Reaction (H2 + O2 → H2O):

      • Net reduction of gases to liquids → ΔS° < 0

      1. Solid to gas (NH4Cl):

      • Produces gaseous products → ΔS° > 0

      1. Equal number of gaseous molecules (H2 + Br2 → 2HBr):

      • Cannot predict ΔS° precisely, expect small magnitude.

    Entropy Changes in Surroundings

    • Exothermic Processes:

      • ΔS_{surr} > 0

    • Endothermic Processes:

      • ΔS_{surr} < 0

    Third Law of Thermodynamics

    • Definition:

      • The entropy of a perfect crystalline substance is zero at absolute zero temperature.

      • S = k ext{ln} W \ (W=1)\Rightarrow S=0

    Standard Free Energy Change

    • Standard Free Energy of Reaction (ΔG°₍rxn₎):

      • Defined as the change in free energy under standard state conditions. [ ΔG{rxn} = ΣG{products} - ΣG_{reactants} ]

      • The standard free energy of formation (ΔG°₍f₎) of elements in their standard state is zero.

    Gibbs Free Energy and Spontaneity

    • Equilibrium and Spontaneity:

      • ΔG < 0 indicates spontaneous reaction in forward direction.

      • ΔG > 0 indicates nonspontaneous reaction; spontaneous in reverse.

      • ΔG = 0 indicates system at equilibrium.

    Conventions for Standard States

    • Definition:

      • The most stable form of a substance at 25°C and 1 atm.

    Example Calculations of Standard Free Energy Changes

    Example 17.4

    1. For the reaction [ ext{CH}4(g) + 2 ext{O}2(g) → ext{CO}2(g) + 2 ext{H}2 ext{O}(l) ]

      • Calculate using standard free energy values from Appendix 3.

    2. For the equation [ 2 ext{MgO}(s) → 2 ext{Mg}(s) + ext{O}_2(g) ]

      • Follow similar calculation as above,

      • Incorporate equation ΔG = ΔGf^{products} - ΔGf^{reactants} to compute.

    Control Efficiency of Heat Engines

    • Efficiency Formula:

      • ext{Efficiency} = rac{Th - Tc}{Th} imes 100 ext{%} Where $Th$ is the high temperature and $T_c$ is the cold temperature of the engine.

    Relationship of ΔG, ΔH, and ΔS

    • Mathematical Expression: [ ΔG = ΔH - TΔS ]

      • This equation relates Gibbs free energy to changes in enthalpy and entropy.

    Temperature and Chemical Reactions

    • Example on Factors Affecting Gibbs Free Energy:

      • Provided reactions involving calcium carbonate, its decomposition, changes in temperatures and changes in entropies.

    Gibbs Free Energy and Phase Transitions

    • Mathematical Representation for Phase Transition:

      • When considering phases: [ ΔG = ΔHT - T ΔSl ]

    Calculating Entropy Changes for Phase Transitions

    Example 17.5

    1. Calculating entropy changes for solid → liquid (melting) phase change of benzene:

      • ΔS{fus} = rac{ΔH{fus}}{T_{melt}}

      • Use heats of fusion at appropriate volume and pressure conditions.

    2. Calculating liquid → vapor:

      • Similar process for vaporization at 80.1°C.

    Gibbs Free Energy and Chemical Equilibrium

    • Formulation: [ ΔG = ΔG° + RT ext{ln} Q ]

    • At equilibrium, [ ΔG = 0 ]

    Relationship of ΔG and K

    • Connection between Free Energy and Equilibrium Constant: [ ΔG° = -RT ext{ln} K ]

      • K values are influenced based on ΔG° and predict product/reactant favorability.

    Calculating Equilibrium Constants (Kp)

    Example 17.6

    1. Calculation for the reaction [ ext{2H}2(g) + ext{O}2(g) ↔ 2 ext{H}_2 ext{O}(g) ]

      • Utilize free energy changes and connect to equilibrium constant computation.

    Example of Solubility Product and Free Energy Calculation

    Example 17.7

    1. Calculate ΔG° from Ksp for AgCl process

      • Use solubility product to infer Gibbs free energy change during precipitation.

    Calculate ΔG under Non-Standard The T Conditions

    Example 17.8

    Claims to calculate the non-standard ΔG based on given pressures of each reactant and utilizing known equilibrium constants under non-standard concentrations.

    Predict the Direction of Net Reaction

    • Net reaction determined by comparing the free energy results between standard and non-standard states.

    Conclusion and Summary

    • The knowledge of entropy and free energy dynamics aids in understanding spontaneity and equilibrium in chemical processes. Concepts related to Gibbs Free Energy and statistical mechanics play a pivotal role in thermodynamics.