Chapter 8: Entropy, Free Energy and the Second Law of Thermodynamics University Chemistry   Chapter 8: Entropy, Free Energy and the Second Law of Thermodynamics Copyright © The McGraw-Hill Companies, Inc.  Permission required for reproduction or display.

Spontaneous Processes A spontaneous reaction occurs without external intervention under the given set of conditions. A reaction is nonspontaneous if it does not occur without external intervention under the specified set of conditions.. Spontaneous (자발적) Nonspontaneous (비자발적) In general, processes that occur spontaneously in one direction cannot, under the same conditions, also take place spontaneously in the reverse direction.

The expansion of a gas into an evacuated bulb is spontaneous, Heat flows from a hotter object to a colder one, but the reverse never happens spontaneously. The expansion of a gas into an evacuated bulb is spontaneous, but the reverse process (the concentration of all the molecules into one bulb) is nonspontaneous. A piece of sodium metal reacts violently with water to form sodium hydroxide and hydrogen gas, but hydrogen gas does not react with sodium hydroxide to form water and sodium metal. Iron exposed to water and oxygen forms rust, but rust does not spontaneously change back to iron. Can we predict the direction? Quantitatively? By enthalpy?

Does a decrease in enthalpy mean a reaction proceeds spontaneously? Spontaneous reactions CH4 (g) + 2O2 (g) CO2 (g) + 2H2O (l) DH0 = -890.4 kJ H+ (aq) + OH- (aq) H2O (l) DH0 = -56.2 kJ H2O (s) H2O (l) DH0 = 6.01 kJ NH4NO3 (s) NH4+(aq) + NO3- (aq) DH0 = 25 kJ H2O

How do we tell the direction of a spontaneous process? Reversibly Exothermic Process Irreversibly Exothermic Process Heat Transfer to the Surroundings Define entropy change:

Statistical Definition of Entropy The microstates that arise from the combination of two dice and the corresponding macrostates. The most probable macrostate has an overwhelmingly large number of microstates compared to other macrostates.

Microstates, Entropy, and the Second Law of Thermodynamics Some possible ways of distributing four molecules between two equal compartments. Entropy is a measure of the number of possible microstates available to a system in a given macrostate. Entropy change

Second law of thermodynamics: The entropy of any isolated system increases in any spontaneous process and remains unchanged in an equilibrium (reversible) process. spontaneous process: reversible (or equilibrium) process: DSuniv is negative, the process is nonspontaneous in the direction described. Instead, it is spontaneous in the opposite direction.

Processes that lead to an increase in entropy (DS > 0)

Thermodynamic Definition of Entropy between two states A and B Clausius inequality Constant T Constant T

Entropy Change Due to Heating

Phase Transitions

The Efficiency of Heat Engines: The Carnot Cycle A Simple Heat Engine

Department of Chemistry, KAIST Sadi Carnot invented such a conceptual engine in 1824, which operates in a cycle consisting of the 4 reversible cycles shown in Fig.11.5. Isothermal expansion Adiabatic compression Net work Adiabatic expansion Isothermal compression P-V diagram for the Carnot Cycle Department of Chemistry, KAIST

Carnot heat engine, four-step cycle: For a cyclic process: DUsys(cycle) = 0 DSsys(cycle) = 0.

efficiency (e) Restrictions: second law

Carnot engine working in the reverse direction. coefficient of performance Refrigerators and air conditioners supply work to remove heat qc from a cold heat source and deposit heat qh into a hot heat sink.

Changes in temperature Third law of thermodynamics states that the entropy of a pure substance in its thermodynamically most stable form (i.e., crystalline form) is zero at the absolute zero of temperature, independent of pressure. Or for a pure substance in its thermodynamically most stable state the absolute entropy is zero. Changes in temperature Third law entropies Third-law entropies per mole of material measured at the standard pressure of 1 bar are referred to as standard molar entropies, denoted by So.

The increase in the entropy of a substance at constant pressure from absolute zero to its gaseous state at some temperature. phase transitions

Residual entropy: value of the entropy at 0 K for systems for which the third law is not applicable. real crystal defects in orientation S > 0 at 0 K. defect free arrangement third law will hold for this crystal, S = 0 at 0 K. experimental

Entropy Changes in the System by Reaction(DSrxn) Standart state: most stable state at p=1 atm at a given T The standard entropy of reaction (DS0 ) is the difference in standard entropies between the products and reactants: rxn aA + bB cC + dD DS0 rxn dS0(D) cS0(C) = [ + ] - bS0(B) aS0(A) What is the standard entropy change for the following reaction at 250C? 2CO (g) + O2 (g) 2CO2 (g) S0(CO) = 197.9 J K-1 mol-1 S0(CO2) = 213.6 J K-1 mol-1 S0(O2) = 205.0 J K-1 mol-1 DS0 rxn = 2 x S0(CO2) – [2 x S0(CO) + S0 (O2)] DS0 rxn = 427.2 – [395.8 + 205.0] = -173.6 J K-1 mol-1

A guideline to judge the sign of DSrxn When gases are produced (or consumed) If a reaction produces more gas molecules than it consumes, DS0 > 0. If the total number of gas molecules diminishes, DS0 < 0. If there is no net change in the total number of gas molecules, then DS0 may be positive or negative BUT DS0 will be a small number. What is the sign of the entropy change for the following reaction? 2Zn (s) + O2 (g) 2ZnO (s) The total number of gas molecules goes down, DS is negative.

Temperature Dependence of Standard Entropy Changes Assume is temperature independent.

Spontaneity and Gibbs Free Energy Spontaneity in a nonisolated system at constant T Clausius inequality: constant P

Define Gibbs free energy by Spontaneity criterion for a process occurring at constant P and T, DGsystem < 0 for a spontaneous process at constant T & P DGsystem = 0 reversible process (or simply DG = 0) DGsystem < 0 forbidden process

Gibbs Free Energy and Nonexpansion Work DU = q + w We will see in Chap. 13 that Wmax electric = -DGchem reaction

states are converted to products in their standard states. Standard Gibbs free energy of reaction (DG°rxn) is the Gibbs free energy change for a reaction that occurs under standard-state conditions when reactants in their standard states are converted to products in their standard states. aA + bB cC + dD DG0 rxn dDG0 (D) f cDG0 (C) = [ + ] - bDG0 (B) aDG0 (A) Standard Gibbs free energy of formation (DGf0) of a compound is the Gibbs free-energy change that occurs when 1 mole of the compound is synthesized from its elements in their standard states. DG0 of any element in its stable form is zero. f

Temperature Dependence of DG DH and DS are both +, DG will be + at low temperatures (where enthalpy dominates) and become - at high temperatures (where entropy dominates). The temperature at which DG crosses over from + to - (when DH = T DS) depends upon the relative magnitudes of DH and DS. DH is + and DS is -, DG will always be positive regardless of temperature. DH is - and DS is +, DG will always be negative regardless of temperature. DH and DS are both -, DG will be - at low temperatures (where enthalpy dominates) and become + at high temperatures (where entropy dominates). The temperature at which DG crosses over from - to + (when DH = T DS) depends upon the relative magnitudes of DH and DS.

Equilibrium Pressure of CO2 Temperature and Spontaneity of Chemical Reactions CaCO3 (s) CaO (s) + CO2 (g) DH0 = 179.2 kJ Equilibrium Pressure of CO2 DS0 = 160.0 J K-1 DG0 = DH0 – TDS0 At 25 0C, DG0 = 131.5 kJ For DG0 = 0 0 = DH0 – TDS0 DG0 = 0 at 830 0C

The Thermodynamics of a Rubber Band DG = DH - TDS Upon stretching DG > 0 DS < 0 Heat is released, DH < 0 High Entropy Low Entropy

Mixing of Pure Substances

DHmix = 0, Avogadro’s law entropy of mixing Gibbs free energy of mixing,

For an ideal solution. ideal solution

Coupled reactions: In systems, unfavorable reactions are coupled to energetically favorable processes. The smaller weight will move upward (a nonspontaneous process) by coupling it with the falling of a larger weight ( a spontaneous process).

The Structure of ATP and ADP in Ionized Forms -

- Alanine + Glycine Alanylglycine DG0 = +29 kJ 31 kJ mol-1 -31 kJ mol-1 Alanine + Glycine Alanylglycine DG0 = +29 kJ - ATP + H2O + Alanine + Glycine ADP + H3PO4 + Alanylglycine DG0 = -31 kJ + 29 kJ = -2 kJ