Thermodynamics: Entropy, Free Energy, & Equilibrium McMurry & Fay ch. 16

A quick introduction to Entropy A measure of disorder possibilities

Factors affecting entropy Mixture vs. Pure Substance Number of Particles Volume Temperature Physical State

Will entropy increase or decrease in each reaction? H2C=CH2 (g) + Br2 (g)  BrCH2CH2Br (l) 2 C2H6 (g) + 7 O2 (g) 4CO2 (g) + 6 H2O (g) BaCl2 (s)  Ba2+ (aq) + 2 Cl- (aq)

Third law of thermodynamics The entropy of a perfectly ordered pure crystalline system is zero

Entropy increases with temperature As T increases, movement increases Crystals become more disordered Solid crystals can melt or sublime S = 0 only when T = 0 K!

Side effect of 3rd law: Can calculate total amount of entropy a substance has at temperatures above 0 K.

Standard entropy, S0: T = 298 K, P = 1 atm

Entropy is a State Function

DS0 of a reaction can be calculated using standard entropy tables: DS0rxn = S S0products - S S0reactants

Calculate DS0rxn for SO3 (g) + H2O (l) H2SO4 (aq)

Calculate DS0rxn for 4 Al (s) + 3 O2 (g)  2Al2O3 (s)

2nd law of thermodynamics Entropy is increasing in the universe

Entropy (S) DSuniverse > 0 How can DSsystem < 0?

Vocabulary: SPONTANEITY (Spontaneous reaction vs Vocabulary: SPONTANEITY (Spontaneous reaction vs. Non-spontaneous reaction) A measure of whether a reaction will continue to occur without outside input

Spontaneous reaction

Non-spontaneous reaction

Spontaneous or non-spontaneous? Ice cream melting at room temperature Water evaporating at room temperature Photosynthesis Propane burning Egg cooking

Will a reaction occur? Enthalpy: is there enough energy to make the reaction happen? Entropy: will this increase the entropy of the universe?

Gibbs Free Energy: A measure of spontaneity Combines enthalpic & entropic considerations at constant temperature and pressure: DG = DH –T DS Change in Entropy Change in Gibbs Free Energy Change in Enthalpy Temperature (K)

What DG represents Free energy = maximum work that can be done by a system

(some energy is lost as heat) What DG represents Free energy = maximum work that can be done by a system DE = q + w (some energy is lost as heat)

What DG values tell us DG < 0 reaction is spontaneous DG > 0 reaction is non- spontaneous DG = 0 system is at equilibrium (reverse reaction is spontaneous)

When is a reaction spontaneous? Always positive! DG = DH –T DS DH < 0, DS >0 T & DS are both positive -TDS must be negative Negative Reaction is always spontaneous

When is a reaction spontaneous? Always positive! DG = DH –T DS DH < 0, DS < 0 T is positive but DS is negative -TDS must be positive Negative Reaction is only spontaneous when T is small

When is a reaction spontaneous? Always positive! DG = DH –T DS DH > 0, DS < 0 T is positive but DS is negative -TDS must be positive Positive Reaction is only spontaneous when T is large

When is a reaction spontaneous? Always positive! DG = DH –T DS DH > 0, DS < 0 T is positive but DS is negative -TDS must be positive Positive Reaction is never spontaneous

DH DS Reaction is… - + Always spontaneous Spontaneous at low T Spontaneous at high T Never spontaneous

Two ways to calculate DG0 from thermodynamic tables Find DH0 & DS0 of reaction, use DG0 = DH0 – TDS0 Use values for DG0

Calculating DG0 using DH0 & DS0 DG0 = DH0 – (298.15K) DS0 Use standard heats of formation (DHf0) Use standard entropy from table (DS0) T

Is the reaction N2 (g) + 2 H2 (g)  N2H4 (g) spontaneous under standard conditions? DHf0 (N2H4) = 95.4 kJ/mol S0 (N2H4) = 23.4 J/mol K S0 (N2 gas) = 191.5 J/mol K S0 (H2 gas) = 130.6 J/mol K

DGf0rxn = S Gf0products – S Gf0reactants

Calculate DG0rxn for CaCO3 (s) + 2 HCl(aq)  CaCl2 (aq) + H2O (l) + CO2 (g)

Calculate DG0rxn for NaHCO3 (s) + HCl (aq)  NaCl (aq) + H2O (l) + CO2 (g)

DG at temperatures other than 25oC DGT = DH0 – TDS0

What is DG for the reaction CH4 + 3O2  CO2 + 2 H2O at 25 oC? at 250 oC? DGT ≈ DH0 – TDS0 DH0rxn = 802.3 kJ/mol DS0rxn = 404.8 J/mol K

DG values can be used to find phase change temperatures At a phase change boundary, two phases are in equilibrium

DG values can be used to find phase change temperatures At a phase change boundary, two phases are in equilibrium: DG0 = DH0 –T DS0 = 0

DG values can be used to find phase change temperatures DH0 –T DS0 = 0 DH0 = T DS0

DG values can be used to find phase change temperatures 𝑇= ∆𝐻 0 ∆𝑆 0

DH0: Fe (g) 416.3 kJ/mol S0 : Fe (s) 27.3 J/mol K Fe (g) 180.5 J/mol K At what temperature will solid iron vaporize? 𝑇= ∆𝐻 0 ∆𝑆 0 DH0: Fe (g) 416.3 kJ/mol S0 : Fe (s) 27.3 J/mol K Fe (g) 180.5 J/mol K

Free Energy and Equilibrium Temperature (Kelvin) DG = DG0 + RT ln Q Free energy change Standard free energy change (from table) Reaction quotient Gas constant

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At equilibrium DG = DG0 + RT ln Q DG0 = - RT ln K