# Entropy, Free Energy, and Equilibrium

Entropy, Free Energy, PowerPoint Lecture Presentation by J. David Robertson University of Missouri andChapter Equilibrium 18 Copyright The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Spontaneous Physical and Chemical Processes A waterfall runs downhill A lump of sugar dissolves in a cup of coffee

At 1 atm, water freezes below 0 0C and ice melts above 0 0C 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 spontaneous nonspontaneous 18.2 spontaneous nonspontaneous 18.2 Does a decrease in enthalpy mean a reaction proceeds

spontaneously? Spontaneous reactions CH4 (g) + 2O2 (g) CO2 (g) + 2H2O (l) H0 = -890.4 kJ H+ (aq) + OH- (aq) H2O (l) H0 = -56.2 kJ H2O (s) NH4NO3 (s) H2O (l) H0 = 6.01 kJ H2O

NH4+(aq) + NO3- (aq) H0 = 25 kJ 18.2 Entropy (S) is a measure of the randomness or disorder of a system. order disorder S S S = Sf - Si If the change from initial to final results in an increase in randomness

Sf > Si S > 0 For any substance, the solid state is more ordered than the liquid state and the liquid state is more ordered than gas state Ssolid < Sliquid << Sgas H2O (s) H2O (l) S > 0 18.3 Entropy

W=1 W = number of microstates S = k ln W S = Sf - Si S = k ln W=4 Wf Wi Wf > Wi then S > 0 W=6

Wf < Wi then S < 0 18.3 Processes that lead to an increase in entropy (S > 0) 18.2 How does the entropy of a system change for each of the following processes? (a) Condensing water vapor Randomness decreases

Entropy decreases (S < 0) (b) Forming sucrose crystals from a supersaturated solution Randomness decreases Entropy decreases (S < 0) (c) Heating hydrogen gas from 600C to 800C Randomness increases Entropy increases (S > 0) (d) Subliming dry ice Randomness increases Entropy increases (S > 0) 18.3

Entropy State functions are properties that are determined by the state of the system, regardless of how that condition was achieved. energy, enthalpy, pressure, volume, temperature, entropy Potential energy of hiker 1 and hiker 2 is the same even though they took different paths. 18.3 First Law of Thermodynamics Energy can be converted from one form to another but energy cannot be created or destroyed. Second Law of Thermodynamics The entropy of the universe increases in a spontaneous

process and remains unchanged in an equilibrium process. Spontaneous process: Suniv = Ssys + Ssurr > 0 Equilibrium process: Suniv = Ssys + Ssurr = 0 18.4 Entropy Changes in the System (Ssys) The standard entropy of reaction (S0rxn) is the entropy change for a reaction carried out at 1 atm and 250C. aA + bB S0rxn =

cC + dD [ cS0(C) + dS0(D) ] - [ aS0(A) + bS0(B) ] S0rxn = nS0(products) - mS0(reactants) What is the standard entropy change for the following reaction at 250C? 2CO (g) + O2 (g) 2CO2 (g) S0(CO) = 197.9 J/Kmol S0(O2) = 205.0 J/Kmol S0(CO2) = 213.6 J/Kmol S0rxn = 2 x S0(CO2) [2 x S0(CO) + S0 (O2)] S0rxn = 427.2 [395.8 + 205.0] = -173.6 J/Kmol

18.4 Entropy Changes in the System (Ssys) When gases are produced (or consumed) If a reaction produces more gas molecules than it consumes, S0 > 0. If the total number of gas molecules diminishes, S0 < 0.

If there is no net change in the total number of gas molecules, then S0 may be positive or negative BUT S0 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, S is negative. 18.4 Entropy Changes in the Surroundings (Ssurr) Exothermic Process Ssurr > 0 Endothermic Process

Ssurr < 0 18.4 Third Law of Thermodynamics The entropy of a perfect crystalline substance is zero at the absolute zero of temperature. S = k ln W W=1 S=0 18.3 Gibbs Free Energy Spontaneous process:

Suniv = Ssys + Ssurr > 0 Equilibrium process: Suniv = Ssys + Ssurr = 0 For a constant-temperature process: Gibbs free energy (G) G = Hsys -TSsys G < 0 The reaction is spontaneous in the forward direction.

G > 0 The reaction is nonspontaneous as written. The reaction is spontaneous in the reverse direction. G = 0 The reaction is at equilibrium. 18.5 The standard free-energy of reaction (G0rxn) is the freeenergy change for a reaction when it occurs under standardstate conditions. aA + bB cC + dD 0 Grxn

= [ cG0f (C) + dG0f (D) ] - [ aG0f (A) + bG0f (B) ] 0 Grxn = nG0f (products) - mG0f (reactants) Standard free energy of formation (G0f ) is the free-energy change that occurs when 1 mole of the compound is formed from its elements in their standard states. G0f of any element in its stable form is zero. 18.5 What is the standard free-energy change for the following reaction at 25 0C?

2C6H6 (l) + 15O2 (g) 12CO2 (g) + 6H2O (l) 0 Grxn = nG0f (products) - mG0f (reactants) 0 Grxn = [ 12G0f (CO2) + 6G0f (H2O)] - [ 2Gf0 (C6H6) ] 0 Grxn = [ 12x394.4 + 6x237.2 ] [ 2x124.5 ] = -6405 kJ -6156 249

Is the reaction spontaneous at 25 0C? G0 = -6405 kJ < 0 spontaneous 18.5 G = H - TS 18.5 Temperature and Spontaneity of Chemical Reactions CaCO3 (s) CaO (s) + CO2 (g)

K=? H0 = 177.8 kJ S0 = 160.5 J/K G0 = H0 TS0 At 25 0C (=298K), G0 = 177.8 kJ Tx160.5 J/K = 130.0 kJ > 0 No decomposition G0 = 177.8 kJ Tx160.5 J/K =0 solve for T, T835 0C 18.5 Gibbs Free Energy and Entropy Change for Phase Transitions (Eg, Vaporization of water)

For any equilibrium G0 = 0 = H0 TS0 H2O (l) S = H2O (g) H 40.79 kJ = T 373 K = 109 J/K S for a Phase Change = H for a Phase Change/T

18.5 Free Energy and Equilibrium Under any conditions, standard or nonstandard, the free energy change can be found this way: G = G + RT lnQ R is the gas constant (8.314 J/Kmol) T is the absolute temperature (K) Q is the reaction quotient (Under standard conditions, all concentrations are 1 M, so Q = 1 and lnQ = 0; the last term drops out.) Free Energy and Equilibrium At equilibrium, Q = K, and G = 0.

The equation becomes 0 = G + RT lnK Rearranging, this becomes G = RT lnK or, K = eG/RT G0 = RT lnK K = eG/RT 18.6 Alanine + Glycine G0 = +29 kJ

ATP + H2O + Alanine + Glycine G0 = -2 kJ Alanylglycine K<1 ADP + H3PO4 + Alanylglycine K>1 18.7 18.7 Chemistry In Action: The Thermodynamics of a Rubber Band H = G + TS Stretch a Rubber Band, then feel a its temperature High Entropy

Low Entropy Nonspontaneous (Work done), thus G Heat is generated, thus H Therefore, T S +, 0, +, 0, +, 0, - G = H - TS

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