 # Chemical Thermodynamics: Entropy, Free Energy and Equilibrium Chapter 18 18.1-18.6.

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Chemical Thermodynamics: Entropy, Free Energy and Equilibrium Chapter 18 18.1-18.6

Chemical Thermodynamics Science of interconversion of energy Science of interconversion of energy Heat into other forms of energy Heat into other forms of energy Amount of heat gained/released from a system Amount of heat gained/released from a system Spontaneity of a reaction Spontaneity of a reaction Gibbs free energy function Gibbs free energy function Relationship between Gibbs Free Energy and chemical equilibrium Relationship between Gibbs Free Energy and chemical equilibrium

Spontaneous Processes Main objective Main objective Spontaneous Reaction- a reaction does occur under specific conditions Spontaneous Reaction- a reaction does occur under specific conditions Non-spontaneous Reaction- a reaction does not occur under specific conditions Non-spontaneous Reaction- a reaction does not occur under specific conditions

Spontaneous Processes A waterfall runs downhill A lump of sugar dissolves in a cup of coffee At 1 atm, water freezes below 0ºC and ice melts above 0ºC Heat flows from a hotter object to a colder object Iron exposed to oxygen and water forms rust

Spontaneous Processes

Does a decrease in enthalpy mean a reaction proceeds spontaneously? Spontaneous reactions CH 4 (g) + 2O 2 (g) CO 2 (g) + 2H 2 O (l)  H 0 = -890.4 kJ H + (aq) + OH - (aq) H 2 O (l)  H 0 = -56.2 kJ H 2 O (s) H 2 O (l)  H 0 = 6.01 kJ NH 4 NO 3 (s) NH 4 + (aq) + NO 3 - (aq)  H 0 = 25 kJ H2OH2O

Entropy To predict spontaneity we need: To predict spontaneity we need: Change in enthalpy Change in enthalpy Entropy Entropy Entropy- a measure of the randomness or disorder of a system. Entropy- a measure of the randomness or disorder of a system. ↑ Disorder = ↑ Entropy ↑ Disorder = ↑ Entropy

Entropy New Deck Order New Deck Order Shuffled Deck Order Shuffled Deck Order Probability Probability Ordered state Ordered state Disordered State Disordered State

Microstates and Entropy

Boltzmann, 1868 Boltzmann, 1868 S = k ln W S = k ln W k = 1.38 x 10 -23 J/K k = 1.38 x 10 -23 J/K ↑ W = ↑ Entropy ↑ W = ↑ Entropy ∆ S = S f – S i ∆ S = S f – S i ∆ S = k ln W f ∆ S = k ln W f W i W i W f > W i then  S > 0 W f < W i then  S < 0

Entropy and Disorder Entropy and Disorder If the change from initial to final results in an increase in randomness S f > S i  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 S solid < S liquid << S gas

Entropy and Disorder

How does the entropy of a system change for each of the following processes? (a) Forming sucrose crystals from a supersaturated solution Randomness decreases Entropy decreases (  S < 0) (b) Heating hydrogen gas from 60 0 C to 80 0 C Randomness increases Entropy increases (  S > 0)

Entropy and Disorder

Standard Entropy Standard Entropy The standard entropy of reaction (  S 0 ) is the entropy change for a reaction carried out at 1 atm and 25 0 C. rxn

The Second Law of Thermodynamics The entropy of the universe increases in a spontaneous process and remains unchanged in an equilibrium process. The entropy of the universe increases in a spontaneous process and remains unchanged in an equilibrium process. Importance? Importance? Spontaneous process:  S univ =  S sys +  S surr > 0 Equilibrium process:  S univ =  S sys +  S surr = 0

Entropy Changes in the System To calculate ΔS univ, we need both ΔS sys ΔS surr To calculate ΔS univ, we need both ΔS sys ΔS surr ΔS sys ΔS sys aA + bB cC + dD S0S0 rxn nS 0 (products) =  mS 0 (reactants)  -

Entropy Changes in the System

When gases are produced (or consumed) If a reaction produces more gas molecules than it consumes,  S 0 > 0. If the total number of gas molecules diminishes,  S 0 < 0. If there is no net change in the total number of gas molecules, then  S 0 may be positive or negative BUT  S 0 will be a small number.

Entropy Changes in the System

Entropy Changes in the Surroundings

ΔS surr = -ΔH sys T Using the information from Example 18.2, determine whether or not the reaction is spontaneous. N 2 (g) + 3H 2 (g) → 2 NH 3 (g) ΔHº rxn = -92.6 kJ/mol ΔS sys = -199 J/K ∙ mol ΔS sys = -199 J/K ∙ mol ΔS surr = -(-92.6 x 1000) J/mol ΔS surr = -(-92.6 x 1000) J/mol 298 K 298 K ΔS surr = 311 J/mol ΔS surr = 311 J/mol ΔS univ = ΔS sys + ΔS surr ΔS univ = ΔS sys + ΔS surr ΔS univ = -199 J/K ∙ mol + 311 J/mol ΔS univ = -199 J/K ∙ mol + 311 J/mol ΔS UNIV = 112 J/K ∙ mol ΔS UNIV = 112 J/K ∙ mol

The Third Law of Thermodynamics and Absolute Entropy Third Law of Thermodynamics- the entropy of a perfect crystalline substance is zero at the absolute zero of temperature. Third Law of Thermodynamics- the entropy of a perfect crystalline substance is zero at the absolute zero of temperature.

Gibbs Free Energy Predicts the direction of a spontaneous reaction. Predicts the direction of a spontaneous reaction. Uses properties of the system to calculate. Uses properties of the system to calculate. For a constant pressure-temperature process: For a constant pressure-temperature process:  G =  H sys -T  S sys  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.

Standard Free-Energy Changes Standard Free-Energy Changes The standard free-energy of reaction (  G 0 ) is the free- energy change for a reaction when it occurs under standard- state conditions. rxn Standard free energy of formation (  G 0 ) is the free-energy change that occurs when 1 mole of the compound is formed from its elements in their standard states. f G0G0 rxn n  G 0 (products) f =  m  G 0 (reactants) f  -

Standard Free-Energy Changes

Factors Affecting ΔG

Free Energy and Chemical Equilibrium Free Energy and Chemical Equilibrium  G =  G 0 + RT lnQ R is the gas constant (8.314 J/K mol) T is the absolute temperature (K) Q is the reaction quotient At Equilibrium  G = 0 Q = K 0 =  G 0 + RT lnK  G 0 =  RT lnK

Free Energy and Chemical Equilibrium

Thermodynamics of a Rubber Band

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