Entropy (S) is a measure of the randomness or disorder of a system. orderS disorder S  S = S f - S i 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 H 2 O (s) H 2 O (l)  S > 0

Entropy Changes in the System (  S sys ) 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. Also remember that S(gas) >> S(liquid) > S(solid) As temperature increases, S increases Changes in # gas molecules have the greatest impact by far!!

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 60 0 C to 80 0 C Randomness increases Entropy increases (  S > 0) (d) 2 H 2 (g) + O 2 (g)  2H 2 O(g) Randomness decreases Entropy decreases (  S < 0) (d) H 2 O(g) + C(s)  H 2 (g) + CO(g) Randomness increases Entropy increases (  S > 0)

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.  S univ =  S sys +  S surr > 0 Spontaneous process:  S univ =  S sys +  S surr = 0 Equilibrium process: Third Law of Thermodynamics The entropy of a perfect crystalline substance is zero at the absolute zero of temperature. Note that  S sys can be positive OR negative

Entropy Changes in the System (  S sys ) S0S0 rxn nS 0 (products) =  mS 0 (reactants)  - The standard entropy of reaction (  S 0 ) is the entropy change for a reaction carried out at 1 atm and 25 0 C. rxn Works just like  Hº, only in Appendix 2, you will see Sº instead of  Sº because absolute Sº can be measured. Unlike  H, S 0 of any element in its standard state is not necessarily zero.

Entropy Changes in the Surroundings (  S surr ) Exothermic Process  S surr > 0 Endothermic Process  S surr < 0  S surr = -  H sys /T

 S univ =  S sys +  S surr > 0 Spontaneous process: Gibbs Free Energy  S univ =  S sys -  H sys /T > 0  T  S univ =  H sys  T  S sys  G =  H sys  T  S sys < 0 For a constant-temperature process: Gibbs free energy (G)  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.

 G =  H - T  S

G0G0 rxn n  G 0 (products) f =  m  G 0 (reactants) f  - 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  G 0 of any element in its standard state is zero. f