Lecture 7: The Second and Third Laws of Thermodynamics Reading: Zumdahl 10.5, 10.6 Outline –Definition of the Second Law –Determining  S –Definition of the Third Law

Weight and Entropy The connection between weight (  ) and entropy (S) is given by Boltzmann’s Formula: S = k ln  k = Boltzmann’s constant = R/N a = 1.38 x J/K The dominant configuration will have the largest  ; therefore, S is greatest for this configuration

Calculating Entropy  T = 0  V = 0  P = 0

Connecting with Dr Boltzmann From this lecture: Exactly the same as derived in the previous lecture!

The Second Law The Second Law: there is always an increase in the entropy of the universe. From our definitions of system and surroundings:  S universe =  S system +  S surroundings

The Second Law (cont.) Three possibilities: –If  S univ > 0…..process is spontaneous –If  S univ < 0…..process is spontaneous in opposite direction. –If  S univ = 0….equilibrium We need to know  S for both the system and surroundings to predict if a reaction will be spontaneous!

The Second Law (cont.) Consider a reaction driven by heat flow from the surroundings at constant P. –Exothermic Process:  S surr = heat/T –Endothermic Process:  S surr = -heat/T Heat transferred = q P,surr = - q P,system= -  H sys

Example For the following reaction at 298 K: Sb 4 O 6 (s) + 6C(s) 4Sb(s) + 6CO 2 (g)  H = 778 kJ What is  S surr ?  S surr = -  H/T = -778 kJ/298K = -2.6 kJ/K

The Third Law Recall, in determining enthalpies we had standard state values to use. Does the same thing exist for entropy? The third law: The entropy of a perfect crystal at 0K is zero. The third law provides the reference state for use in calculating absolute entropies.

What is a Perfect Crystal? Perfect crystal at 0 K Crystal deforms at T > 0 K

Standard Entropies With reference to this state, standard entropies have been tabulated (Appendix 4). Recall, entropy is a state function; therefore, the entropy change for a chemical reaction can be calculated as follows:

Example Balance the following reaction and determine  S° rxn. Fe(s) + H 2 O(g) Fe 2 O 3 (s) + H 2 (g) 2Fe(s) + 3H 2 O(g) Fe 2 O 3 (s) + 3H 2 (g)  S° rxn = (S°(Fe 2 O 3 (s)) + 3S°H 2 (g)) -(2S°Fe(s) + 3S ° H 2 O(g))  S° rxn = J/K

Big Example Is the following reaction spontaneous at 298 K? 2Fe(s) + 3H 2 O(g) Fe 2 O 3 (s) + 3H 2 (g)  S° rxn =  S° system = J/K  S° surr = -  H° sys /T = -  H° rxn /T (Is  S° univ > 0?)  H° rxn =  H° f (Fe 2 O 3 (s)) + 3  H° f (H 2 (g)) - 2  H° f (Fe (s)) - 3  H° f (H 2 O(g))

Big Example (cont.)  S° surr = -  H° sys /T = 348 J/K  H° rxn = -100 kJ  S° univ =  S° sys +  S° surr = J/K J/K = J/K  S° univ > 0 ; therefore, reaction is spontaneous

Entropy and Phase Changes Phase Change: Reaction in which a substance goes from one phase of state to another. Example: H 2 O(l) H K Phase changes are equilibrium processes such that:  S univ = 0

S and Phase Changes (cont.) H 2 O(l) H K Now,  S° rxn = S°(H 2 O(g)) - S°(H 2 O(l)) = J/K J/K = J/K And,  S° surr = -  H sys /T = kJ/373 K = J/K Therefore,  S univ =  S sys +  S surr = 0

Example Determine the temperature at which liquid bromine boils: Br 2 (l) Br 2 (g) Now,  S° rxn = S°(Br 2 (g)) - S°(Br 2 (l)) = J/K J/K = 93.2 J/K

Example (cont.) Now,  S° surr = -  S° sys = J/K = -  sys /T Therefore, calculate  H sys and solve for T! Now,  H° rxn =  H° f (Br 2 (g)) -  H° f (Br 2 (l)) = kJ - 0 = kJ Such that, J/K = -  kJ/T T boiling = K (standard state) 0