Chem 1B Dr. White 1 Chapter 17: Thermodynamics Review From Chem 1A (Chapter 6, section 1) A. The First Law of Thermodynamics 17.1 Spontaneous Processes and Entropy A. Spontaneous Change
Chem 1B Dr. White 2 B. Entropy (S)
Chem 1B Dr. White 3 C. Ways to Increase the Entropy (17.5)
Chem 1B Dr. White 4 Example - A. Without reference to any data tables, which member of the following pairs has the greater predicted amount of entropy. B. Without reference to any data tables, which member of the following pairs has the lesser predicted amount of entropy. CO 2 (g) or CO 2 (s) H 2 O (l) or H 2 O (s) C 3 H 8 (g) or C 2 H 6 (g) P 4 O 6 (g) or P 4 O 10 (g) H 2 (g) in a 1 L vessel or H 2 (g) in a 2 L vessel Fe (s) at 25 C or Fe (s) at 100 C Example: For each of the following reactions, indicate whether you would expect the entropy of the system to increase or decrease, and explain why. If you cannot tell just by inspecting the equation, explain why. (a) CH 3 OH(l) --> CH 3 OH(g) (b) N 2 O 4 (g) --> 2NO 2 (g) (c) CO(g) + H 2 O(g) --> CO 2 (g) + H 2 (g) 17.2 Entropy and the Second Law of Thermodynamics A. The 2 nd Law of Thermo
Chem 1B Dr. White 5 17.3-4 The Effect of Temperature on Spontaneity/Free Energy A. ΔS surr depends on ΔH sys and Temperature 1. ΔH sys 2. Temperature a. checkbook analogy: Account Deposit % Change Magnitude of Change $10 $10 $100 $10 b. cheering analogy:
Chem 1B Dr. White 6 B. New Thermodynaic Variable: Free Energy (G) Spontaneity and the Signs of ΔH, ΔS, and ΔG ΔH ΔS -TΔS ΔG Spontaneous?
Chem 1B Dr. White 7 H 2 O (s) + heat H 2 O (l) H 2 O (l) H 2 O (s) + heat Example: A key step in the production of sulfuric acid is the oxidation of sulfur dioxide to sulfur trioxide as shown by the reaction below: 2SO 2 (g) + O 2 (g) 2SO 3 (g) At 298 K, ΔH = -198.4 kj; and ΔS = -187.9 J/K. a. Is the reaction spontaneous at 25 C? b. How will ΔG change with an increase in temperature? c. Assuming that ΔH and ΔS are constant with T, is the reaction spontaneous at 900. C? C. Crossover Temperature
Chem 1B Dr. White 8 Example: What is the crossover temperature for the reaction in the previous example? 2SO 2 (g) + O 2 (g) 2SO 3 (g) ΔH = -198.4 kj; and ΔS = -187.9 J/K. Example: The temperature at which the following process changes from nonspontaneous to spontaneous is the normal boiling point of hydrogen peroxide. If ΔH rxn = 51.4 kj and ΔS rxn = 123.1 J/mol, what is the normal boiling point of hydrogen peroxide? 17.5-17.6 Calculating ΔS and ΔG for Chemical Reactions A. Standard Entropy (S ) B. ΔS for a reaction Example: What is the standard entropy change when one mole of ethane reacts with oxygen?
Chem 1B Dr. White 9 C 2 H 6 (g) + 7/2 O 2 (g) 2 CO 2 (g) + 3 H 2 O(g) C. Standard Free energy of formation (ΔG f ) for a substance Example: Write the formation reaction for water D. ΔG for a reaction Example: Find the ΔG of the reaction from the previous example using ΔG f values. C 2 H 6 (g) + 7/2 O 2 (g) 2 CO 2 (g) + 3 H 2 O(g)
Chem 1B Dr. White 10
Chem 1B Dr. White 11 Example: Repeat the calculation for the ΔG for the same reaction at 25 C. This time, use the ΔS found from S values and ΔH f values. C 2 H 6 (g) + 7/2 O 2 (g) 2 CO 2 (g) + 3 H 2 O(g) Example: Calculate ΔG for the same reaction at 100. C (Assume that ΔS and ΔH are temperature independent). C 2 H 6 (g) + 7/2 O 2 (g) 2 CO 2 (g) + 3 H 2 O(g)
Chem 1B Dr. White 12 17.7-17.8 Free Energy and Equilibrium A. ΔG and Reaction Direction (Consider A B) B. Q and K also tell us the reaction direction 1. 2. 3. K compared to Q Rxn Direction Q/K ln (Q/K) C. Relationship between Q, K, and ΔG ln (Q/K) ΔG RXN Direction 1. 2. 3. D. Standard Conditions (1 M, 1 atm, usually 298K) Relationship between K and ΔG K ΔG Consequence? a. b. c.
Chem 1B Dr. White 13 Example: Consider the following reaction: N 2 O 4 (g) 2NO 2 (g) a. Write the thermodynamic K expression. b. At 298 K, the equilibrium pressure for NO 2 is 0.372 atm and the equilibrium pressure for N 2 O 4 is 0.814 atm. What is the ΔG for the reaction? c. 0.900 atm of N 2 O 4 is mixed with 0.200 atm of NO 2. What is the ΔG of the reaction? Is it spontaneous if the forward direction? d. 0.200 atm of N 2 O 4 is mixed with 0.200 atm of NO 2. What is the ΔG of the reaction? Is it spontaneous if the forward direction?
Chem 1B Dr. White 14 Example: HBrO (aq) H + (aq) + BrO - (aq) K a = 2.3 x 10-9 at 298K. a. Calculate ΔG b. Calculate ΔG if [H + ] = 6.0 x 10-4 M, [BrO - ] = 0.10 M, and [HBrO] = 0.20M. Is the reaction spontaneous in the forward direction? E. Difference between ΔG and ΔG 1. ΔG 2. ΔG 3. Free Energy Diagrams a. Free Energy Diagram for a reaction with a -ΔG
Chem 1B Dr. White 15 b. Free Energy Diagram for a reaction with a +ΔG F. Temperature dependence of K and ΔG 1. Derivation of the Van t Hoff Equation: 2. Exothermic reaction 3. Endothermic Reaction
Chem 1B Dr. White 16 Example: The equilibrium constant for the solubility of calcium hydroxide was studied at different temperatures. The following graph was generated: The equation of the line is y = 2.0x10 3 x+13.1. What are the ΔH and ΔS of the reaction?
Chem 1B Dr. White 17 Example: If the equilibrium constant is 1.5 x 10 8 at 298 K for a reaction with a ΔH of +77.2 kj/mol, what is the equilibrium constant at 400. K? 17.9 Free Energy and work A. Gibbs Free Energy Revisited