#### Transcript Entropy

Chapter 20 Thermodynamics: Entropy, Free Energy and the Direction of Chemical Reactions Limitations of the First Law of Thermodynamics DE = q + w Euniverse = Esystem + Esurroundings DEsystem = -DEsurroundings The total energy-mass of the universe is constant. However, this does not tell us anything about the direction of change in the universe. A spontaneous endothermic chemical reaction water Ba(OH)2.8H2O(s) + 2NH4NO3(s) Ba2+(aq) + 2NO3-(aq) + 2NH3(aq) + 10H2O(l) DH0rxn = +62.3 kJ The Concept of Entropy (S) Entropy refers to the state of order. A change in order is a change in the number of ways of arranging the particles, and it is a key factor in determining the direction of a spontaneous process. more order solid more order crystal + liquid more order crystal + crystal less order liquid gas less order ions in solution less order gases + ions in solution The number of ways to arrange a deck of playing cards Spontaneous expansion of a gas stopcock closed 1 atm evacuated stopcock opened 0.5 atm 0.5 atm 1877 Ludwig Boltzman S = k ln W where S is entropy, W is the number of ways of arranging the components of a system, and k is a constant (the Boltzman constant), R/NA (R = universal gas constant, NA = Avogadro’s number. •A system with relatively few equivalent ways to arrange its components (smaller W) has relatively less disorder and low entropy. •A system with many equivalent ways to arrange its components (larger W) has relatively more disorder and high entropy. DSuniverse = DSsystem + DSsurroundings > 0 This is the second law of thermodynamics. Random motion in a crystal The third law of thermodynamics. A perfect crystal has zero entropy at a temperature of absolute zero. Ssystem = 0 at 0 K Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Predicting Relative S0 Values of a System 1. Temperature changes S0 increases as the temperature rises. 2. Physical states and phase changes S0 increases as a more ordered phase changes to a less ordered phase. 3. Dissolution of a solid or liquid S0 of a dissolved solid or liquid is usually greater than the S0 of the pure solute. However, the extent depends upon the nature of the solute and solvent. 4. Dissolution of a gas A gas becomes more ordered when it dissolves in a liquid or solid. 5. Atomic size or molecular complexity In similar substances, increases in mass relate directly to entropy. In allotropic substances, increases in complexity (e.g. bond flexibility) relate directly to entropy. The increase in entropy from solid to liquid to gas Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. The entropy change accompanying the dissolution of a salt pure solid MIX pure liquid solution Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. The small increase in entropy when ethanol dissolves in water Ethanol Water Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Solution of ethanol and water The large decrease in entropy when a gas dissolves in a liquid O2 gas Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Entropy and vibrational motion NO NO2 N 2 O4 Sample 1 Predicting Relative Entropy Values PROBLEM: Choose the member with the higher entropy in each of the following pairs, and justify your choice [assume constant temperature, except in part (e)]: (a) 1mol of SO2(g) or 1mol of SO3(g) (b) 1mol of CO2(s) or 1mol of CO2(g) (c) 3mol of oxygen gas (O2) or 2mol of ozone gas (O3) (d) 1mol of KBr(s) or 1mol of KBr(aq) (e) Seawater in midwinter at 20C or in midsummer at 230C (f) 1mol of CF4(g) or 1mol of CCl4(g) Sample 2 PROBLEM: Calculating the Standard Entropy of Reaction, DS0rxn Calculate DS0rxn for the combustion of 1mol of propane at 250C. C3H8(g) + 5O2(g) 3CO2(g) + 4H2O(l) Components of DS0universe for spontaneous reactions exothermic endothermic system becomes more disordered exothermic system becomes more disordered system becomes more ordered Sample 3 PROBLEM: Determining Reaction Spontaneity At 298K, the formation of ammonia has a negative DS0sys; N2(g) + 3H2(g) 2NH3(g) DS0sys = -197J/K Calculate DS0rxn, and state whether the reaction occurs spontaneously at this temperature. DH0fNH3 = -45.9 kJ/mol DG0system = DH0system - TDS0system DG0rxn = S mDG0products - S nDG0reactants Sample 4 PROBLEM: Calculating DG0 from Enthalpy and Entropy Values Potassium chlorate, one of the common oxidizing agents in explosives, fireworks, and matchheads, undergoes a solid-state redox reaction when heated. In this reaction, note that the oxidation number of Cl in the reactant is higher in one of the products and lower in the other (disproportionation): +5 +7 -1 D 4KClO3(s) 3KClO4(s) + KCl(s) Use DH0f and S0 values to calculate DG0sys at 250C for this reaction. Sample 5 PROBLEM: Calculating DG0rxn from DG0f Values Use DG0f values to calculate DGrxn for the reaction: 4KClO3(s) D 3KClO4(s) + KCl(s) Sample 6 PROBLEM: Determining the Effect of Temperature on DG0 An important reaction in the production of sulfuric acid is the oxidation of SO2(g) to SO3(g): 2SO2(g) + O2(g) 2SO3(g) At 298K, DG0 = -141.6kJ; DH0 = -198.4kJ; and DS0 = -187.9J/K (a) Use the data to decide if this reaction is spontaneous at 250C, and predict how DG0 will change with increasing T. (b) Assuming DH0 and DS0 are constant with increasing T, is the reaction spontaneous at 900.0C? Sample 7 PROBLEM: Determining the Effect of Temperature on DG0 A reaction is nonspontaneous at room temperature but is spontaneous at -40 0C. What can you say about the signs and relative magnitudes of DH0 DS0 and -TDS0 Reaction Spontaneity and the Signs of DH0, DS0, and DG0 DH0 DS0 -TDS0 DG0 - + - - Spontaneous at all T + - + + Nonspontaneous at all T + + - + or - Spontaneous at higher T; nonspontaneous at lower T - - + + or - Spontaneous at lower T; nonspontaneous at higher T Description The effect of temperature on reaction spontaneity DG and the Work a System Can Do For a spontaneous process, DG is the maximum work obtainable from the system as the process takes place: DG = workmax For a nonspontaneous process, DG is the maximum work that must be done to the system as the process takes place: DG = workmax An example The coupling of a nonspontaneous reaction to the hydrolysis of ATP. The cycling of metabolic free enery through ATP Free Energy, Equilibrium and Reaction Direction •If Q/K < 1, then ln Q/K < 0; the reaction proceeds to the right (DG < 0) •If Q/K > 1, then ln Q/K > 0; the reaction proceeds to the left (DG > 0) •If Q/K = 1, then ln Q/K = 0; the reaction is at equilibrium (DG = 0) DG = RT ln Q/K = RT lnQ - RT lnK Under standard conditions (1M concentrations, 1atm for gases), Q = 1 and lnQ = 0 so DG0 = - RT lnK The Relationship Between DG0 and K at 250C DG0(kJ) K 100 3x10-18 50 2x10-9 10 2x10-2 1 7x10-1 0 1 -1 1.5 -10 5x101 -50 6x108 -100 3x1017 -200 1x1035 Essentially no forward reaction; reverse reaction goes to completion Forward and reverse reactions proceed to same extent Forward reaction goes to completion; essentially no reverse reaction REVERSE REACTION 9x10-36 FORWARD REACTION 200 Significance Sample Problem 6 Calculating DG at Nonstandard Conditions PROBLEM: The oxidation of SO2, which we considered in Sample Problem 6 2SO2(g) + O2(g) 2SO3(g) is too slow at 298K to be useful in the manufacture of sulfuric acid. To overcome this low rate, the process is conducted at an elevated temperature. (a) Calculate K at 298K and at 973K. (DG0298 = -141.6kJ/mol of reaction as written using DH0 and DS0 values at 973K. DG0973 = -12.12kJ/mol of reaction as written.) (b) In experiments to determine the effect of temperature on reaction spontaneity, two sealed containers are filled with 0.500atm of SO2, 0.0100atm of O2, and 0.100atm of SO3 and kept at 250C and at 700.0C. In which direction, if any, will the reaction proceed to reach equilibrium at each temperature? (c) Calculate DG for the system in part (b) at each temperature. Sample Problem 7 Calculating DG at Nonstandard Conditions PROBLEM: At 298 K hypobromous acid (HBrO) dissociates in water with a Ka of 2.3 x 10-9. (a) Calculate DG0298 (b) Calculate DG if [H3O+] = 6.0 x 10-4M, [BrO-] = 0.1 M and [HBrO]=0.20 M The relation between free energy and the extent of reaction DG0 < 0 K >1 DG0 > 0 K <1