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Chapter 17 Spontaneity, Entropy, and Free Energy Chapter 17 Table of Contents 17.1 17.2 17.3 17.4 17.5 17.6 17.7 17.8 17.9 Spontaneous Processes and Entropy Entropy and the Second Law of Thermodynamics The Effect of Temperature on Spontaneity Free Energy Entropy Changes in Chemical Reactions Free Energy and Chemical Reactions The Dependence of Free Energy on Pressure Free Energy and Equilibrium Free Energy and Work Copyright © Cengage Learning. All rights reserved 2 Section 17.1 Spontaneous Processes and Entropy Why does a reaction occur in a particular direction? • Kinetics – Gives info about amount of time required for the process. – Rate of a reaction depends on the pathway from reactants to products. • Thermodynamics – Predicts whether a reaction is spontaneous based only on the properties of reactants and products. Return to TOC Copyright © Cengage Learning. All rights reserved 3 Section 17.1 Spontaneous Processes and Entropy Spontaneity & Entropy • spontaneous process - occurs without outside intervention – Spontaneous does NOT mean fast. – Ex: heat flows from hot object to cooler one, but not the reverse Return to TOC Copyright © Cengage Learning. All rights reserved 4 Section 17.1 Spontaneous Processes and Entropy • • Entropy, S - a measure of molecular randomness or disorder. • The driving force for a spontaneous process is an increase in the entropy of the universe • Order (lower entropy) to disorder (higher entropy) • Thermodynamic function that describes the number of arrangements (positions and/or energy levels) available to a system in a given state. Associated with probability. • Nature spontaneously proceeds toward states that have the highest probabilities of existing. Return to TOC Copyright © Cengage Learning. All rights reserved 5 Section 17.1 Spontaneous Processes and Entropy The Expansion of An Ideal Gas Into an Evacuated Bulb Why do the gas molecules evenly spread throughout the container when the valve is open?? Why is it spontaneous? Return to TOC Copyright © Cengage Learning. All rights reserved 6 Section 17.1 Spontaneous Processes and Entropy The Microstates That Give a Particular Arrangement (State) • Consider a system with 4 gas molecules in a twobulbed container. • Microstate – a particular arrangement. • How many states (arrangements) are possible? • Which state is most likely to occur? Return to TOC Copyright © Cengage Learning. All rights reserved 7 Section 17.1 Spontaneous Processes and Entropy Positional Entropy • A gas expands into a vacuum because the expanded state has the highest positional probability (probability based upon configurations in space) of states available to the system. • Changes of state: Ssolid < Sliquid << Sgas • Formation of solutions: increase in entropy because of increased volume available for a given particle. Return to TOC Copyright © Cengage Learning. All rights reserved 8 Section 17.1 Spontaneous Processes and Entropy Concept Check Predict the sign of S for each of the following, and explain: + a) The evaporation of alcohol – b) The freezing of water – c) Compressing an ideal gas at constant temperature + d) Heating an ideal gas at constant pressure + e) Dissolving NaCl in water Copyright © Cengage Learning. All rights reserved Return to TOC 9 Section 17.2 Atomic Masses Entropy and the Second Law of Thermodynamics Second Law of Thermodynamics • spontaneous process -always an increase in the entropy of the universe. • The entropy of the universe is increasing. • The total energy of the universe is constant, but the entropy is increasing. Suniverse = ΔSsystem + ΔSsurroundings Return to TOC Copyright © Cengage Learning. All rights reserved 10 Section 17.3 The Effect Mole of Temperature on Spontaneity Concept Check For the process A(l) A(s), which direction involves an increase in energy randomness? Positional randomness? Explain your answer. As temperature increases/decreases (answer for both), which takes precedence? Why? At what temperature is there a balance between energy randomness and positional randomness? Return to TOC Copyright © Cengage Learning. All rights reserved 11 Section 17.3 The Effect Mole of Temperature on Spontaneity ΔSsurr • The sign of ΔSsurr depends on the direction of the heat flow. • The magnitude of ΔSsurr depends on the temperature. – directly proportional to quantity of heat transferred – Inversely proportional to temperature Ssurr H = T Heat flow (constant P) = change in enthalpy (system) = ΔH * Exothermic reactions increase the entropy of the surroundings Return to TOC Copyright © Cengage Learning. All rights reserved 12 Section 17.3 The Effect Mole of Temperature on Spontaneity ΔSsurr Return to TOC Copyright © Cengage Learning. All rights reserved 13 Section 17.3 The Effect Mole of Temperature on Spontaneity Example: Sb2S3 (s) + 3Fe (s) 2Sb (s) + 3FeS (s) ΔH = -125 kJ Calculate Δsurr for the reaction above. Return to TOC Copyright © Cengage Learning. All rights reserved 14 Section 17.3 The Effect Mole of Temperature on Spontaneity Interplay of S sys and S surr in Determining the Sign of S univ Return to TOC Copyright © Cengage Learning. All rights reserved 15 Section 17.4 Free Energy Free Energy (G) • • • Another thermodynamic function used to predict spontaneity. Is the maximum usable energy that can be utilized or trapped to do work. Useful when considering temperature dependence of spontaneity. • ΔG = ΔH – TΔS (at constant T and P) • ΔG° = ΔH ° – TΔS ° – ΔH at constant P = to energy flow as heat – T = temp in K – ΔS (ΔSsys) = change in entropy in J/K – °=> standard state Return to TOC Copyright © Cengage Learning. All rights reserved 16 Section 17.4 Free Energy Free Energy (G) Suniv G = (at constant T and P ) T • A process (at constant T and P) is spontaneous in the direction in which the free energy decreases. – Spontaneous : ΔG <0 • - ΔG means + ΔSuniv. – At equilibrium: ΔG = 0 Return to TOC Copyright © Cengage Learning. All rights reserved 17 Section 17.4 Free Energy Concept Check A liquid is vaporized at its boiling point. Predict the signs of: H + S + Ssurr – G 0 Explain your answers. Return to TOC Copyright © Cengage Learning. All rights reserved 18 Section 17.4 Free Energy Will ∆G be negative (& process spontaneous)? • Which dominates: ∆H or ∆S? Also can depend on T. • *Always spontaneous: exothermic & increase in entropy; always NONspontaneous: endothermic & decrease in entropy Return to TOC Copyright © Cengage Learning. All rights reserved 19 Section 17.4 Free Energy Example: • Predict whether each of the following sets of data represent spontaneous or nonspontaneous processes. ΔH (kJ) ΔS (J/K) T (K) 40 300 130 -40 -300 130 Return to TOC Copyright © Cengage Learning. All rights reserved 20 Section 17.4 Free Energy Example • For mercury, the enthalpy of vaporization is 58.51 kJ/mol and the entropy of vaporization is 92.92 J/K∙mol. What is the normal boiling point of mercury? Return to TOC Copyright © Cengage Learning. All rights reserved 21 Section 17.4 Free Energy Exercise The value of Hvaporization of substance X is 45.7 kJ/mol, and its normal boiling point is 72.5°C. Calculate S, Ssurr, and G for the vaporization of one mole of this substance at 72.5°C and 1 atm. S = 132 J/K·mol Ssurr = -132 J/K·mol G = 0 kJ/mol Return to TOC Copyright © Cengage Learning. All rights reserved 22 Section 17.5 Entropy Changes in Chemical Reactions ΔSsys is related to positional probabilities of the reactants • Reaction involving only gas phase: increase in total # of moles of gas means higher entropy. • Reaction with different phases: production of gas generally increases entropy more than an increase in # moles of a liquid or solid. Example: Predict the sign of ΔS°for each of the reactions: 1. (NH4)2Cr2O7 (s) Cr2O3 (s) + 4H2O (l) + N2 (g) 2. Mg(OH) 2 (s) MgO (s) + H2O (g) Return to TOC Copyright © Cengage Learning. All rights reserved 23 Section 17.5 Entropy Changes in Chemical Reactions Third Law of Thermodynamics • The entropy of a perfect crystal at 0 K is zero. • Standard entropy values: Represent the increase in entropy that occurs when a substance is heated from 0 K to 298 K at 1 atm pressure. ΔS°reaction = ΣnpS°products – ΣnrS°reactants Return to TOC Copyright © Cengage Learning. All rights reserved 24 Section 17.5 Entropy Changes in Chemical Reactions Exercise Calculate S° for the following reaction: 2Na(s) + 2H2O(l) → 2NaOH(aq) + H2(g) Given the following information: S° (J/K·mol) Na(s) 51 H2O(l) 70 NaOH(aq) 50 H2(g) 131 S°= –11 J/K Copyright © Cengage Learning. All rights reserved Return to TOC 25 Section 17.6 Free Energy and Chemical Reactions Standard Free Energy Change (ΔG°) • The change in free energy that will occur if the reactants in their standard states are converted to the products in their standard states. • Three methods of calculating ΔG°: 1) ΔG° = ΔH° – TΔS° 2) By manipulating known equations, (similar to Hess’s law) 3) ΔG°reaction = ΣnpGf (products) – ΣnrGf (reactants) Return to TOC Copyright © Cengage Learning. All rights reserved 26 Section 17.6 Free Energy and Chemical Reactions Concept Check A stable diatomic molecule spontaneously forms from its atoms. Predict the signs of: H° S° – – G° – Explain. Return to TOC Copyright © Cengage Learning. All rights reserved 27 Section 17.6 Free Energy and Chemical Reactions Concept Check Consider the following system at equilibrium at 25°C. PCl3(g) + Cl2(g) PCl5(g) G° = −92.50 kJ What will happen to the ratio of partial pressure of PCl5 to partial pressure of PCl3 if the temperature is raised? Explain. The ratio will decrease. Copyright © Cengage Learning. All rights reserved Return to TOC 28 Section 17.7 The Dependence of Free Energy on Pressure • System at constant T and P proceed spontaneously in the direction that lowers its free energy. • Reactions proceed until equilibrium is reached. – Equilibrium position: lowest free energy value available to a particular reaction system. • Free energy at nonstandard pressures: – For ideal gas: entropy is affected by pressure but enthalpy is not. • Slarge volume > Ssmall volume • Slow pressure > Shigh pressure Return to TOC Copyright © Cengage Learning. All rights reserved 29 Section 17.7 The Dependence of Free Energy on Pressure Free Energy at NON Standard pressures G = G° + RT ln(P) or ΔG = ΔG° + RT ln(Q) ΔG°= free energy change at 1 atm ΔG = free energy change at specified pressure P T = temp in K R = 8.3145 J/K∙mol Q = reaction quotient in terms of P Return to TOC Copyright © Cengage Learning. All rights reserved 30 Section 17.7 The Dependence of Free Energy on Pressure Example CO (g) + 2H2 (g) CH3OH (l) Calculate ∆G at 25°C for this reaction where CO at 5.0 atm and H2 gas at 3.0 atm are converted to liquid methanol. Return to TOC Copyright © Cengage Learning. All rights reserved 31 Section 17.7 The Dependence of Free Energy on Pressure The Meaning of ΔG for a Chemical Reaction • • A system can achieve the lowest possible free energy by going to equilibrium, not by going to completion. – ∆G<0 does NOT mean system proceeds to pure products – ∆G>0 does NOT mean system remains at pure reactants System spontaneously goes to equilibrium, the lowest possible free energy available. SO what is this value of ∆G at equilibrium??? Return to TOC Copyright © Cengage Learning. All rights reserved 32 Section 17.8 Free Energy and Equilibrium • The equilibrium point occurs at the lowest value of free energy available to the reaction system. Gproducts = Greactants or ΔG = 0 so… ΔG = 0 = ΔG° + RT ln(K) so… ΔG° = –RT ln(K) Return to TOC Copyright © Cengage Learning. All rights reserved 33 Section 17.8 Free Energy and Equilibrium Qualitative Relationship Between the Change in Standard Free Energy and the Equilibrium Constant for a Given Reaction • Given ∆G, which direction will the system shift to reach equilibrium? – Look at the value of K! Shift RIGHT RIGHT LEFT Return to TOC Copyright © Cengage Learning. All rights reserved 34 Section 17.8 Free Energy and Equilibrium Example • The rusting of iron by oxygen is: 4Fe (s) + 3O2 (g) 2Fe2O3 (s) • Using the following data, calculate the equilibrium constant for this reaction at 25ºC. Substance ΔHf° (kJ/mol) S° (J/K*mol) Fe2O3 (s) -826 90 Fe (s) 0 27 O2 (g) 0 205 Return to TOC Copyright © Cengage Learning. All rights reserved 35 Section 17.7 The Dependence of Free Energy on Pressure Return to TOC Copyright © Cengage Learning. All rights reserved 36 Section 17.9 Free Energy and Work • Maximum possible useful work obtainable from a process at constant temperature and pressure is equal to the change in free energy. wmax = ΔG Return to TOC Copyright © Cengage Learning. All rights reserved 37 Section 17.9 Free Energy and Work • Achieving the maximum work available from a spontaneous process can occur only via a hypothetical pathway. Any real pathway wastes energy. • All real processes are irreversible. • First law: You can’t win, you can only break even. • Second law: You can’t break even. Return to TOC Copyright © Cengage Learning. All rights reserved 38