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Chapter 17 Spontaneity, Entropy, and Free Energy Section 17.1 Spontaneous Processes and Entropy Thermodynamics vs. Kinetics Domain of Kinetics Rate of a reaction depends on the pathway from reactants to products. Thermodynamics tells us whether a reaction is spontaneous based only on the properties of reactants and products. Copyright © Cengage Learning. All rights reserved 2 Section 17.1 Spontaneous Processes and Entropy Spontaneous Processes and Entropy Thermodynamics predict the direction in which a process will occur but gives no information about the speed of the process. A spontaneous process is one that occurs without outside intervention. It may be slow or fast. A gas fills its container uniformly. It never spontaneously collects at one end of the container. Heat flow always occur from hot to a cooler one. The reverse process never occurs spontaneously. Copyright © Cengage Learning. All rights reserved 3 Section 17.1 Spontaneous Processes and Entropy CONCEPT CHECK! Consider 2.4 moles of a gas contained in a 4.0 L bulb at a constant temperature of 32°C. This bulb is connected by a valve to an evacuated 20.0 L bulb. Assume the temperature is constant. a) What should happen to the gas when you open the valve? Copyright © Cengage Learning. All rights reserved 4 Section 17.1 Spontaneous Processes and Entropy CONCEPT CHECK! Consider 2.4 moles of a gas contained in a 4.0 L bulb at a constant temperature of 32°C. This bulb is connected by a valve to an evacuated 20.0 L bulb. Assume the temperature is constant. b) Calculate ΔH, ΔE, q, and w for the process you described above. All are equal to zero. Copyright © Cengage Learning. All rights reserved 5 Section 17.1 Spontaneous Processes and Entropy CONCEPT CHECK! Consider 2.4 moles of a gas contained in a 4.0 L bulb at a constant temperature of 32°C. This bulb is connected by a valve to an evacuated 20.0 L bulb. Assume the temperature is constant. c) Given your answer to part b, what is the driving force for the process? Entropy Copyright © Cengage Learning. All rights reserved 6 Section 17.1 Spontaneous Processes and Entropy The Expansion of An Ideal Gas Into an Evacuated Bulb Copyright © Cengage Learning. All rights reserved 7 Section 17.1 Spontaneous Processes and Entropy Entropy Spontaneous processes is an increase in property called entropy (s). The driving force for a spontaneous process is an increase in the entropy of the universe. It is a measure of molecular randomness or disorder. Copyright © Cengage Learning. All rights reserved 8 Section 17.1 Spontaneous Processes and Entropy Entropy Entropy is a thermodynamic function that describes the number of arrangements that are available to a system existing in a given state. Nature spontaneously proceeds toward the states that have the highest probabilities of existing. Copyright © Cengage Learning. All rights reserved 9 Section 17.1 Spontaneous Processes and Entropy The Microstates That Give a Particular Arrangement (State) Section 17.2 Entropy and the Second Law of Thermodynamics Each configuration that gives a particular arrangement is called microstate. Which arrangement is most likely to occur. Table 17.2 shows relative probabilities of finding all the molecules in the left bulb. Section 17.1 Spontaneous Processes and Entropy Positional Entropy A gas expands into a vacuum to give a uniform distribution because the expanded state has the highest positional probability of states available to the system. Therefore: Ssolid < Sliquid << Sgas Question 17.31, 32 Section 17.1 Spontaneous Processes and Entropy CONCEPT CHECK! Predict the sign of ΔS 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 13 Section 17.2 Entropy and the Second Law of Thermodynamics Second Law of Thermodynamics In any spontaneous process there is 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 Copyright © Cengage Learning. All rights reserved 14 Section 17.2 Entropy and the Second Law of Thermodynamics ΔSuniv ΔSuniv = +; entropy of the universe increases ΔSuniv = -; process is spontaneous in opposite direction ΔSuniv = 0; process has no tendency to occur, and the system is at equilibrium. Copyright © Cengage Learning. All rights reserved 15 Section 17.3 The Effect 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? Copyright © Cengage Learning. All rights reserved 16 Section 17.3 The Effect of Temperature on Spontaneity CONCEPT CHECK! Describe the following as spontaneous/non-spontaneous/cannot tell, and explain. A reaction that is: a) Exothermic and becomes more positionally random Spontaneous b) Exothermic and becomes less positionally random Cannot tell a) Endothermic and becomes more positionally random Cannot tell a) Endothermic and becomes less positionally random Not spontaneous Explain how temperature affects your answers. Section 17.3 The Effect of Temperature on Spontaneity ΔSsurr There are two important characteristics of the entropy changes that occur in the surroundings. The sign of ΔSsurr depends on the direction of the heat flow. At constant temperature , an exothermic process in the system causes the heat flow into the surrounding. It increases the random motions and the entropy of the surroundings. ΔSsurr is positive The magnitude of ΔSsurr depends on the temperature. The transfer of a given quantity of energy as a heat produces much greater percent change in the randomness of the surrounding at a low temperature than it does at a high temperature. Thus depends directly on the quantity of heat transferred and inversely proportional on the temperature. In other words, the tendency for the system to lower its energy becomes a more important driving force at lower temperatures. Copyright © Cengage Learning. All rights reserved 18 Section 17.3 The Effect of Temperature on Spontaneity ΔSsurr Copyright © Cengage Learning. All rights reserved 19 Section 17.3 The Effect of Temperature on Spontaneity ΔSsurr Copyright © Cengage Learning. All rights reserved 20 Section 17.3 The Effect of Temperature on Spontaneity ΔSsurr We can express Δssurr in terms of the change in enthalpy ΔH for a process occurring at constant pressure. Heat flow (constant P) = change in enthalpy = ΔH Questions 17.33, 17.34 Ssurr Copyright © Cengage Learning. All rights reserved H = T 21 Section 17.3 The Effect of Temperature on Spontaneity Copyright © Cengage Learning. All rights reserved 22 Section 17.4 Free Energy Free energy (G) Free energy (another thermodynamic term) is also related to spontaneity in dealing with temperature dependence of spontaneity. Section 17.4 Free Energy Free Energy (G) Suniv G = (at constant T and P ) T A process carried out at constant T and P is spontaneous if the ΔG is negative. Negative (-ΔG) means positive (+Δsuniv). So we have two functions that can be used to predict spontaneity. i) Entropy of universe, which apply to all processes. Ii) Free energy which can be used for processes carried out at constant temperature and pressure. Question 17.37 Copyright © Cengage Learning. All rights reserved 24 Section 17.4 Free Energy Free Energy (G) ΔG = ΔH – TΔS (at constant T and P) Copyright © Cengage Learning. All rights reserved 25 Section 17.4 Free Energy CONCEPT CHECK! A liquid is vaporized at its boiling point. Predict the signs of: – w + q + ΔH + ΔS – ΔSsurr 0 ΔG Explain your answers. Copyright © Cengage Learning. All rights reserved 26 Section 17.4 Free Energy EXERCISE! The value of ΔHvaporization of substance X is 45.7 kJ/mol, and its normal boiling point is 72.5°C. Calculate ΔS, ΔSsurr, and ΔG for the vaporization of one mole of this substance at 72.5°C and 1 atm. ΔS = 132 J/K·mol ΔSsurr = -132 J/K·mol ΔG = 0 kJ/mol Copyright © Cengage Learning. All rights reserved 27 Section 17.4 Free Energy Spontaneous Reactions To play movie you must be in Slide Show Mode PC Users: Please wait for content to load, then click to play Mac Users: CLICK HERE Copyright © Cengage Learning. All rights reserved 28 Section 17.4 Free Energy Effect of ΔH and ΔS on Spontaneity Copyright © Cengage Learning. All rights reserved 29 Section 17.5 Entropy Changes in Chemical Reactions CONCEPT CHECK! Gas A2 reacts with gas B2 to form gas AB at constant temperature and pressure. The bond energy of AB is much greater than that of either reactant. Predict the signs of: ΔH ΔSsurr – + ΔS ΔSuniv 0 + Explain. Copyright © Cengage Learning. All rights reserved 30 Section 17.5 Entropy Changes in Chemical Reactions Entropy changes in the system are determined by positional probability. Fewer molecule means fewer possible configurations. Gases molecules generally possess more entropy than solid. So whenever the products contains more moles of gases than reactant the entropy change is probably positive. Question 17.41, 42 Section 17.5 Entropy Changes in Chemical Reactions Third Law of Thermodynamics: In thermodynamics change in a certain function is usually important. The change in enthalpy determines if the reaction is exothermic or endothermic at constant temperature. The change in free energy determines if a process is spontaneous at constant temperature and pressure. A perfect crystal represents the lowest possible entropy. Law: The entropy of a perfect crystal at 0 K is zero. The entropy of a substance increases with temperature. Since S is zero for a perfect crystal at 0 K, the entropy value for a substance at a particular temperature can be calculated by knowing the temperature dependence entropy. The standard entropy values (S0) of many common substances at 298 K and 1 atm. are listed in appendix 4. Because the entropy is a state function of the system , the entropy change can be calculated by the following equation. Copyright © Cengage Learning. All rights reserved 32 Section 17.5 Entropy Changes in Chemical Reactions Standard Entropy Values (S°) Represent the increase in entropy that occurs when a substance is heated from 0 K to 298 K at 1 atm pressure. Question 17.45,46 ΔS°reaction = ΣnpS°products – ΣnrS°reactants Copyright © Cengage Learning. All rights reserved 33 Section 17.5 Entropy Changes in Chemical Reactions EXERCISE! Calculate ΔS° 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 ΔS°= –11 J/K Copyright © Cengage Learning. All rights reserved 34 Section 17.6 Free Energy and Chemical Reactions Standard Free Energy Change (ΔG°) For a chemical reaction we are interested in the 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. It is important to note that the ΔG° for a reaction is not measure directly. ΔG° values for several reactions allow us to compare the relative tendency of these reactions . More negative the value of ΔG°, the further a reaction will go to the right to reach the equilibrium. Question:17.53, 57, 59 ΔG° = ΔH° – TΔS° ΔG°reaction = ΣnpG°products – ΣnrG°reactants Copyright © Cengage Learning. All rights reserved 35 Section 17.6 Free Energy and Chemical Reactions CONCEPT CHECK! A stable diatomic molecule spontaneously forms from its atoms. Predict the signs of: ΔH° ΔS° – – ΔG° – Explain. Copyright © Cengage Learning. All rights reserved 36 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) ΔG° = −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 37 Section 17.7 The Dependence of Free Energy on Pressure Free Energy and Pressure G = G° + RT ln(P) or ΔG = ΔG° + RT ln(Q) Copyright © Cengage Learning. All rights reserved 38 Section 17.7 The Dependence of Free Energy on Pressure CONCEPT CHECK! Sketch graphs of: 1. G vs. P 2. H vs. P 3. ln(K) vs. 1/T (for both endothermic and exothermic cases) Copyright © Cengage Learning. All rights reserved 39 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. Copyright © Cengage Learning. All rights reserved 40 Section 17.8 Free Energy and Equilibrium The equilibrium point occurs at the lowest value of free energy available to the reaction system. ΔG = 0 = ΔG° + RT ln(K) ΔG° = –RT ln(K) Copyright © Cengage Learning. All rights reserved 41 Section 17.8 Free Energy and Equilibrium Change in Free Energy to Reach Equilibrium Copyright © Cengage Learning. All rights reserved 42 Section 17.8 Free Energy and Equilibrium Copyright © Cengage Learning. All rights reserved 43 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 Copyright © Cengage Learning. All rights reserved 44 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. As we use energy, we degrade its usefulness. Copyright © Cengage Learning. All rights reserved 45