CHEM 1B: GENERAL CHEMISTRY Chapter 20: Thermodynamics: Entropy, Free Energy, and the Direction of Chemical Reactions Instructor: Dr. Orlando E. Raola 20-1 Santa Rosa Junior College Chapter 20 Thermodynamics: Entropy, Free Energy, and the Direction of Chemical Reactions 20-2 Thermodynamics: Entropy, Free Energy, and the Direction of Chemical Reactions 20.1 The Second Law of Thermodynamics: Predicting Spontaneous Change 20.2 Calculating Entropy Change of a Reaction 20.3 Entropy, Free Energy, and Work 20.4 Free Energy, Equilibrium, and Reaction Direction 20-3 Spontaneous Change A spontaneous change is one that occurs without a continuous input of energy from outside the system. All chemical processes require energy (activation energy) to take place, but once a spontaneous process has begun, no further input of energy is needed. A nonspontaneous change occurs only if the surroundings continuously supply energy to the system. If a change is spontaneous in one direction, it will be nonspontaneous in the reverse direction. 20-4 The First Law of Thermodynamics Does Not Predict Spontaneous Change Energy is conserved. It is neither created nor destroyed, but is transferred in the form of heat and/or work. DE = q + w The total energy of the universe is constant: DEsys = -DEsurr or DEsys + DEsurr = DEuniv = 0 The law of conservation of energy applies to all changes, and does not allow us to predict the direction of a spontaneous change. 20-5 DH Does Not Predict Spontaneous Change A spontaneous change may be exothermic or endothermic. Spontaneous exothermic processes include: • freezing and condensation at low temperatures, • combustion reactions, • oxidation of iron and other metals. Spontaneous endothermic processes include: • melting and vaporization at higher temperatures, • dissolving of most soluble salts. The sign of DH does not by itself predict the direction of a spontaneous change. 20-6 Figure 20.1 A spontaneous endothermic chemical reaction. 2+ - Ba(OH)2 ·8H2O(s) + 2NH4NO3(s) → Ba (aq) + 2NO3 (aq) + 2NH3(aq) + 10H2O(l) DH°rxn = +62.3 kJ water This reaction occurs spontaneously when the solids are mixed. The reaction mixture absorbs heat from the surroundings so quickly that the beaker freezes to a wet block. 20-7 Freedom of Particle Motion All spontaneous endothermic processes result in an increase in the freedom of motion of the particles in the system. solid → liquid → gas crystalline solid + liquid → ions in solution less freedom of particle motion more freedom of particle motion localized energy of motion dispersed energy of motion A change in the freedom of motion of particles in a system is a key factor affecting the direction of a spontaneous process. 20-8 Microstates and Dispersal of Energy • Just as the electronic energy levels within an atom are quantized, a system of particles also has different allowed energy states. • Each quantized energy state for a system of particles is called a microstate. – At any instant, the total energy of the system is dispersed throughout one microstate. • At a given set of conditions, each microstate has the same total energy as any other. – Each microstate is therefore equally likely. • The larger the number of possible microstates, the larger the number of ways in which a system can disperse its energy. 20-9 Entropy The number of microstates (W) in a system is related to the entropy (S) of the system. S = k lnW A system with fewer microstates has lower entropy. A system with more microstates has higher entropy. All spontaneous endothermic processes exhibit an increase in entropy. Entropy, like enthalpy, is a state function and is therefore independent of the path taken between the final and initial states. 20-10 Figure 20.2 Spontaneous expansion of a gas. When the stopcock is opened, the gas spontaneously expands to fill both flasks. Increasing the volume increases the number of translational energy levels the particles can occupy. The number of microstates – and the entropy – increases. 20-11 Figure 20.3 The entropy increase due to the expansion of a gas. Opening the stopcock increases the number of possible energy levels, which are closer together on average. More distributions of particles are possible. 20-12 Figure 20.4 Expansion of a gas and the increase in number of microstates. When the stopcock opens, the number of microstates is 2n, where n is the number of particles. 20-13 DS for a Reversible Process q DS = rev T A reversible process is one that occurs in such tiny increments that the system remains at equilibrium, and the direction of the change can be reversed by an infinitesimal reversal of conditions. 20-14 Figure 20.5 Simulating a reversible process. A sample of Ne gas is confined to a volume of 1 L by the “pressure” of a beaker of sand on the piston. We remove one grain of sand (an “infinitesimal” decrease in pressure), causing the gas to expand a tiny amount. The gas does work on its surroundings, absorbing a tiny increment of heat, q, from the heat reservoir. This simulates a reversible process, since it can be reversed by replacing the grain of sand. 20-15 The Second Law of Thermodynamics The sign of ΔS for a reaction does not, by itself, predict the direction of a spontaneous reaction. If we consider both the system and the surroundings, we find that all real processes occur spontaneously in the direction that increases the entropy of the universe. For a process to be spontaneous, a decrease in the entropy of the system must be offset by a larger increase in the entropy of the surroundings. DSuniv = DSsys + DSsurr > 0 20-16 Comparing Energy and Entropy The total energy of the universe remains constant. DEsys + DEsurr =DEuniv = 0 DH is often used to approximateDE. For enthalpy there is no zero point; we can only measure changes in enthalpy. The total entropy of the universe increases. DSuniv =DSsys +DSsurr > 0 For entropy there is a zero point, and we can determine absolute entropy values. 20-17 The Third Law of Thermodynamics A perfect crystal has zero entropy at absolute zero. Ssys = 0 at 0 K A “perfect” crystal has flawless alignment of all its particles. At absolute zero, the particles have minimum energy, so there is only one microstate. S = k lnW = k ln 1 = 0 To find the entropy of a substance at a given temperature, we cool it as close to 0 K as possible. We then heat in small increments, measure q and T, and calculate DS for each increment. The sum of these DS values gives the absolute entropy at the temperature of interest. 20-18 Standard Molar Entropies S° is the standard molar entropy of a substance, measured for a substance in its standard state in units of J/mol·K. The conventions for defining a standard state include: • 1 bar for gases • 1 mol/L for solutions, and • the pure substance in its most stable form for solids and liquids. 20-19 Factors Affecting Entropy • Entropy depends on temperature. – For any substance, S° increases as temperature increases. • Entropy depends on the physical state of a substance. – S° increases as the phase changes from solid to liquid to gas. • The formation of a solution affects entropy. • Entropy is related to atomic size and molecular complexity. – Remember to compare substances in the same physical state. 20-20 Figure 20.6A Visualizing the effect of temperature on entropy. Computer simulations show each particle in a crystal moving about its lattice position. Adding heat increases T and the total energy, so the particles have greater freedom of motion, and their energy is more dispersed. S therefore increases. 20-21 Figure 20.6B Visualizing the effect of temperature on entropy. At any T, there is a range of occupied energy levels and therefore a certain number of microstates. Adding heat increases the total energy (area under the curve), so the range of occupied energy levels becomes greater, as does the number of microstates. 20-22 Figure 20.6C Visualizing the effect of temperature on entropy. A system of 21 particles occupy energy levels (lines) in a box whose height represents the total energy. When heat is added, the total energy increases and becomes more dispersed, so S increases. 20-23 Figure 20.7 The increase in entropy during phase changes from solid to liquid to gas. 20-24 Figure 20.8 The entropy change accompanying the dissolution of a salt. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. pure solid MIX pure liquid solution The entropy of a salt solution is usually greater than that of the solid and of water, but it is affected by the organization of the water molecules around each ion. 20-25 Figure 20.9 The small increase in entropy when ethanol dissolves in water. Ethanol (A) and water (B) each have many H bonds between their own molecules. In solution (C) they form H bonds to each other, so their freedom of motion does not change significantly. 20-26 Figure 20.10 The entropy of a gas dissolved in a liquid. 20-27 Entropy and Atomic Size S° is higher for larger atoms or molecules of the same type. Li Na K Rb Cs Atomic radius (pm) 152 186 227 248 265 Molar mass (g/mol) 6.941 22.99 39.10 85.47 132.9 S°(s) 29.1 51.4 64.7 69.5 85.2 HF HCl HBr HI Molar mass (g/mol) 20.01 36.46 80.91 127.9 S°(s) 173.7 186.8 198.6 206.3 20-28 Entropy and Structure For allotropes, S° is higher in the form that allows the atoms more freedom of motion.