Chapter 16 Thermodynamics CHEM 0120 PDF

Chapter 16 CHEM 0120  Thermodynamics Thermodynamics: the study of the relationship between heat and other forms of energy involved in a chemical or physical process Used to predict whether a process will occur under the specified conditions. Processes that wi...

Chapter 16 CHEM 0120  Thermodynamics Thermodynamics: the study of the relationship between heat and other forms of energy involved in a chemical or physical process Used to predict whether a process will occur under the specified conditions. Processes that will occur are spontaneous. Nonspontaneous processes require the application of an external force. 2  First Law of Thermodynamics The change in internal energy of a system, ΔU, equals heat plus work (q + w). Total energy must be conserved. Energy is neither created nor destroyed, only transferred and transformed. ∆𝑈𝑈 = 𝑞𝑞 + 𝑤𝑤 Internal energy: Sum of potential and kinetic energy of all particles that compose the system. It is a state function (it is not affected by the path). 3  Pressure-Volume Work Pressure is a force that acts against the sides of a container. If a part of that container can move, then work can be done w = -PΔV Pressure-volume work – volume change against an external pressure  Enthalpy Enthalpy – the heat exchanged in a reaction under constant pressure Constant pressure generally means an open system It is a state function Enthalpy can also be defined as the internal energy plus the product of pressure and volume H = U + PV If we want to look at the change in enthalpy: ΔH = ΔU + PΔV  Enthalpy The value of ΔH is the amount of heat absorbed or released by a reaction under constant pressure If the value of ΔH is positive, then the system has absorbed energy from the surroundings, and the reaction is endothermic If the value of ΔH is negative, then the system has given off energy to the surroundings (heat has evolved), and the reaction is exothermic  Spontaneity Determined by comparing the chemical potential energy of the system before the reaction with the free energy of the system after the reaction. If the system after the reaction has less potential energy than the system before the reaction, the reaction is thermodynamically favorable. Spontaneity ≠ fast or slow 7  Spontaneous vs Reversible Processes A spontaneous process is irreversible because there is a net release of energy when it proceeds in that direction. Proceeds in one direction. If one direction is spontaneous, the opposite direction must be nonspontaneous. A reversible process will proceed back and forth between the two end conditions. The result is no change in free energy. 8  Spontaneous Processes Spontaneous processes occur because they release energy from the system. Most spontaneous processes proceed from a system of higher potential energy to a system at lower potential energy. Exothermic But there are some spontaneous processes that proceed from a system of lower potential energy to a system at higher potential energy. Endothermic 9  Determining Whether a Reaction is Spontaneous. Two factors determine whether a reaction is spontaneous: Enthalpy change and Entropy change of the system. The enthalpy change, ΔH, is the difference between the sum of the internal energy and PV work energy of the reactants and that of the products. The entropy change, ΔS, is the difference between the randomness of the reactants and that of the products. 10  Entropy Entropy (S): a thermodynamic quantity that is a measure of how dispersed the energy of a system is among the different possible ways that a system can contain energy It is a state function. In spontaneous processes, the entropy of the system plus its surroundings increases. *Entropy change entirely in the system for the flasks. 11  Entropy A state function that is a measure of the matter and/or energy dispersal within a system, determined by the number of system microstates; often described as a measure of the disorder of the system 12  Changes in Entropy (ΔS) ΔS = Sfinal − Sinitial Entropy change is favorable when the result is a more random system. ΔS is positive. Changes that increase the entropy are as follows: Reactions whose products are in a more random state Solid more ordered than liquid; liquid more ordered than gas Reactions that have larger numbers of product molecules than reactant molecules Increase in temperature Solids dissociating into ions upon dissolving 13  Example of the Change in Entropy Ssolid < Sliquid < Sgas Calculate ΔS for the melting of ice. Entropy of 1 mol of ice = 41 J/K Entropy of 1 mol of liquid water = 63 J/K H2O(s) → H2O(l) 14  Second Law of Thermodynamics The total entropy of a system and its surroundings always increases for a spontaneous process. Energy can be neither created nor destroyed during a spontaneous process, but the energy is dispersed, so entropy is produced. 𝑞𝑞 ∆𝑆𝑆 = entropy created + 𝑇𝑇 Second Law restated: For a spontaneous process at a given temperature (T), the change in entropy of the system is greater than the heat divided by the absolute temperature, q/T 𝑞𝑞 ∆𝑆𝑆 > 𝑇𝑇 15  Entropy Change for a Phase Transition At equilibrium, entropy change results from the absorption of heat. 𝑞𝑞 ∆𝑆𝑆 = 𝑇𝑇 Repeat the calculation for change in entropy for the melting of ice. ΔHfus = 6.0 kJ / 1 mol of ice 16  Example #1 The enthalpy change when liquid methanol, CH3OH, vaporizes at 25 ℃ is 38.0 kJ/mol. What is the entropy change when 1.00 mol of vapor in equilibrium with liquid condenses to liquid at 25 ℃? 17  Standard States The state of a material at a defined set of conditions. Represented by a superscript degree sign on the symbol of the quantity For gases: pure gas at exactly 1 atm pressure For pure liquids and solids: 1 atm pressure Temperature is usually 298 K For solutions: 1 M concentration 18  Third Law of Thermodynamics A substance that is perfectly crystalline at 0 K has an entropy of zero. Therefore, every substance that is not a perfect crystal at absolute zero has some energy from entropy. Therefore, the absolute entropy of substances is always positive. 19  Standard Absolute Entropies, S° S° designates standard state conditions. Entropy is an extensive physical property of matter. Entropies are for 1 mol of a substance at 298 K for a particular state, a particular allotrope, a particular molecular complexity, a particular molar mass, and a particular degree of dissolution. 20  Relative Standard Entropies: States The gas state has a larger entropy than the liquid state at a particular temperature. The liquid state has a larger entropy than the solid state at a particular temperature. 21 Standard Molar Entropy Values 22  Relative Standard Entropies: Molar Mass The larger the molar mass, the larger the entropy. Available energy states are more closely spaced, allowing more dispersal of energy through the states. 23  Relative Standard Entropies: Allotropes The less constrained the structure of an allotrope is, the larger its entropy. The fact that the layers in graphite are not bonded together makes graphite less constrained. 24  Relative Standard Entropies: Dissolution Dissolved solids generally have larger entropy, distributing particles throughout the mixture. 25  Relative Standard Entropies: Molecular Complexity Larger, more complex molecules generally have larger entropy. More energy states are available, allowing more dispersal of energy through the states. 26  Free Energy (G) Free energy: a thermodynamic quantity defined by the equation G = H – TS Gives a direct relationship to the spontaneity of a reaction. ∆𝐺𝐺 = ∆𝐻𝐻 − 𝑇𝑇∆𝑆𝑆 ΔS is positive when spontaneous, so ΔG must be negative. Standard free-energy change ∆𝐺𝐺𝐺 = ∆𝐻𝐻𝐻 − 𝑇𝑇∆𝑆𝑆𝑆 27  Standard Free Energy of Formation, ΔGf° ΔGf°: the free-energy change that occurs when 1 mole of substance is formed from its elements in their reference forms at 1 atmosphere and at a specified temperature For elements in their most stable states, the value is zero. ∆𝐺𝐺𝐺 = 𝑛𝑛 ∆𝐺𝐺𝑓𝑓° 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 − 𝑚𝑚 ∆𝐺𝐺𝑓𝑓° 𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 28  Spontaneity of a Reaction using ΔG° Useful rules in judging the spontaneity of a reaction: If ΔG°is a large negative number, the reaction is spontaneous Reactants transform almost entirely to products at equilibrium. If ΔG°is a large positive number, the reaction is nonspontaneous Reactants do not give significant amounts of products at equilibrium. When ΔG°has a small negative or positive value, the reaction gives an equilibrium mixture with significant amounts of both reactants and products. 29  Why is it “free” energy? The free energy is the maximum amount of energy released from a system that is available to do work on the surroundings. For many exothermic reactions, some of the heat released as a result of the enthalpy change goes into increasing the entropy of the surroundings, so it is not available to do work. And even some of this free energy is generally lost to heating up the surroundings. 30  Free Energy Change During a Reaction A decrease in free energy can show up as work done (to give maximum work), but also appears as an increase in entropy. 31  Gibbs Free Energy, ΔG A process will be spontaneous when ΔG is negative. ΔG will be negative under the following conditions: ΔH is negative and ΔS is positive. Exothermic and more random ΔH is negative and large and ΔS is negative but small. ΔH is positive but small and ΔS is positive and large. Or high temperature ΔG will be positive under the following conditions: ΔH is positive and ΔS is negative. Never spontaneous at any temperature When ΔG = 0, the reaction is at equilibrium. 32  Relating ΔG° to the equilibrium constant, K ΔG = ΔG° only when the reactants and products are in their standard states. Their normal state at that temperature Partial pressure of gas = 1 atm Concentration = 1 M Under nonstandard conditions, ΔG = ΔG° + RT ln Q. Q is the reaction quotient. At equilibrium, ΔG = 0. ΔG° = −RT ln K 33  Thermodynamic Equilibrium Constant, K K is the equilibrium constant in which: The concentrations of gases are expressed in partial pressures in atmospheres; The concentrations of solutes in liquid solutions are expressed in molarities. 34  Spontaneity using ΔG° and K Since ΔG = 0 at equilibrium, ∆𝐺𝐺𝐺 = −𝑅𝑅𝑅𝑅 ln 𝐾𝐾 When K > 1, ΔG° is negative and the reaction is spontaneous in the forward direction under standard conditions. When K < 1, ΔG° is positive and the reaction is nonspontaneous as written. 35  Example #2 What is the standard free-energy change ΔG°at 25 ℃ for the following reaction? (What information is required?) H2(g) + Br2(l) → 2 HBr(g) What is the value of the thermodynamic equilibrium constant K? 36  Why is K temperature dependent? Combining these two equations, ΔG° = ΔH° – TΔS° and ΔG° = – RT ln(K) it can be shown that – ΔH°rxn 1 ΔS°rxn ln(K) = + R T R This equation is in the form y = mx + b. The graph of ln(K) versus inverse T is a straight line. 37  Changes of Free Energy with Temperature Assume ΔH°and ΔS°are constant with respect to temperature; ° ∆𝐺𝐺𝑇𝑇 = ∆𝐻𝐻𝐻 − 𝑇𝑇∆𝑆𝑆𝑆 38  Example #3 Sodium carbonate can be prepared by heating sodium hydrogen carbonate. 2 NaHCO3(s) → Na2CO3(s) + H2O(g) + CO2(g) Estimate the temperature at which NaHCO3 decomposes to products at 1 atm. (What info is required?) 39