Thermodynamics Chapter 18 Free Energy and Equilibrium Note

Thermodynamics Chapter 18

Free Energy and Equilibrium Note: at equilibrium, ΔG = 0 as the definition of equilibrium is that there is no net preference for the direction of a reaction. However, when the concentrations of all components are 1 M or 1 atm (standard conditions, ΔGo), there is often a preference for the direction of a reaction, and ΔGo describes this preference. Under standard conditions, ΔG = ΔGo Under equilibrium conditions, ΔG = 0 Under nonequilibrium, nonstandard conditions, ΔG = something other than 0 or ΔGo Under any conditions, the free energy change can be found this way: G = G + RT ln. Q (Under standard conditions, all concentrations are 1 M, so Q = 1 and ln. Q = 0; the last term drops out and G = G )

Free Energy and Equilibrium • At equilibrium, Q = K, and G = 0. • The equation becomes 0 = G + RT ln. K • Rearranging, this becomes G = RT ln. K or, K = e G /RT

SAMPLE EXERCISE Identifying Spontaneous Processes Predict whether the following processes are spontaneous as described, spontaneous in the reverse direction, or in equilibrium: (a) When a piece of metal heated to 150°C is added to water at 40°C, the water gets hotter. (b) Water at room temperature decomposes into H 2(g) and O 2(g). (c) Benzene vapor, C 6 H 6(g), at a pressure of 1 atm condenses to liquid benzene at the normal boiling point of benzene, 80. 1°C. Solution (a) This process is spontaneous. (b) Experience tells us that this process is not spontaneous—we certainly have never seen hydrogen and oxygen gas bubbling up out of water! (c) By definition, the normal boiling point is the temperature at which a vapor at 1 atm is in equilibrium with its liquid. Thus, this is an equilibrium situation.

SAMPLE EXERCISE Calculating S for a Phase Change The element mercury, Hg, is a silvery liquid at room temperature. The normal freezing point of mercury is – 38. 9ºC, and its molar enthalpy of fusion is fusion = 2. 29 k. J/mol. What is the entropy change of the system when 50. 0 g of Hg(l) freezes at the normal freezing point? Solution Plan: We can use – fusion and the molar mass of Hg to calculate q for freezing 50. 0 g of Hg: We can use this value of q as qrev. We must first, however, convert the temperature to K: Solve: We can now calculate the value of Ssys:

SAMPLE EXERCISE Calculating S from Tabulated Entropies Calculate S° for the synthesis of ammonia from N 2(g) and H 2(g) at 298 K: Solution Solve: Using Equation 18. 7, we have Substituting the appropriate S° values yields

SAMPLE EXERCISE Calculating Standard Free-Energy Change from Free Energies of Formation (a) By using data from the Appendix, calculate the standard free-energy change for the following reaction at 298 K: (b) What is G° for the reverse of the above reaction? Solution Solve: (a) Cl 2(g) is in its standard state, so is zero for this reactant. P 4(g), however, is not in its standard state, so is not zero for this reactant. From the balanced equation and using the Appendix, we have: The fact that G° is negative tells us that a mixture of P 4(g), Cl 2(g), and PCl 3(g), at 25°C, each present at a partial pressure of 1 atm, would react spontaneously in the forward direction to form more PCl 3. Remember, however, that the value of G° tells us nothing about the rate at which the reaction occurs.

SAMPLE EXERCISE continued (b) Remember that G = G (products) – G (reactants). If we reverse the reaction, we reverse the roles of the reactants and products. Thus, reversing the reaction changes the sign of G, just as reversing the reaction changes the sign of H. Hence, using the result from part (a):

SAMPLE EXERCISE Determining the Effect of Temperature on Spontaneity The Haber process for the production of ammonia involves the equilibrium Assume that H° and S° for this reaction do not change with temperature. (a) Predict the direction in which G° for this reaction changes with increasing temperature. (b) Calculate the values of G° for the reaction at 25°C and 500°C. Solution G° = H° – T S° Solve: (a) Equation 18. 10 tells us that G° is the sum of the enthalpy term H° and the entropy term –T S°. The temperature dependence of G° comes from the entropy term. We expect S° for this reaction to be negative because the number of molecules of gas is smaller in the products. Because S° is negative, the term –T S° is positive and grows larger with increasing temperature. As a result, G° becomes less negative (or more positive) with increasing temperature. Thus, the driving force for the production of NH 3 becomes smaller with increasing temperature.

SAMPLE EXERCISE continued (b) H° = – 92. 38 k. J and S° = – 198. 4 J/K. If we assume that these values don’t change with temperature, we can calculate G° at any temperature by using Equation 18. 10. At T = 298 K we have: G° = H° – T S° Notice that we have been careful to convert –T S° into units of k. J so that it can be added to H°, which has units of k. J.

Comment: Increasing the temperature from 298 K to 773 K changes G° from – 33. 3 k. J to +61 k. J. Of course, the result at 773 K depends on the assumption that H° and S° do not change with temperature. In fact, these values do change slightly with temperature. Nevertheless, the result at 773 K should be a reasonable approximation. The positive increase in G° with increasing T agrees with our prediction in part (a) of this exercise. Our result indicates that a mixture of N 2(g), H 2(g), and NH 3(g), each present at a partial pressure of 1 atm, will react spontaneously at 298 K to form more NH 3(g). In contrast, at 773 K the positive value of G° tells us that the reverse reaction is spontaneous. Thus, when the mixture of three gases, each at a partial pressure of 1 atm, is heated to 773 K, some of the NH 3(g) spontaneously decomposes into N 2(g) and H 2(g).

SAMPLE EXERCISE Calculating the Free-Energy Change Under Nonstandard Conditions We will continue to explore the Haber process for the synthesis of ammonia: Calculate G at 298 K for a reaction mixture that consists of 1. 0 atm N 2, 3. 0 atm H 2, and 0. 50 atm NH 3. Solution Solve: Solving for the reaction quotient gives: We can now use Equation 18. 13 to calculate G for these nonstandard conditions:

SAMPLE EXERCISE 19. 11 Calculating an Equilibrium Constant from G° Use standard free energies of formation to calculate the equilibrium constant, K, at 25°C for the reaction involved in the Haber process: The standard free-energy change for this reaction was calculated in a previous Sample Exercise: G° = – 33. 3 k. J/mol = – 33, 300 J/mol. Solution In this expression the gas pressures are expressed in atmospheres. (Remember that we use k. J/mol as the units of G° when using Equations like 18. 14). Solve: Solving Equation 18. 14 for the exponent – G°/RT, we have We insert this value into a rearranged form of Equation 18. 14 to obtain K:

Redox Reactions and Electrochemistry Chapter 19

Electrochemical processes are oxidation-reduction reactions in which: • the energy released by a spontaneous reaction is converted to electricity or • electrical energy is used to cause a nonspontaneous reaction to occur 0 0 2+ 2 - 2 Mg (s) + O 2 (g) 2 Mg O 2 + 4 e- 2 Mg. O (s) 2 Mg 2+ + 4 e- Oxidation half-reaction (lose e-) 2 O 2 - Reduction half-reaction (gain e-) 19. 1

Oxidation Numbers In order to keep track of what loses electrons and what gains them, we assign oxidation numbers.

Oxidation and Reduction • A species is oxidized when it loses electrons. – Here, zinc loses two electrons to go from neutral zinc metal to the Zn 2+ ion.

Oxidation and Reduction • A species is reduced when it gains electrons. – Here, each of the H+ gains an electron and they combine to form H 2.

Oxidation and Reduction • What is reduced is the oxidizing agent. – H+ oxidizes Zn by taking electrons from it. • What is oxidized is the reducing agent. – Zn reduces H+ by giving it electrons.