Chemical Thermodynamics Thermo Part 2 Chemical Thermodynamics 1

Chemical Thermodynamics Thermo Part 2 Chemical Thermodynamics 1

First Law of Thermodynamics • You will recall from Chapter 5 that energy cannot be created nor destroyed. • Therefore, the total energy of the universe is a constant. • Energy can, however, be converted from one form to another or transferred from a system to the surroundings or vice versa. 2 Chemical Thermodynamics 2

Spontaneous Processes • Spontaneous processes are those that can proceed without any outside intervention. • The gas in vessel B will spontaneously effuse into vessel A, but once the gas is in both vessels, it will not spontaneously go back to one container 3 Chemical Thermodynamics 3

Spontaneous Processes that are spontaneous in one direction are nonspontaneous in the reverse direction. 4 Chemical Thermodynamics 4

Spontaneous Processes • Processes that are spontaneous at one temperature may be nonspontaneous at other temperatures. • Above 0 C it is spontaneous for ice to melt. • Below 0 C the reverse process is spontaneous. 5 Chemical Thermodynamics 5

SAMPLE EXERCISE 19. 1 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 150ºC is added to water at 40ºC, 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. 1ºC. PRACTICE EXERCISE Under 1 atm pressure CO 2(s) sublimes at – 78ºC. Is the transformation of CO 2(s) to CO 2(g) a spontaneous process at – 100ºC and 1 atm pressure? Chemical 6 Thermodynamics 6

Reversible Processes In a reversible process the system changes in such a way that the system and surroundings can be put back in their original states by exactly reversing the process. 7 Chemical Thermodynamics 7

Irreversible Processes • Irreversible processes cannot be undone by exactly reversing the change to the system. • Spontaneous processes are irreversible. 8 Chemical Thermodynamics 8

Entropy • Entropy (S) is a term coined by Rudolph Clausius in the 19 th century. • Clausius was convinced of the significance of the ratio of heat delivered and the temperature at which it is delivered, q T • Entropy can be thought of as a measure of the randomness of a system. • It is related to the various modes of motion in molecules. 9 Chemical Thermodynamics 9

Entropy • Like total energy, E, and enthalpy, H, entropy is a state function. • Therefore, S = Sfinal Sinitial 10 Chemical Thermodynamics 10

Entropy • For a process occurring at constant temperature (an isothermal process), the change in entropy is equal to the heat that would be transferred if the process were reversible divided by the temperature: qrev S = T 11 Chemical Thermodynamics 11

Second Law of Thermodynamics The second law of thermodynamics states that the entropy of the universe increases for spontaneous processes, and the entropy of the universe does not change for reversible processes. 12 Chemical Thermodynamics 12

Second Law of Thermodynamics In other words: For reversible processes: Suniv = Ssystem + Ssurroundings = 0 For irreversible processes: Suniv = Ssystem + Ssurroundings > 0 S is entropy. H is enthalpy. 13 Chemical Thermodynamics 13

Second Law of Thermodynamics These last truths mean that as a result of all spontaneous processes the entropy of the universe increases. 14 Chemical Thermodynamics 14

Entropy on the Molecular Scale • Ludwig Boltzmann described the concept of entropy on the molecular level. • Temperature is a measure of the average kinetic energy of the molecules in a sample. 15 Chemical Thermodynamics 15

Entropy on the Molecular Scale • Molecules exhibit several types of motion: • Translational: Movement of the entire molecule from one place to another. • Vibrational: Periodic motion of atoms within a molecule. • Rotational: Rotation of the molecule on about an axis or rotation about bonds. 16 Chemical Thermodynamics 16

Entropy on the Molecular Scale • Boltzmann envisioned the motions of a sample of molecules at a particular instant in time. • This would be akin to taking a snapshot of all the molecules. • He referred to this sampling as a microstate of thermodynamic system. 17 Chemical Thermodynamics 17

Entropy on the Molecular Scale • Each thermodynamic state has a specific number of microstates, W, associated with it. • Entropy is S = k ln. W where k is the Boltzmann constant, 1. 38 10 23 J/K. 18 Chemical Thermodynamics 18

Entropy on the Molecular Scale • The change in entropy for a process, then, is S = k ln. Wfinal k ln. Winitial ln. Wfinal S = k ln ln. Winitial • Entropy increases with the number of 19 Chemical microstates in the system. Thermodynamics 19

Entropy on the Molecular Scale • The number of microstates and, therefore, the entropy tends to increase with increases in • Temperature. • Volume. • The number of independently moving molecules. 20 Chemical Thermodynamics 20

Entropy and Physical States • Entropy increases with the freedom of motion of molecules. • Therefore, S(g) > S(l) > S(s) 21 Chemical Thermodynamics 21

Solutions Generally, when a solid is dissolved in a solvent, entropy increases. 22 Chemical Thermodynamics 22

Entropy Changes • In general, entropy increases when • Gases are formed from liquids and solids. • Liquids or solutions are formed from solids. • The number of gas molecules increases. • The number of moles increases. 23 Chemical Thermodynamics 23

SAMPLE EXERCISE 19. 3 Predicting the Sign of S Predict whether S is positive or negative for each of the following processes, assuming each occurs at constant temperature: Chemical 24 Thermodynamics 24

PRACTICE EXERCISE Indicate whether each of the following processes produces an increase or decrease in the entropy of the system: Chemical 25 Thermodynamics 25

SAMPLE EXERCISE 19. 4 Predicting Which Sample of Matter Has the Higher Entropy Choose the sample of matter that has greater entropy in each pair, and explain your choice: (a) 1 mol of Na. Cl(s) or 1 mol of HCl(g) at 25ºC, (b) 2 mol of HCl(g) or 1 mol of HCl(g) at 25ºC, (c) 1 mol of HCl(g) or 1 mol of Ar(g) at 298 K. PRACTICE EXERCISE Choose the substance with the greater entropy in each case: (a) 1 mol of H 2(g) at STP or 1 mol of H 2(g) at 100ºC and 0. 5 atm, (b) 1 mol of H 2 O(s) at 0ºC or 1 mol of H 2 O(l) at 25ºC, (c) 1 mol of H 2(g) at STP or 1 mol of SO 2(g) at STP, (d) 1 mol of N 2 O 4(g) at STP or 2 mol of NO 2(g) at STP. Chemical 26 Thermodynamics 26

Third Law of Thermodynamics The entropy of a pure crystalline substance at absolute zero is 0. 27 Chemical Thermodynamics 27

Standard Entropies • These are molar entropy values of substances in their standard states. • Standard entropies tend to increase with increasing molar mass. 28 Chemical Thermodynamics 28

Standard Entropies Larger and more complex molecules have greater entropies. (More stuff, more entropy) 29 Chemical Thermodynamics 29

Entropy Changes Entropy changes for a reaction can be estimated in a manner analogous to that by which H is estimated: S° = n S°(products) - m S°(reactants) where n and m are the coefficients in the balanced chemical equation. 30 Chemical Thermodynamics 30

SAMPLE EXERCISE 19. 5 Calculating S from Tabulated Entropies Calculate S° for the synthesis of ammonia from N 2(g) and H 2(g) at 298 K: Step 1 Formula with substitutions: Step 2 Gather data from chart or question provided. We would fine these in Appendix C of your book: PRACTICE EXERCISE Using the standard entropies in Appendix C, calculate the standard entropy change, S°, for the following reaction at 298 K: Chemical 31 Thermodynamics 31

Entropy Changes in Surroundings • Heat that flows into or out of the system changes the entropy of the surroundings. • For an isothermal process: Ssurr = qsys T • At constant pressure, qsys is simply H for the system. 32 Chemical Thermodynamics 32

Entropy Change in the Universe • The universe is composed of the system and the surroundings. • Therefore, Suniverse = Ssystem + Ssurroundings • For spontaneous processes Suniverse > 0 33 Chemical Thermodynamics 33

Entropy Change in the Universe • This becomes: Suniverse = Ssystem + Hsystem T Multiplying both sides by T, T Suniverse = Hsystem T Ssystem 34 Chemical Thermodynamics 34

Gibbs Free Energy • T Suniverse is defined as the Gibbs free energy, G. • When Suniverse is positive, G is negative. • Therefore, when G is negative, a process is spontaneous. 35 Chemical Thermodynamics 35

Gibbs Free Energy 1. If G is negative, the forward reaction is spontaneous. 2. If G is 0, the system is at equilibrium. 3. If G is positive, the reaction is spontaneous in the reverse direction. 36 Chemical Thermodynamics 36

Standard Free Energy Changes Analogous to standard enthalpies of formation are standard free energies of formation, G. G f = n G f (products) m G f (reactants) where n and m are the stoichiometric coefficients. 37 Chemical Thermodynamics 37

SAMPLE EXERCISE 19. 6 Calculating Standard Free-Energy Change from Free Energies of Formation (a) By using data from Appendix C, calculate the standard free-energy change for the following reaction at 298 K: (b) What is Gºfor the reverse of the above reaction? Chemical 38 Thermodynamics 38

PRACTICE EXERCISE By using data from Appendix C, calculate Gº at 298 K for the combustion of methane: Chemical 39 Thermodynamics 39

SAMPLE EXERCISE 19. 7 Estimating and Calculating G° In Section 5. 7 we used Hess’s law to calculate Hº for the combustion of propane gas at 298 K: (a) Without using data from Appendix C, predict whether Gº for this reaction is more negative or less negative than Hº. (b) Use data from Appendix C to calculate the standard free-energy change for the reaction at 298 K. Is your prediction from part (a) correct? Chemical 40 Thermodynamics 40

PRACTICE EXERCISE Consider the combustion of propane to form CO 2(g) and H 2 O(g) at 298 K: Would you expect Gº to be more negative or less negative than H°? Chemical 41 Thermodynamics 41

Free Energy Changes At temperatures other than 25°C, G° = H T S How does G change with temperature? 42 Chemical Thermodynamics 42

Free Energy and Temperature • There are two parts to the free energy equation: • H — the enthalpy term • T S — the entropy term • The temperature dependence of free energy, then comes from the entropy term. 43 Chemical Thermodynamics 43

Free Energy and Temperature 44 Chemical Thermodynamics 44

SAMPLE EXERCISE 19. 8 Determining the Effect of Temperature on Spontaneity The Haber process for the production of ammonia involves the equilibrium Assume that Hº and Sº for this reaction do not change with temperature. (a) Predict the direction in which Gº for this reaction changes with increasing temperature. (b) Calculate the values of Gº for the reaction at 25ºC and 500ºC. Chemical 45 Thermodynamics 45

SAMPLE EXERCISE 19. 8 continued PRACTICE EXERCISE (a) Using standard enthalpies of formation and standard entropies in Appendix C, calculate Hº and Sº at 298 K for the following reaction: (b) Using the values obtained in part (a), estimate Gº at 400 K. Chemical 46 Thermodynamics 46

Free Energy and Equilibrium Under any conditions, standard or nonstandard, 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. ) 47 Chemical Thermodynamics 47

SAMPLE EXERCISE 19. 9 Relating G to a Phase Change at Equilibrium As we saw in Section 11. 5, the normal boiling point is the temperature at which a pure liquid is in equilibrium with its vapor at a pressure of 1 atm. (a) Write the chemical equation that defines the normal boiling point of liquid carbon tetrachloride, CCl 4(l). (b) What is the value of Gº for the equilibrium in part (a)? (c) Use thermodynamic data in Appendix C and Equation 19. 20 to estimate the normal boiling point of CCl 4. Chemical 48 Thermodynamics 48

PRACTICE EXERCISE Use data in Appendix C to estimate the normal boiling point, in K, for elemental bromine, Br 2(l). (The experimental value is given in Table 11. 3. ) Chemical 49 Thermodynamics 49

SAMPLE EXERCISE 19. 10 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. Chemical 50 Thermodynamics 50

PRACTICE EXERCISE Calculate G at 298 K for the reaction of nitrogen and hydrogen to form ammonia if the reaction mixture consists of 0. 50 atm N 2, 0. 75 atm H 2, and 2. 0 atm NH 3. Chemical 51 Thermodynamics 51

Free Energy and Equilibrium • At equilibrium, Q = K, and G = 0. • The equation becomes 0 = G + RT ln. K • Rearranging, G = RT ln. K K = e G /RT 52 Chemical Thermodynamics 52

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 Sample Exercise 19. 8: Gº = – 33. 3 k. J/mol = – 33, 300 J/mol. Chemical 53 Thermodynamics 53

PRACTICE EXERCISE Use data from Appendix C to calculate the standard free-energy change, Gº, and the equilibrium constant, K, at 298 K for the reaction Chemical 54 Thermodynamics 54

SAMPLE INTEGRATIVE EXERCISE Putting Concepts Together Consider the simple salts Na. Cl(s) and Ag. Cl(s). We will examine the equilibria in which these salts dissolve in water to form aqueous solutions of ions: (a) Calculate the value of Gº at 298 K for each of the preceding reactions. (b) The two values from part (a) are very different. Is this difference primarily due to the enthalpy term or the entropy term of the standard freeenergy change? (c) Use the values of Gº to calculate the Ksp values for the two salts at 298 K. (d) Sodium chloride is considered a soluble salt, whereas silver chloride is considered insoluble. Are these descriptions consistent with the answers to part (c)? (e) How will Gº for the solution process of these salts change with increasing T? What effect should this change have on the solubility of the salts? Chemical 55 Thermodynamics 55