Chemical Thermodynamics. Chapter 18

Transcription

1 Chemical Thermodynamics Chapter 18

2 Thermodynamics Spontaneous Processes Entropy and Second Law of Thermodynamics Entropy Changes Gibbs Free Energy Free Energy and Temperature Free Energy and Equilibrium

3 Spontaneous Processes A process that does occur under a specific set of conditions is called a spontaneous process. A process that does not occur under a specific set of conditions is called nonspontaneous.

4 Spontaneous Processes A process that results in a decrease in the energy of a system often is spontaneous: CH 4 (g) + 2O 2 (g) CO 2 (g) + 2H 2 O(l) ΔH = kj/mol The sign of ΔH alone is insufficient to predict spontaneity in every circumstance: H 2 O(l) H 2 O(s) T > 0 C; ΔH = 6.01 kj/mol

5 Entropy To predict spontaneity, both the enthalpy and entropy must be known. Entropy (S) of a system is a measure of how spread out or how dispersed the system s energy is.

6 Entropy Spontaneity is favored by an increase in entropy. S = k ln W k is the Boltzmann constant (1.38 x J/K) W is the number of different arrangements The number of arrangements possible is given by: W = X N X is the number of cells in a volume N is the number of molecules

7 Entropy

8 Entropy There are three possible states for this system: 1) One molecule on each side (eight possible arrangements) 2) Both molecules on the left (four possible arrangements) 3) Both molecules on the right (four possible arrangements) The most probable state has the largest number of arrangements.

9 Entropy Changes in a System The change in entropy for a system is the difference in entropy of the final state and the entropy of the initial state. ΔS sys = S final S initial Alternatively:

10 Practice Problem Determine the change in entropy (ΔS sys ) for the expansion of 0.10 mole of an ideal gas from 2.0 L to 3.0 L at constant temperature.

11 Entropy Changes in a System The standard entropy is the absolute entropy of a substance at 1 atm. Temperature is not part of the standard state definition and must be specified.

12 Entropy Changes in a System There are several important trends in entropy: S liquid > S solid S gas > S liquid S increases with molar mass S increases with molecular complexity S increases with the mobility of a phase (for an element with two or more allotropes)

13 Entropy Changes in a System In addition to translational motion, molecules exhibit vibrations and rotations.

14 Entropy Changes in a System For a chemical reaction aa + bb cc + dd ΔS rxn = [cs (C) + ds (D)] [as (A) + bs (B)] Alternatively, ΔS rxn = ΣnS (products) ΣmS (reactants)

15 Practice Problems Calculate the standard entropy change for the following reactions at 25 C. 2CO 2 (g) 2CO(g) + O 2 (g)

16 Entropy Changes in a System Several processes that lead to an increase in entropy are: Melting Vaporization or sublimation Temperature increase Reaction resulting in a greater number of gas molecules

17 Entropy Changes in a System The process of dissolving a substance can lead to either an increase or a decrease in entropy, depending on the nature of the solute. Molecular solutes (i.e. sugar): entropy increases Ionic compounds: entropy could decrease or increase

18 Entropy Changes in a System Determine the sign of ΔS for the following: 1) crystallization of sucrose from a supersaturated solution. 2) cooling water vapor from 150 C to 110 C. 3) Sublimation of dry ice.

19 Entropy Changes in the Universe Correctly predicting the spontaneity of a process requires us to consider entropy changes in both the system and the surroundings. An ice cube spontaneously melts in a room at 25 C. Perspective Components ΔS System ice positive Surroundings everything else negative A cup of hot water spontaneously cools to room temperature. Perspective Components ΔS System hot water negative Surroundings everything else positive The entropy of both the system AND surroundings are important!

20 Entropy Changes in the Universe The change in entropy of the surroundings is directly proportional to the enthalpy of the system. The second law of thermodynamics states that for a process to be spontaneous, ΔS universe must be positive. ΔS universe = ΔS sys + ΔS surr

21 Entropy Changes in the Universe The second law of thermodynamics states that for a process to be spontaneous, ΔS universe must be positive. ΔS universe = ΔS sys + ΔS surr ΔS universe > 0 for a spontaneous process ΔS universe < 0 for a nonspontaneous process ΔS universe = 0 for an equilibrium process

22 Practice Problems Consider the synthesis of ammonia at 25 C: N 2 (g) + 3H 2 (g) 2NH 3 (g) ΔS sys = 199 J/K mol ΔH sys = 92.6 kj/mol Is this process spontaneous or non spontaneous?

23 Practice Problem Is the following reaction spontaneous, non-spontaneous, or at equilibrium when T = 10.4 C? N 2 O 4 (g) 2NO 2 (g) ΔS sys = J/K mol; ΔH sys = kj/mol

24 Entropy Changes in the Universe The third law of thermodynamics states that the entropy of a perfect crystalline substance is zero at absolute zero. Entropy increases in a substance as temperature increases from absolute zero.

25 Predicting Spontaneity Measurements on the surroundings are seldom made, limiting the use of the second law of thermodynamics. Gibbs free energy (G) or simply free energy can be used to express spontaneity more directly. G = H TS The change in free energy for a system is: ΔG = ΔH TΔS

26 Predicting Spontaneity Using the Gibbs free energy, it is possible to make predictions on spontaneity. ΔG = ΔH TΔS ΔG < 0 The reaction is spontaneous in the forward direction. ΔG > 0 The reaction is nonspontaneous in the forward direction. ΔG = 0 The system is at equilibrium

27 Predicting Spontaneity The standard free energy of reaction (ΔG rxn ) is free-energy change for a reaction when it occurs under standard-state conditions. The following conditions define the standard states of pure substances and solutions are: Gases 1 atm pressure Liquids pure liquid Solids pure solid Elements the most stable allotropic form at 1 atm and 25 C Solutions 1 molar concentration

28 Entropy Changes in a System For a chemical reaction aa + bb cc + dd ΔG rxn = [cδg f (C) + dδg f (D)] [aδg f (A) + bδg f (B)] Alternatively, ΔG rxn = ΣnΔG f (products) ΣmΔG f (reactants) ΔG f for any element in its most stable allotropic form at 1 atm is defined as zero.

29 Practice Problems Calculate the standard free-energy for the following reaction at 25 C: 2C 2 H 6 (g) + 7O 2 (g) 4CO 2 (g) + 6H 2 O(l)

30 Free Energy and Chemical Equilibrium It is the sign of ΔG (not ΔG ) that determines spontaneity. The relationship between ΔG and ΔG is: ΔG = ΔG + RT lnq R is the gas constant (8.314 J/K mol). T is the kelvin temperature. Q is the reaction quotient.

31 Free Energy and Chemical Equilibrium Consider the following equilibrium: H 2 (g) + I 2 (g) 2HI(g) ΔG at 25 C = 2.60 kj/mol ΔG depends on the partial pressures of each chemical species. If P H2 = 2.0 atm; P I2 = 2.0 atm; and P HI = 3.0 atm: Then:

32 Free Energy and Chemical Equilibrium The spontaneity can be manipulated by changing the partial pressures of the reaction components: ΔG at 25 C = 2.60 kj/mol H 2 (g) + I 2 (g) 2HI(g) If P H2 = 2.0 atm; P I2 = 2.0 atm; and P HI = 1.0 atm: Then:

33 Free Energy and Chemical Equilibrium At equilibrium, ΔG = 0 and Q = K: 0 = ΔG + RT ln K ΔG = RT ln K

34 Free Energy and Chemical Equilibrium At equilibrium, ΔG = 0 and Q = K: 0 = ΔG + RT ln K ΔG = RT ln K

35 Free Energy and Chemical Equilibrium At equilibrium, ΔG = 0 and Q = K: 0 = ΔG + RT ln K ΔG = RT ln K

36 Practice Problems Calculate the equilibrium constant, Kp, for the following reaction at 25 C. 2O 3 (g) 3O 2 (g) ΔG = kj/mol

37 Thermodynamics of Living Systems Many biological reactions have positive ΔG value, making the reaction nonspontaneous. None spontaneous reactions can be coupled with spontaneous reactions in order to drive a process forward: alanine + glycine alanylglycine Δ G = 29 kj/mol ATP + H 2 O ADP + H 3 PO 4 ΔG = 31 kj/mol ATP + H 2 O + alanine + glycine ADP + H 3 PO 4 + alanylglycine ΔG = 29 kj/mol + 31 kj/mol = 2 kj/mol

38 Thermodynamics of Living Systems Many biological reactions have positive ΔG value, making the reaction nonspontaneous.

39 Objective Understand the meaning of spontaneous and nonspontaneous processes Know what the second and third law of thermodynamic are Be able to predict the sign of S for physical and chemical processes Be able to calculate the standard entropy for a system Know what Gibbs free energy is and how to calculate it from the enthalpy change and entropy change at a given temperature Know how to use Gibbs free energy to predict whether reactions are spontaneous Be able to calculate G and Gº Know how Gº and equilibrium constant are related and be able to solve these types of problems