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Spontaneous Processes and Entropy
Thermodynamics lets us predict whether a process will occur but gives no information about the amount of time required for the process. A spontaneous process is one that occurs without outside intervention.
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Figure 16.3: The expansion of an ideal gas into an evacuated bulb.
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Figure 16.4: Possible arrangements (states) of four molecules in a two-bulbed flask.
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The hypothetical contraction of a gas.
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DSuniverse = DSsystem + DSsurroundings > 0
1877 Ludwig Boltzman S = k ln W where S is entropy, W is the number of ways of arranging the components of a system, and k is a constant (the Boltzman constant), R/NA (R = universal gas constant, NA = Avogadro’s number. A system with relatively few equivalent ways to arrange its components (smaller W) has relatively less disorder and low entropy. A system with many equivalent ways to arrange its components (larger W) has relatively more disorder and high entropy. DSuniverse = DSsystem + DSsurroundings > 0 This is the second law of thermodynamics.
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The Concept of Entropy (S)
Entropy refers to the state of order. A change in order is a change in the number of ways of arranging the particles, and it is a key factor in determining the direction of a spontaneous process. more order less order solid liquid gas more order less order crystal + liquid ions in solution more order less order crystal + crystal gases + ions in solution
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Predicting Relative S0 Values of a System
1. Temperature changes S0 increases as the temperature rises. 2. Physical states and phase changes S0 increases as a more ordered phase changes to a less ordered phase. 3. Dissolution of a solid or liquid S0 of a dissolved solid or liquid is usually greater than the S0 of the pure solute. However, the extent depends upon the nature of the solute and solvent. 4. Dissolution of a gas A gas becomes more ordered when it dissolves in a liquid or solid. 5. Atomic size or molecular complexity In similar substances, increases in mass relate directly to entropy. In allotropic substances, increases in complexity (e.g. bond flexibility) relate directly to entropy.
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Figure 16.6: The H2O molecule can vibrate and rotate in several ways, some of which are shown here.
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Entropy and vibrational motion
Figure 20.9 Entropy and vibrational motion N2O4 NO NO2
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The entropy change accompanying the dissolution of a salt
Figure 20.6 The entropy change accompanying the dissolution of a salt pure solid solution MIX pure liquid Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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The small increase in entropy when ethanol dissolves in water
Figure 20.7 The small increase in entropy when ethanol dissolves in water Ethanol Solution of ethanol and water Water Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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The large decrease in entropy when a gas dissolves in a liquid
Figure 20.8 The large decrease in entropy when a gas dissolves in a liquid O2 gas Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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The increase in entropy from solid to liquid to gas
Figure 20.5 The increase in entropy from solid to liquid to gas Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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Components of DS0universe for spontaneous reactions
Figure 20.10 Components of DS0universe for spontaneous reactions exothermic endothermic system becomes more disordered exothermic system becomes more disordered system becomes more ordered
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Effect of H and S on Spontaneity
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The Third Law of Thermodynamics
. . . the entropy of a perfect crystal at 0 K is zero. Because S is explicitly known (= 0) at 0 K, S values at other temps can be calculated.
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Figure 16. 5: (a) A perfect crystal of hydrogen chloride at 0 K
Figure 16.5: (a) A perfect crystal of hydrogen chloride at 0 K. (b) As the temperature rises above 0 K, lattice vibrations allow some dipoles to change their orientations, producing some disorder and an increase in entropy.
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Free Energy Change and Chemical Reactions
G = standard free energy change that occurs if reactants in their standard state are converted to products in their standard state. G = npGf(products) nrGf(reactants)
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DG0system = DH0system - TDS0system
DG0rxn = S mDG0products - S nDG0reactants
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Free Energy and Pressure
G = G + RT ln(Q) Q = reaction quotient from the law of mass action.
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Free Energy and Equilibrium
G = RT ln(K) K = equilibrium constant This is so because G = 0 and Q = K at equilibrium.
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Free Energy, Equilibrium and Reaction Direction
If Q/K < 1, then ln Q/K < 0; the reaction proceeds to the right (DG < 0) If Q/K > 1, then ln Q/K > 0; the reaction proceeds to the left (DG > 0) If Q/K = 1, then ln Q/K = 0; the reaction is at equilibrium (DG = 0) DG = DGo+RT ln Q DG0 = - RT lnK
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Figure 16.7: Schematic representations of balls rolling down two types of hills.
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Figure 16.9: (a) The change in free energy to reach equilibrium, beginning with 1.0 mol A(g) at PA = 2.0 atm. (b) The change in free energy to reach equilibrium, beginning with 1.0 mol B(g) at PB = 2.0 atm. (c) The free energy profile for A(g) B(g) in a system containing 1.0 mol (A plus B) at PTOTAL = 2.0 atm. Each point on the curve corresponds to the total free energy of the system for a given combination of A and B.
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The relation between free energy and the extent of reaction
Figure 20.12 The relation between free energy and the extent of reaction DG0 < 0 K >1 DG0 > 0 K <1 Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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Table 20.2 The Relationship Between DG0 and K at 250C
DG0(kJ) K Significance Essentially no forward reaction; reverse reaction goes to completion REVERSE REACTION 200 9x10-36 FORWARD REACTION 100 3x10-18 50 2x10-9 10 2x10-2 1 7x10-1 Forward and reverse reactions proceed to same extent 1 -1 1.5 -10 5x101 -50 6x108 Forward reaction goes to completion; essentially no reverse reaction -100 3x1017 -200 1x1035
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DG and the Work a System Can Do
For a spontaneous process, DG is the maximum work obtainable from the system as the process takes place: DG = workmax For a nonspontaneous process, DG is the maximum work that must be done to the system as the process takes place: DG = workmax An example
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