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Chapter 20

Chapter 20. Thermodynamics and Equilibrium. Overview. First Law of Thermodynamics Spontaneous Processes and Entropy Entropy and the Second Law of Thermodynamics Standard Entropies and the Third Law of Thermodynamics. Free Energy Concept Free Energy and Spontaneity

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Chapter 20

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  1. Chapter 20 Thermodynamics and Equilibrium

  2. Overview • First Law of Thermodynamics • Spontaneous Processes and Entropy • Entropy and the Second Law of Thermodynamics • Standard Entropies and the Third Law of Thermodynamics

  3. Free Energy Concept • Free Energy and Spontaneity • Interpretation of Free Energy • Free Energy and Equilibrium Constants • Relating DG° to the Equilibrium Constant • Change of Free Energy with Temperature

  4. Definitions • Spontaneous or Product-favored reaction: reaction in which most of the reactants can eventually be converted to products, given sufficient time • Nonspontaneous or Reactant-favored reaction: misleading - does not mean that it does not occur at all, rather, it means that when equilibrium is achieved, not many reactant molecules have been converted into products.

  5. Definitions Continued • Thermodynamics: the science of energy transfer, it helps us to predict whether a reaction can occur given enough time. Thermodynamics tells us nothing about the speed of the reactions.

  6. Reaction Probability • After an exothermic reaction, energy is distributed more randomly - dispersed over a much larger number of atoms and molecules - than it was before. Energy dispersal is favored because it is much more probable that energy will be dispersed than that it will be concentrated. • Just as there is a tendency for highly concentrated energy to disperse, highly concentrated matter also tends to disperse.

  7. There are two ways that the final state of a system can be more probable than the initial one • 1. Having energy dispersed over a greater number of atoms and molecules and • 2. Having the atoms and molecules themselves more disordered

  8. Entropy: A Measure of Matter Dispersal or Disorder • The dispersal or disorder in sample of matter can be measured with a calorimeter, the same instrument needed to measure the enthalpy change when a reaction occurs. The result is a thermodynamic function called entropy and symbolized by S.

  9. Entropy and the Third Law • Measurement of entropy depends on the assumption that in a perfect crystal at the absolute zero temperature all translational motion ceases and there is not any disorder.

  10. Calculating Entropy Change • When energy is transferred to matter in very small increments, so that the temperature change is very small, the entropy change can be calculated as DS = q/T, the heat absorbed divided by the absolute temperature at which the change occurs.

  11. Standard Molar Entropies • Apply to one mole of a substance at standard pressure. Expressed in units of joules per kelvin mole. DS = Sproducts – Sreactants

  12. Example

  13. Generalizations About Entropy • 1. When comparing the same or very similar substances, entropies of gases are much larger than those of liquids, which are larger than for solids. • 2. Entropies of more complex molecules are larger than those of simpler molecules, especially in a series of closely related compounds. • 3. Entropies of ionic solids become larger as the attractions among the ions become weaker. • 4. Entropy usually increases when a pure liquid or solid dissolves in a solution. • 5. Entropy increases when a dissolved gas escapes from a solution.

  14. Entropy and the Second Law of Thermodynamics • In a product-favored process there is a net increase in the entropy of the system and the surroundings. In other words when a product favored reaction occurs the entropy (disorder) of the universe increases. This means that even if the entropy of a particular system decreases in a product favored process, the total change in the entropy of the universe (the system and all its surroundings) must be positive.

  15. Entropy of the Surroundings • The sign of DSsurr depends on the direction of heat flow (q).

  16. A positive DSsurr occurs when heat flows out of the system into the surroundings and increases thermal motion. This should make sense to you because heat is a form of energy and when the energy increases the molecular motion increases which causes more randomness.

  17. A negative DSsurr occurs when heat flows into the system from the surroundings, decreasing the thermal motion of the surroundings and therefore decreasing the entropy.

  18. DSsurr and absolute temperature • If the surroundings are at a high temperature, the various types of molecular motion are already sufficiently energetic. Therefore, the absorption of heat from an exothermic process in the system will have relatively little impact on molecular motions and the resulting increase in entropy will be small.

  19. If the temperature of the surroundings is low, then the addition of the same amount of heat will cause a more drastic increase in molecular motions and hence a larger increase in entropy. So, the entropy change produced when a given amount of heat is transferred is greater at low temperatures than at high temperatures.

  20. The result is that DSsurr = qsurr/T ; where qsurr is the heat flow into the surroundings at the absolute (Kelvin) temperature, T. If you recall, when we first studied thermochemistry, for constant-pressure processes DH was defined as being equal to the qsystem which would be equal to -qsurr. • So this means that DSsurr = -DH/T

  21. DS and DH What this all means is that for a product-favored process: DSsystem - DH/T > 0 or TDS - DH > 0

  22. Second Law of Thermodynamics • To be product favored a reaction must lead to an increase in the entropy of the universe. We now know that for a product favored process TDS - DH > 0 or if we multiply the equation throughout by -1: DH - TDS < 0. Now we have a criterion for a product-favored reaction that is expressed only in terms of the properties of the system and we no longer need be concerned with the surroundings.

  23. Gibbs Free Energy • A new thermodynamic function can now be introduced, its called the Gibbs Free Energy, or simply Free Energy, as follows: • G = H - TS • G has the units of energy and, like H and S, it is a state function. (State Function = A quantity whose value is determined only by the state of the system)

  24. DG • The change in free energy (DG) of a system (which if what we're interested in) for a process at constant temperature is given by DG = DH - TDS

  25. Standard Free Energies of Formation The standard free energy of formation, Gf, of a substance is defined similarly to the standard enthalpy of formation. That is, DGf is the free-energy change that occurs when 1 mol of a substance is formed from its elements in their most stable states at 1 atm and at a specified temperature (usually 25 C)

  26. By tabulating DGf for substances we can easily calculate DG for any reaction involving those substances using the following formula: DG = DGf (products) - DGf (reactants) • NOTE: If you are confused about the two different ways to calculate the DG - this last one can only be used when the temperature is that of the tabulated values - usually 25 C.

  27. Example

  28. Product-Favored or Reactant-Favored? • Reactions at constant temperature and pressure go in such a direction as to decrease the free energy of the system. DG < 0 Product-Favored Reaction DG > 0 Reactant-Favored. DG = 0 The system is at equilibrium. There is no net change.

  29. Free-Energy and Temperature DH DS Low Temperature High Temperature • + + reactant-favored product-favored • + - reactant-favored reactant-favored • - + product-favored product-favored • - - product-favored reactant-favored

  30. G – Temperature Dependence • Spontaneity: Reaction becomes spontaneous when G goes from + to . We use G = 0 to tell us when reaction just becomes spontaneous or 0 = H  TS or T = H/S.

  31. Example Determine the temperature at which the synthesis of HI(g) becomes spontaneous. Ho = +52.96 kJ and So = +166.4 J/mol H2(g) + I2(g)  2HI(g)

  32. EQUILIBRIUM CONSTANTS AND G • Equilibrium constant for a reaction aA + bB +...  mM + nN + ... is defined as • Tells how far to right reaction proceeds. • Large value  mostly products. • Small value  mostly reactants. • At equilibrium this equation must always be obeyed no matter what relative amount of reactant and was started with.

  33. Thermodynamics and the Equilibrium Constant DG = DGo + RT InQ • At equilibrium Q = K and DG = 0 DGo = -RT InK where R is 8.31 J/mol K

  34. Thermodynamics • First Law: The total energy of the universe is constant • Second Law: The total entropy of the universe is always increasing • Third Law: The entropy of a pure, perfectly formed crystalline substance at absolute zero is zero

  35. Neither of the first two laws of thermodynamics has ever been or can be proven. However, there has never been a single, concrete example showing otherwise.

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