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Characteristic functions . Thermodynamics of chemical equilibrium

Characteristic functions . Thermodynamics of chemical equilibrium. Plan 1. Criterion of the Process’s Direction . 2. Gibbs Helmholtz equation and thermodynamics gas’s functiion . 3. The third law of thermodynamics. Prepared by Kozachok S.S.

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Characteristic functions . Thermodynamics of chemical equilibrium

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  1. Characteristic functions. Thermodynamics of chemical equilibrium Plan 1. Criterion of the Process’sDirection. 2. Gibbs Helmholtzequation and thermodynamics gas’s functiion. 3. The third law of thermodynamics. Prepared by Kozachok S.S.

  2. Definition of the process’s direction according to the caracteristic functions (internal energy) Uis the function of the isochoric-isoentropic process: U dU = TdS – pdV dWmax = -dU For the random process: U0 nonspontaneous spontaneous direction

  3. Definition of the process’s direction according to the enthalpy Нis the function of the isobaric-isoentropic process:: Н dН = TdS + Vdp dWmax = -dН For the random process: Н0 spontaneous nonspontaneous direction

  4. Definition of the process’s direction according to the entropy S is the function of isolated system: S dWmax =TdS For the random process: S0 nonspontaneous spontaneous direction

  5. Determination of a direction of a process using Helmholtz’ energy F is the function of isochoric-isothermal process: F dF = dU - TdS dWmax = -dF For random process:F0 Spontaneous Forced process Direction of a process

  6. Determination of a direction of a process using Gibbs’ free energy Gis the function of isobaric-isothermal process : G dG = dH- TdS dWmax = -dG For spontaneous process:G0 Spontaneous Forced process Direction of a process

  7. Helmholtz’ equation: Gibbs’ equation: F = U - TS G = H - TS

  8. Thermodynamic functions of the ideal gases F = kF - RTlnV, wherekFis the constant, which depends from temperature (kF = U – TkS) Gi = kG,I + RTlnPi For real gases: G = G0 + RTlnf, wheref - a fugacity;f = γ · P; γ is a coefficient of a fugacity;γ = P/Pideal.

  9. Nernst’ heat theorem: NearТ = 0: G = Н - TS = H E Н TS G 0 T

  10. THIRD LAW OF THERMODYNAMICS:the entropy of a perfectly pure crystal at absolute zero T=273 K is zero. Ludwig Boltzmann’ equation: S = klnW, wherek is Boltzmann’s constantk= R/Na k=1.38 *10-23 J/K. At Т→0: W = 1; S = 0.

  11. Calculation of a standard and an absolute meaning of Entropy Cp ∫ ln T , ifS0 = 0

  12. Chemical equilibrium Plan Chemical potential. Calculation of the chemical equilibrium. Phase equilibrium. Gibb’s phase rule.

  13. The calculation of the chemical potential For ideal gas : For real gas: For ideal solution: For real solution :

  14. CHEMICAL EQUILIBRIUM The state reached when the concentrations of reactantsand products remain constant over timeA mixture of reactants and products in the equilibrium state is called anequilibrium mixture.

  15. According to the balanced equation, 2.0 mol of NO2 forms for each mole ofN2O4 that disappears, so the concentration of N2O4 at any time equals the initial concentration of N2O4 minus half the concentration ofNO2. As time passes, the concentration ofN2O4 decreases and the concentration of NO2 increases until both concentrations level off at constant, equilibrium values:

  16. The Equilibrium Constant Kc

  17. Calculation of the equilibrium constant The equilibrium constant for a reaction at a particular temperature alwayshas the same value. аА + bВ = сС + dD

  18. Pi = CiRT, thatKp = Kc (RT)n, хi = CiRT/Ptotal, that wherenisthe change of moles of gases

  19. The physical content of the equilibrium constants If n= 0 that Kp=Kc=Kx

  20. N.B. This equations are true for ideal gases or solutions. For the real systems the equilibrium constant is expressed by using activity and is named thermodynamic equilibrium constant

  21. Heterogeneous Equilibria Thus far we’ve been discussing homogeneousequilibria, in which all reactants and products are in a single phase, usually either gaseous or solution. Heterogeneous equilibria, by contrast, are those in which reactants and products are present in more than one phase.

  22. Because both CaO and CaCO3 are pure solids, their molar “concentrations” areconstants. In general, the concentration of any pure solid (or pure liquid) is independent of its amount because its concentration is the ratio of its amount (in moles) to its volume (in liters). If, for example, you double the amount of CaCO3 you also double its volume, but the ratio of the two (the concentration) remains constant. Rearranging the equilibrium equation for the decomposition of CaCO3 tocombine the constants [CaCO3], [CaO], and “Kc”, we obtain

  23. N.B.As a general rule, the concentrations of pure solids and pure liquids are not included when writing an equilibrium equation because their concentrations are constants that are incorporated into the value of the equilibrium constant. We include only the concentrations of gases and the concentrations of solutes in solutions because only those concentrations can be varied.

  24. Judging the Extent of Reaction

  25. Predicting the Direction of Reaction The reaction quotient Qc is defined in the same way as the equilibrium constant Kc except that the concentrations in are not necessarily equilibrium values.

  26. Altering an Equilibrium Mixture:Changes in Concentration In general, when an equilibrium is disturbed by the addition or removal of anyreactant or product, Le Châtelier’s principle predicts that • The concentration stress of an added reactant or product is relieved by net reaction in the direction that consumes the added substance. • The concentration stress of a removed reactant or product is relieved by net reaction in the direction that replenishes the removed substance.

  27. If these rules are applied to the equilibrium then the yield of ammonia is increased by an increase in the N2 or H2concentration or by a decrease in the NH3 concentration

  28. Altering an Equilibrium Mixture:Changes in Pressure and Volume

  29. Altering an Equilibrium Mixture:Changes in number of mokes If n <0 at increasing pressure ↑p →↑ increasing in the equilibrium constant K →↑ increasing in product’s quantity (products predominate over reactants) If n >0 at ↑p →↓K →↓ decreasing in product’s quantity (reactants predominate over reactants) If n =0 pressure doesn’t influence on the the equilibrium constant K

  30. Altering an Equilibrium Mixture:Changes in Temperature

  31. Van't Hoff'sisotherm equation Isobar equation G = -RT ln K G = G0 + RT ln K Isochor equation

  32. Van't Hoff'sisotherm equation G = G0 + RT ln K G = RT ln - RT lnKp Predicting the Direction of Reaction according to isotherm equation G <0, when < lnKp, the spontaneous process of net reaction goes from left to right G >0, when > lnKp, the spontaneous process of net reaction goes from right to left G = 0 that is equilibrium state

  33. Thanks for attention

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