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Chemistry 434

Chemistry 434. A Brief Review of Thermodynamics. Internal Energy and the First Law. The infinitesimal change in the internal energy . For a general process. The First Law of Thermodynamics. The Constant Volume Heat Capacity. Define the constant volume heat capacity, C V. Enthalpy.

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Chemistry 434

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  1. Chemistry 434 A Brief Review of Thermodynamics

  2. Internal Energy and the First Law • The infinitesimal change in the internal energy • For a general process The First Law of Thermodynamics

  3. The Constant Volume Heat Capacity • Define the constant volume heat capacity, CV

  4. Enthalpy • We define the enthalpy of the system, H

  5. The Constant Pressure Heat Capacity • Define the constant pressure heat capacity, CP

  6. Thermodynamic Definition • Spontaneous Process – the process occurs without outside work being done on the system.

  7. Mathematical Definition of Entropy • The entropy of the system is defined as follows

  8. The Fundamental Equation of Thermodynamics • Combine the first law of thermodynamics with the definition of entropy.

  9. The Temperature dependence of the Entropy • Under isochoric conditions, the entropy dependence on temperature is related to CV

  10. Entropy changes Under Constant Volume Conditions • For a system undergoing an isochoric temperature change • For a macroscopic system

  11. The Temperature dependence of the Entropy • Under isobaric conditions, the entropy dependence on temperature is related to CP

  12. Entropy changes Under Constant Pressure Conditions • For a system undergoing an isobaric temperature change • For a macroscopic system

  13. The Second Law of Thermodynamics • The second law of thermodynamics concerns itself with the entropy of the universe (univS). • univS unchanged in a reversible process • univS always increases for an irreversible process

  14. The Third Law of Thermodynamics • The Third Law - the entropy of any perfect crystal is 0 J /(K mole) at 0 K (absolute 0!) • Due to the Third Law, we are able to calculate absolute entropy values.

  15. Combining the First and Second Laws • From the first law

  16. Pressure Volume and Other Types of Work • Many types of work can be done on or by chemical systems. • Electrical work. • Surface expansion. • Stress-strain work. dw=-Pext dV+dwa where dwa includes all other types of work

  17. The General Condition of Equilibrium and Spontaneity • For a general system

  18. Isothermal Processes • For a systems where the temperature is constant and equal to Tsurr

  19. The Helmholtz Energy • Define the Helmholtz energy A A(T,V) =U – TS • Note that for an isothermal process dA  dw A  w • For an isochoric, isothermal process A  0

  20. The Properties of A • The Helmholtz energy is a function of the temperature and volume

  21. Isothermal Volume Changes • For an ideal gas undergoing an isothermal volume change

  22. Isothermal Processes at Constant Pressure • For an isothermal, isobaric transformation

  23. The Gibbs Energy • Define the Gibbs energy G G(T,P) =U – TS+PV • Note that for an isothermal process dG  dwa G wa • For an isothermal, isobaric process G  0

  24. The Properties of G • The Gibbs energy is a function of temperature and pressure

  25. Isothermal Pressure Changes • For an ideal gas undergoing an isothermal pressure change

  26. Temperature Dependence of A • Under isochoric conditions

  27. Gibbs Energy Changes As a Function of Temperature • The Gibbs energy changes can be calculated at various temperatures

  28. The Chemical Potential • Define the chemical potential  = G/n

  29. Gibbs Energy and Spontaneity sysG < 0 - spontaneous process sysG > 0 - non-spontaneous process (note that this process would be spontaneous in the reverse direction) sysG = 0 - system is in equilibrium

  30. Applications of the Gibbs Energy • The Gibbs energy is used to determine the spontaneous direction of a process. • Two contributions to the Gibbs energy change (G) • Entropy (S) • Enthalpy (H) G = H - TS

  31. Thermodynamics of Ions in Solutions • Electrolyte solutions – deviations from ideal behaviour occur at molalities as low as 0.01 mole/kg. • How do we obtain thermodynamic properties of ionic species in solution?

  32. For the H+(aq) ion, we define • fH = 0 kJ/mole at all temperatures • S = 0 J/(K mole) at all temperatures • fG = 0 kJ/mole at all temperatures

  33. Activities in Electrolyte Solutions • For the following discussion • Solvent “s” • Cation “+” • Anion “=“ • Consider 1 mole of an electrolyte dissociating into + cations and - anions G = nss + n  = nss + n+ + +n- - • Note – since  = + + -   = + + +- -

  34. The Mean Ionic Chemical Potential • We define =  /  • We now proceed to define the activities  =  + RT ln a + = + + RT ln a+ - = - + RT ln a-  =  + RT ln a

  35. The Relationship Between a and a • Since =  /   =  + RT ln a =  ( + RT ln a) Since =  /  • This gives us the relationship between the electrolyte activity and the mean activity (a)= a

  36. The Relationship Between a , a- and a+ • We note that  = + + +- - and =  /  • This gives us the following relationship ( + RT ln a) = n+ (+ + RT ln a+) + - ( - + RT ln a-) • Since  = +++ -- (a) = (a+)+ (a-)-

  37. Activities in Electrolyte Solutions • The activities of various components in an electrolyte solution are defined as follows a+ = + m+ a- = - m- a+ = + m+ • As with the activities () = (+)+ (-)- (m) = (m+)+ (m-)-

  38. The Chemical Potential Expression • This can be factored into two parts Deviations from ideal behaviour The ideal part

  39. Activity Coefficients As a Function of Molality Data obtained from Glasstone et al., Introduction to Electrochemistry, Van Nostrand (1942). CRC Handbook of Chemistry and Physics, 63rd ed.; R.C. Weast Ed.; CRC Press, Boca Raton, Fl (1982). CaCl2 HCl LaCl3 KCl H2SO4

  40. Estimates of Activity Coefficients in Electrolyte Solutions • The are a number of theories that have been proposed to allow the theoretical estimation of the mean activity coefficients of an electrolyte. • Each has a limited range of applicability.

  41. The Debye Hűckel Limiting Law • This is valid in the up to a concentration of 0.010 molal! Z+ = charge of cation; z- = charge of anion

  42. Debye Hűckel Extended Law • This equation can reliably estimate the activity coefficients up to a concentration of 0.10 mole/kg. B = 1.00 (kg/mole)1/2

  43. The Davies Equation • This equation can reliably estimate the activity coefficients up to a concentration of 1.00 mole/kg. k = 0.30 (kg/mole)

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