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Chemistry 232

Chemistry 232. Electrolyte Solutions. 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?. Thermodynamics (II).

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Chemistry 232

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  1. Chemistry 232 Electrolyte Solutions

  2. 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?

  3. Thermodynamics (II) • 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

  4. 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  = + + -   = + + +- -

  5. 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

  6. 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

  7. 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-)-

  8. 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-)-

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

  10. 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

  11. Determination of Activity Coefficients in Solution • Two ways • Use the Gibbs-Duhem equation and  for the solvent to estimate  for the solute. • Determination of osmotic coefficients from • colligative properties • vapour pressure measurements

  12. Estimates of Activity Coefficients in Electrolyte Solutions • A few have been proposed to allow the theoretical estimation of the mean activity coefficients of an electrolyte. • Each has a limited range of applicability.

  13. 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

  14. 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

  15. 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)

  16. The Equilibrium Constant • For a nonideal system, the nonstandard Gibbs energy of reaction is written

  17. The Equilibrium Condition • If we apply the equilibrium conditions to the above equation

  18. The Autoionization of Water • Water autoionizes (self-dissociates) to a small extent 2H2O(l) ⇌ H3O+(aq) + OH-(aq) H2O(l) ⇌ H+(aq) + OH-(aq) • These are both equivalent definitions of the autoionization reaction. • Water is amphoteric.

  19. The Autoionization Equilibrium • From the equilibrium chapter • But we know a(H2O) is 1.00!

  20. The Defination of Kw Kw = a(H+) a(OH-) Ion product constant for water, Kw, is the product of the activities of the H+ and OH- ions in pure water at a temperature of 298.15 K Kw = a(H+) a(OH-) = 1.0x10-14 at 298.2 K

  21. The pH scale • Attributed to Sørenson in 1909 • We should define the pH of the solution in terms of the hydrogen ion activity in solution pH = -log a(H+) • Single ion activities and activity coefficients can’t be measured

  22. Determination of pH • What are we really measuring when we measure the pH? pH = -log a(H+) • a (H+) is the best approximation to the hydrogen ion activity in solution. • How do we measure a(H+)?

  23. For the dissociation of HCl in water HCl (aq)  Cl-(aq) + H+(aq) • We measure the mean activity of the acid a(HCl) = a(H+) a(Cl-) a(H+) a(Cl-) = (a(HCl))2

  24. Under the assumption a(H+) = a(Cl-) • We obtain a´(H+) = (a(HCl))1/2 = a(HCl)

  25. Equilibria in Aqueous Solutions of Weak Acids/ Weak Bases • By definition, a weak acid or a weak base does not ionize completely in water ( <<100%). • How would we calculate the pH of a solution of a weak acid or a weak base in water?

  26. Equilibria of Weak Acids in Water: The Ka Value • Define the acid dissociation constant Ka • For a general weak acid reaction HA (aq) ⇌ H+ (aq) + A- (aq)

  27. Equilibria of Weak Acids in Water • For the dissolution of HF(aq) in water. HF (aq)  H+ (aq) + F- (aq)

  28. The Nonelectrolyte Activity HF (aq) ⇌ H+ (aq) + F- (aq) • The undissociated HF is a nonelectrolyte  a(HF) = (HF) m[HF]  m[HF] (HF)  1

  29. Equilibria of Weak Bases in Water • Calculate the percentage dissociation of a weak base in water (and the pH of the solutions) CH3NH2 (aq) + H2O ⇌ CH3NH3+(aq)+ OH- (aq)

  30. The Kb Value • Define the base dissociation constant Kb • For a general weak base reaction with water B (aq) + H2O (aq) ⇌ B+ (aq) + OH- (aq)

  31. Calculating the pH of Solutions of Strong Acids • For the dissolution of HCl, HI, or any of the other seven strong acids in water HCl (aq)  H+ (aq) + Cl- (aq) • The pH of these solutions can be estimated from the molality and the mean activity coefficient of the dissolved acid pH = -log ( (acid) m[H+])

  32. Calculating the pH of Solution of Strong Bases • For the dissolution of NaOH, Ba(OH)2, or any of the other strong bases in water NaOH (aq)  Na+ (aq) + OH- (aq) pOH = -log ( (base) m[OH-])

  33. Calculating the pH of a Weak Acid Solution • The pH of a weak acid solution is obtained via an iterative procedure. • We begin by making the assumption that the mean activity coefficient of the dissociated acid is 1.00. • We ‘correct’ the value of (H+) by calculating the mean activity coefficient of the dissociated acid. • Repeat the procedure until (H+) converges.

  34. The Definition of a Buffer • Buffer  a reasonably concentrated solution of a weak acid and its conjugate base • Buffers resist pH changes when an additional amount of strong acid or strong base is added to the solutions.

  35. How would we calculate the pH of a buffer solution?

  36. note pH = -log a(H+) Define pKa = -log (Ka )

  37. The Buffer Equation • Substituting and rearranging

  38. The Generalized Buffer Equation • The pH of the solution determined by the ratio of the weak acid to the conjugate base. • Henderson-Hasselbalch equation often used for buffer calculations!

  39. Buffer  CH3COONa (aq) and CH3COOH (aq)) CH3COOH (aq) ⇄ CH3COO- (aq) + H+ (aq) The Equilibrium Data Table

  40. The pH of the solution will be almost entirely due to the original molalities of acid and base!!

  41. Solubility Equilibria • Examine the following systems AgCl (s) ⇌ Ag+ (aq) + Cl- (aq) BaF2 (s) ⇌ Ba2+ (aq) + 2 F- (aq) • Using the principles of chemical equilibrium, we write the equilibrium constant expressions as follows

  42. The Common Ion Effect • What about the solubility of AgCl in solution containing NaCl (aq)? AgCl (s) ⇌ Ag+ (aq) + Cl- (aq) NaCl (aq) Na+ (aq) + Cl- (aq) AgCl (s) ⇌ Ag+ (aq) + Cl- (aq) Equilibrium is displaced to the left by LeChatelier’s principle (an example of the common ion effect).

  43. Solubility in the Presence of an Inert Electrolyte • What happens when we try to dissolve a solid like AgCl in solutions of an inert electrolyte (e.g., KNO3 (aq))? • We must now take into account of the effect of the ionic strength on the mean activity coefficient!

  44. The Salting-In Effect AgCl (s) ⇌ Ag+ (aq) + Cl- (aq). • Designate the solubility of the salt in the absence of the inert electrolyte as so = m(Ag+) = m(Cl-) at equilibrium.

  45. For a dilute solution • Designate s as the solubility of the salt in the presence of varying concentrations of inert electrolyte.

  46. Reaction Equilibria in Nonideal Gaseous Systems • For a nonideal system gaseous, the nonstandard Gibbs energy of reaction is written

  47. The Equilibrium Condition • Calculate the equilibrium composition from the fugacity coefficients from compression factor data

  48. Temperature and Pressure Dependence of Ko • As a function of temperature • As a function of pressure

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