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  f H = 0 kJ/mole at all temperatures S = 0 J/(K mole) at all temperatures  f G = 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 = n s  s + n  = n s  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  ) = + ( +  + 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 The ideal part Deviations from ideal behaviour

10. KCl CaCl 2 H 2 SO 4 HCl LaCl 3 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, 63 rd ed.; R.C. Weast Ed.; CRC Press, Boca Raton, Fl (1982).

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. u This is valid in the up to a concentration of 0.010 molal! The Debye Hűckel Limiting Law 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 2H 2 O(l) ⇌ H 3 O + (aq) + OH - (aq) H 2 O(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 u But we know a(H 2 O) is 1.00!

20. The Defination of K w K w = a(H + ) a(OH - ) Ion product constant for water, K w, is the product of the activities of the H + and OH - ions in pure water at a temperature of 298.15 K K w = 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 K a Value  Define the acid dissociation constant K a  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) CH 3 NH 2 (aq) + H 2 O ⇌ CH 3 NH 3 + (aq) + OH - (aq)

30. The K b Value  Define the base dissociation constant K b  For a general weak base reaction with water B (aq) + H 2 O (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 pK a = -log (K a )

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  CH 3 COONa (aq) and CH 3 COOH (aq)) CH 3 COOH (aq) ⇄ CH 3 COO - (aq) + H + (aq) The Equilibrium Data Table n(CH 3 COOH)n(H + )n(CH 3 COO - ) StartA0B Change -  eq +  eq  m m(A-  eq )(  eq )(B+  eq )

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) BaF 2 (s) ⇌ Ba 2+ (aq) + 2 F - (aq)  Using the principles of chemical equilibrium, we write the equilibrium constant expressions as follows

43. 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).

44. 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., KNO 3 (aq))?  We must now take into account of the effect of the ionic strength on the mean activity coefficient!

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

46.  For a dilute solution u Designate s as the solubility of the salt in the presence of varying concentrations of inert electrolyte.

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

48. The Equilibrium Condition  Calculate the equilibrium composition from the fugacity coefficients from compression factor data

49. Temperature and Pressure Dependence of K o  As a function of temperature As a function of pressure