Activity

1. Chapter 8 Activity

2. Assumptions Thus Far Equilibrium Constants Assumes Naked Ions Assumes that the Ionic Strength is controlled by the ions of interest ONLY being in solution

3. Naked Ions The true radius of the ion in solution is the hydrated radius Hydrated radius - The effective size of an ion or a molecule plus its associated water molecules in solution larger radius of naked ion ? more diffuse electric charge ? fewer water molecules surrounding the ion greater ion charge ? increased solvent attaction ? greater the hydrated radius Effect of Ion Sheath - decreases the frequency in which molecules of interest will interact.

4. Ionic Strength The truth is that the counter ions from the original reactants also exist. Hg2(NO3)2 + 2KIO3 ? Hg2(IO3)2 + 2K+ + 2NO3- Introduction of an inert salt to a sparingly soluble salt increases the solubility of the sparingly soluble salt Introduction of the inert salt increases the ionic strength of the solution

5. Ionic Strength Increased Solubility Anion is surrounded by cations more cations in solution ? increased ionic atmosphere ? decreases the attraction between any particular sets of ions ? the less tendency for the ions to interact Cation is surrounded by anions more anions in solution ? increased ionic atmosphere ? decreases the attraction between any particular sets of ions ? the less tendency for the ions to interact

6. Terminology Ionic Atmosphere - The region of solution around an ion or a charged particle. It contains an excess of oppositely charged ions. The greater the ionic strength of a solution, the higher the charge in the ionic atmosphere. Each ion-plus-atmosphere contains less net charge and there is less attraction between any particular cation and anion

7. Terminology Ionic Strength (?) - a measure of the total concentration of ions in solution. ? = �?icizi2 ci - is the concentration of the ith ion in solution zi - the charge on that ion

8. Ionic Strength Example Find the ionic strength of (a) 0.10 M NaNO3; (b) 0.010 M Na2SO4; and (c) 0.020 M KBr plus 0.010 M Na2SO4

9. Activity Coefficients Equilibrium Constant (K) as previously written, does not predict the effect of ionic strength on a chemical reaction. To take into account the effect of the ionic strength, concentrations are replaced by activities: Ac = [C]?c K = (AccAdd) / (AaaAbb)

10. Activity Coefficients Therefore: K = ([C]?Cc[D] ?Dd) / ([A]?Aa[B] ?Bb) Activity Coefficient determined by the Extended Debye-H�ckel equation log ? = (-0.51z2??) / (1 + (??? / 305)) ? - size of the hydrated ion in picometers

11. Activity Coefficients Table 8-1 lists sizes and activity coefficients of various ions Note: All ions of the same size, charge, and of the same concentration have the same activity coefficient.

12. Ionic Strength, Ion Charge, and Ion Size effect Increased ionic concentration ? decreased activity coefficient Low ionic strengths ? activity coefficients approach unity Increased ion charge (�) ? increased departure of activity coefficient from unity corrections are more important where the charge of the ion is �3 compared to �1 Smaller hydrated radius ? increased importance of activity effects

13. Activity Coefficient Calculation Find the activity coefficient of Hg22+ in a solution of 3.3 mM Hg2(NO3)2. Find the activity coefficient of each ion at the indicated ionic strength: (a) S2- (? = 0.001 M) (b) PO43- (? = 0.001 M) (c) Sn4+ (? = 0.05 M) (d) H2NCH2CO2- ? = 0.01 M)

14. Interpolation Table 8-1 Gives ionic strengths for ions at various concentrations Missing values can be extrapolated using linear interpolation (unknown y interval / ?y) = (known x interval / ?x)

15. Interpolation Calculate the activity coefficient of H+ when ? = 0.025 Calculate the activity coefficient of OH- when ? = 0.030 M. Calculate the activity coefficient of formate, HCO2-, when ? = 0.038 M by using (a) the extended Debye-Huckel Eqn (b) linear interpolation

16. Using Activity Coefficients Write each equilibrium constant with activities in place of concentrations Use the ionic strength of the solution to find the activity coefficients

17. Using Activity Coefficients Solubility Problem What is the Ca2+ concentration in a solution of 0.05 M NaClO4 that is saturated with CaF2? The Common Ion Effect Find the concentration of Ca2+ in 0.050 M NaF saturated with CaF2.

18. Using Activity Coefficients Calculate the solubility of Ag2CrO4 (expressed as moles of CrO42- per liter) in (a) 0.050 M KClO4 (b) 0.0050 M AgNO3

19. Using Activity Coefficients Problem Requiring an Iterative Solution Calculate the solubility of LiF in distilled water. Calculate the concentration of Tl+ in a saturated solution of TlBr in water.

20. pH Revisited Again concentration is replaced with activity pH = -log AH+ = -log [H+]?H+

21. pH Revisited Calculate the pH of pure water using activity coefficients correctly. Calculate the pH of water containing 0.10 M KCl at 25oC. Find the pH of (a) 0.050 M HClO4 and (b) 0.050 M HClO4 plus 0.050 M HBr

22. Chapter 8 - Homework Problems - 3, 5, 7, 8, 12, 13, 19