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.
• ? ½?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?CcD ?Dd) / (A?AaB ?Bb)
• Activity Coefficient determined by the Extended
  Debye-Hückel 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