Chem. 31 – 3/16 Lecture
Announcements I
• More on Additional Problem + Quiz
– When stoichiometry is the same, Ksp gives solubility (e.g.
Ksp(AgCl) = 1.8 x 10-10 and Ksp(AgI) = 8.3 x 10-17)
– When stoichiometry is different, one must look at reaction
(e.g. Ag2CrO4 – Ksp = 1.2 x 10-12 vs. BaCrO4
Ksp = 2.1 x 10-10)
– For Sparingly Soluble Salts, any further reactions of solubility
products lead to greater solubility
– Ca in quiz was tricky because the stoichiometry stayed 1:1
CaSO4 (s) ↔ Ca2+ + SO42- ↔ CaSO4 (aq)
• Water Hardness Lab Report
– Turn in completed report form
– Due Wednesday
Announcements II
• Today’s Lecture – Chapter 7 “Advanced Equilibrium
Theory”
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–
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Replacement Equations: Activity and Activity Coefficients
Consideration of Activity in Solving Equilibrium Problems
The Real Equation for pH
The Systematic Method
• Examples of failures
• 6 steps to method
• More on Mass Balance
Factors Influencing g
• Ionic Strength: as m increase, g decreases
• Charge of Ion: a larger decrease in g occurs for
more highly charged ions
• Size of Ion: Note: very small ions like Li+
actually have large hydrated spheres
ion
Gamma Plots
1.20
Activity coefficient
1.00
0.80
Li+
0.60
Ba2+
Li+
PO430.40
0.20
0.00
0.00
0.02
0.04
0.06
0.08
0.10
0.12
Ionic Strength (M)
Hydrated sphere
Rb+
Ionic Strength Effects on Equilibria
Qualitative Effects
• An increase in ionic strength shifts equilibria to
the side with more ions or more highly charged
ions
• Example Problems: (predict the shift as m
increases)
– NH3(aq) + H2O(l) ↔ NH4+ + OH– Cu2+ + 4OH- ↔ Cu(OH)42– 2HSO3- ↔ S2O32- + H2O(l)
– HSO4- ↔ SO42- + H+
Ionic Strength Effects
Effects on Equilibrium - Quantitative
• Calculate expected [Mg2+] in equilibrium
with solid MgCO3 for cases both with and
without NaCl.
– Go to Board
Ionic Strength Effects
Real Equation for pH
• pH = -logAH+ = -log(gH+[H+])
• Example Problem: Determine the pH of a
solution containing 0.0050 M HCl and
0.020 M CaCl2.
• Note: H2O  H+ + OH- also affected by
ionic strength
Second Part to Chapter 7
The Systematic Method
• Question: Why can’t we apply the ICE (initial,
change, equilibrium) method to any type of
equilibrium problem?
• Answer: That method is best designed for cases
where there is only one relevant equilibrium
reaction.
• Examples of failures:
– Solubility of MgCO3
– pH of 5.0 x 10-8 M HCl solution (Show failure of
Chem. 1B method)
– Note: both problems can be solved using ICE method,
but problem set up is more complicated
The Systematic Method
Solubility of MgCO3 – Why did it fail?
•
•
•
•
•
•
MgCO3  Mg2+ + CO32x
x
Equil. (in ICE)
1/2
So x = (Ksp) = 1.87 x 10-4 M (neglecting ionic strength effects)
Problem is both ions can react further: enhancements: (% over rxn 1 only)
CO32- + H2O  HCO3- + OH90%
And HCO3- + H2O  H2CO3 + OH0%
Also, Mg2+ + OH-  MgOH+
9%
And Mg2+ + CO32-  MgCO3 (aq)
16%
Finally, we also have H2O  H+ + OH- re-establishing equilibrium
Each additional reaction results in greater dissolution
To properly solve problem we must consider 6 reactions not just 1
Measured “[CO32-]” from titration = [CO32-] + 0.5[OH-] + 0.5[HCO3-] + [MgCO3] +
0.5[MgOH+]
• The “further” reactions makes [Mg2+] ≠ [CO32-], so ICE method fails (or needs
modification by ICE tables for other reactions)
• Actual solubility is greater than ICE method finds
[Mg2+]total = solubility ~ 3.3 x 10-4 M (from systematic approach)
Predicted HCl needed = 3.3 mL (close to that measured)
These calculations didn’t include activity which would lead to a ~10% increase in
solubility (~3.6 mL HCl needed). In 0.1 M NaCl, I get 6.1 mL HCl needed
The Systematic Method
The Six Steps
1.
2.
3.
4.
5.
Write out all relevant reactions
Write a “Charge Balance Equation”
Write “Mass Balance Equations”
Write out all equilibrium equations
Check that the number of equations (in 2 to 4
above) = (or maybe >) the number of
unknowns (undefined concentrations)
6. Solve for the desired unknown(s) by reducing
the equations to one equation with one
unknown. Then solve for remaining unknowns
Note: the emphasis of teaching the systematic method is steps 1 to 5.
Step 6 will be reserved for “easy” problems with 2 to max 3 unknowns
The Systematic Method
pH of 5.0 x 10-8 M HCl
• Demonstrate Method on Board
The Systematic Method
Conceptual Approach to Mass Balance Equations
• With every source of related
species, there should be one mass
balance equation (or one set for
ionic compounds)
• Example:
– Solubility of AgCl in water with
0.010 M 1,10-phenathroline (Ph)
– Reactions:
1) AgCl(s)  Ag+ + Cl2) Ag+ + 2Ph  Ag(Ph)2+
– Mass Balance equations:
• if only rxn 1) [Cl-] = [Ag+]
• w/ rxn 2) [Cl-] = [Ag+] +
[Ag(Ph)2+]
1,10-phenathroline
N
N
Ag+
Ph
Ph
Ph
Ph
Ag+
+
Ag Cl
+
Cl- Ag
Cl-
Ag+ Cl-
2nd Mass Balance Equation:
AgCl(s)
+]
+
[Ph]oNotes:
= 0.010
M
=
[Ph]
=
[Ph]
+
2[Ag(Ph)
with rxn 1) Total
only, 2 Ag s = 2 Cl s; 2with rxn 2)
also,
3 Cls
= 22 Phs
Ags++one
1 Ag(Ph)
Initially
4 Phs,
then
complex
2 containing 2 Phs (so total # of Phs remains constant)
The Systematic Method
2nd Example
• An aqueous mixture of CdCl2 and NaSCN is
made
– Initial concentrations are [CdCl2] = 0.0080 M and
[NaSCN] = 0.0040 M
– Cd2+ reacts with SCN- to form CdSCN+ K = 95
– HSCN is a strong acid
– Ignore any other reactions (e.g. formation of CdOH+)
– Ignore activity considerations
– Determine the concentrations of all species