Chem. 31 – 3/18 Lecture
Announcements
• Water Hardness Lab Report – due today
• Today’s Lecture – Chapter 7 “Advanced
Equilibrium Theory” - The Systematic Method
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Examples of failures
6 steps to method
More on Mass Balance
General Comments on the Systematic Method
The Systematic Method
Solubility of MgCO3 – Why did it fail?
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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
The Systematic Method
3rd Example
•
A student prepares a solution that
contains 0.050 mol of AgNO3 and 0.0040
mol NH3 in water with a total volume of
1.00 L. The AgNO3 is totally soluble, NH3
is a weak base, and Ag+ reacts with NH3
to form Ag(NH3)2+. Assume the Ag+
does not react with water or OH-. Go
through the first 5 steps of the
systematic method.
The Systematic Method
Stong Acid/Strong Base Problems
• When do we need to use the systematic
approach?
– when more than 1 coupled reaction occur
(unless coupling is insignificant)
– examples: 4.0 x 10-3 M HCl. 7.2 x 10-3 M
NaOH
– Key point is the charge balance equation:
- for strong acid HX, [H+] = [X-] + [OH-]
- If [X-] >> [OH-], then [H+] = [X-]
– for strong base NaOH, [H+] + [Na+] = [OH-]
The Systematic Method
General Comments
• Effects of secondary reactions
– e.g. MgCO3 dissolution
– Additional reactions increase solubility
– Secondary reactions also can affect pH (CO32+ H2O will produce OH- while Mg2+ + H2O will
produce H+)
• Software is also available to solve these
types of problems (but still need to know
steps 1 → 5 to get problems solved)