chem. 31 – 3/16 lecture. announcements i more on additional problem + quiz –when stoichiometry...
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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 1:1CaSO4 (s) ↔ Ca2+ + SO4
2- ↔ CaSO4 (aq)
• Water Hardness Lab Report– Turn in completed report form– Due Wednesday
Announcements II• Today’s Lecture – Chapter 7 “Advanced
Equilibrium Theory”– 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 spheresGamma Plots
0.00
0.20
0.40
0.60
0.80
1.00
1.20
0.00 0.02 0.04 0.06 0.08 0.10 0.12
Ionic Strength (M)
Act
ivit
y co
effi
cien
t
Li+
Ba2+
PO43-
Li+ Rb+
ion
Hydrated sphere
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- ↔ S2O3
2- + H2O(l)
– HSO4- ↔ SO4
2- + H+
Ionic Strength EffectsEffects on Equilibrium - Quantitative
• Calculate expected [Mg2+] in equilibrium with solid MgCO3 for cases both with and without NaCl.– Go to Board
Ionic Strength EffectsReal 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 7The 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 MethodSolubility of MgCO3 – Why did it fail?
• MgCO3 Mg2+ + CO32-
x x Equil. (in ICE)• So x = (Ksp)1/2 = 1.87 x 10-4 M (neglecting ionic strength effects)• Problem is both ions can react further:
CO32- + H2O HCO3
- + OH-
And HCO3- + H2O H2CO3 + OH-
Also, Mg2+ + OH- MgOH+ And Mg2+ + CO3
2- MgCO3 (aq)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 “[CO3
2-]” 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
enhancements: (% over rxn 1 only)90%0%9%16%
The Systematic MethodThe Six Steps
1. Write out all relevant reactions2. Write a “Charge Balance Equation”3. Write “Mass Balance Equations”4. Write out all equilibrium equations5. 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 MethodpH of 5.0 x 10-8 M HCl
• Demonstrate Method on Board
The Systematic MethodConceptual 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+ + Cl-
2) Ag+ + 2Ph Ag(Ph)2+
– Mass Balance equations:• if only rxn 1) [Cl-] = [Ag+]• w/ rxn 2) [Cl-] = [Ag+] +
[Ag(Ph)2+]
AgCl(s)
Ag+
Ag+
Ag+
Ag+Cl-Cl- Cl-
Cl-
Ph
Ph
Ph
Ph
N N
1,10-phenathroline
Ag+
Notes: with rxn 1) only, 2 Ag+s = 2 Cl-s; with rxn 2) also, 3 Cls = 2 Ags + 1 Ag(Ph)2
2nd Mass Balance Equation:
[Ph]o = 0.010 M = [Ph]Total = [Ph] + 2[Ag(Ph)2+]
Initially 4 Phs, then 2 Phs + one complex containing 2 Phs (so total # of Phs remains constant)
The Systematic Method2nd 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