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