Chem. 31 – 3/11 Lecture

Announcements I• Exam 1

– Grading error on p. 3 (problem 4); was graded as though 10 pts for entire problem – not just part a)

– That was the reason for getting 96 pts total and giving everyone 4 additional points

– Average = 77• Cl lab report

– Due Today• Homework Set 2 – Turn in

Problem 2.1

100s 90s 80s 70s 60s 50s <500

2

4

6

8

10

12

14

16

Axis Title

Announcements II• Quiz 3 Today• Today’s Lecture – Chapter 7 “Advanced

Equilibrium Theory”– Why Equilibirum Theory Can Fail– Ionic Strength: What is it and how do we calculate it– Replacement Equations: Activity and Activity

Coefficients

Chapter 7“Adjustments” to Equilibrium Theory

• There are two areas where the general chemistry equilibrium theory can give wrong results:– When the solution has high

concentrations of ions– When multiple, interacting equilibria

occur– I had planned a demonstration, but due

to distance to class plus finding equipment, I’m skipping the demonstration this year

Demonstration – Slide 1

• Summary of Observation:– Two saturated solutions

of MgCO3 are prepared.– One is prepared in

water and the other is prepared in ~0.1 M NaCl.

– 5.0 mL of each solution was transferred (and filtered) into a beaker.

– 3.5 mL of 0.002 M HCl needed for saturated MgCO3 and 6.0 mL needed in 0.1 M NaCl

SaturatedMgCO3

SaturatedMgCO3 in NaCl(aq)

Demonstration – Slide 2

• Did the moles of HCl used match expectations? and Why did the solution containing NaCl need more HCl?– First Question:How many mL of HCl were expected?MgCO3(s) Mg2+ + CO3

2- Ksp = 3.5 x 10-8 T = 25°CKsp = 3.5 x 10-8 = [Mg2+][CO3

2-]since [Mg2+] = [CO3

2-] (assuming no other reactions), [CO32-] =

(3.5 x 10-8)0.5 = 1.87 x 10-4 Mn(HCl) = (2 mol HCl/mol CO3

2-)(1.87 x 10-4 mmol/mL)(5.0 mL) = 0.001875 mmol HCl

Calculate V(HCl) = 0.001875 mmol HCl/[HCl]= 0.001875 mmol HCl/0.002 mmol/mL = 0.935 mLActual V(HCl) > 1 mL

• ConclusionsIt takes more HCl than expected, so more CO3

2- dissolved than expected.

Also, the NaCl increased the solubility of MgCO3

Demonstration – Slide 3

• What was the affect of the NaCl?– More CO3

2- (and Mg2+) was found to dissolve in the 0.10 M NaCl

• Why?– The Na+ and Cl- ions stabilize CO3

2- and Mg2+ ions

Ionic Strength EffectsSpheres Surrounding Ions

Mg2+

Low Ionic Strength

CO32- H O

H

+d

HO

H

H O

H

Ion – dipole interaction

HO

H HO H

HO

H

Mg2+

CO32- H O

H

H O

H

HO

H

-d

High Ionic Strength

Na+

Stronger ion – ion interaction replaces ion - dipole

Cl-

HO H

Ionic Strength• Definition : m = 0.5*SCiZi

2

where i is an ion of charge Z and molar concentration C.

• But What is Ionic Strength– A measure which allows us to correct for

ion – ion effects• Examples:

– 0.10 M NaCl– 0.010 M MgCl2– 0.010 M Ce(SO4)2

Effects of Ionic Strength on Equilibria

• Equilibrium Equation Learned Previously:– for reaction A ↔ B, K = [B]/[A]

• Replacement Equation:– K = AB/AA – So what is AX?– AX is the activity of X– AX = gX[X], where gX = activity

coefficient– The activity coefficient depends on the

ionic strength

Determination of Activity Coefficients

• Use of Debye-Hückel Equation:

- where Zx = ion charge, ax = hydrated ion radius (pm)- useful for 0.0001 M < m < 0.1 M

• Can also use Table 7-1 for specific m value• Calculate g(Mg2+) at m = 0.050 M a(Mg2+) = 800

pm

3051

51.0log

2

x

xx

Z

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