Lecture 8Lecture 8

Ch i l R ti I d P t E hChemical Reactions: Ion and Proton Exchange

Suggested reading: Chapter 3 & 4 1-4 3Suggested reading: Chapter 3 & 4.1 4.3

Office hours this week: W d (10 12) || Th (2 4) || F i (UG l 9 10 )Wed (10-12) || Thurs (2-4) || Fri (UG only, 9am-10am)

Roadmap of the course

Th i i Quantum chemistry:

H d i & The origin of the

elements

Hydrogenic & multielectron atoms

Quantum

Periodic table trends (radii, ionization

energies

Quantum chemistry of molecules: MO theoryenergies,

electronegativities)

Quantum chemistry

Molecular energies, bond strength, molecular shapes

c e st y of solids:

band theory

Solid bonding

and and stability

The rest of this course: reaction chemistry (acid-base, redox, complexes, nano, bio)

Cation exchange in ionic crystals

CdSe Ag2Se

d2 d A dCd2+ ionic radius = 109 pmSe2- ionic radius = 184 pm

Ag+ ionic radius = 128 pmSe2- ionic radius = 184 pm

The exchange reaction is completely kinetically hindered at ambient temperature and pressure in the bulk.

Tunable fluorescence

Can ion exchange occur in nanocrystals?

Shape controldiameter2 nm 7 nm

Size control

100 nm

50 nm

~ 5 nm

Journal Presentation by Ryan, Scott, Denys

Cd2+

Nanocrystal ion exchange (from B. Sadtler)

CdSe

Ag+

3 nm40 nm 3 nm 40 nm

NC exchange videoNC exchange video

Partial Ag+ exchange produces striped CdS-Ag2S nanorods

Ag+ cation exchange leads to alternating CdS and Ag2S regions along

g2

alternating CdS and Ag2S regions along the nanorod

Small Ag2S regions nucleate over

Increasing Ag+/Cd2+ ratio

nanorod surface and grow into the CdSlattice

10 nm20 nm 20 nm

R. Robinson. B. Sadtler, D. Demchenko, C. Erdonmez, L.-W. Wang, A. P. Alivisatos. Science 2007, 317, 355.

Bright-field TEM Energy filtered TEM

Morphology of CdS-Cu2S nanorods

Bright field TEM Energy filtered TEM

20Cd regions

20 nm 20 nmg

Cu regions

Hi-Res TEM

Cu2S nucleates at the ends and the exchange reaction proceeds into the nanorod

4 nm

nanorod

Epitaxial connection at the CdS-Cu2S interfaceinterface

B. Sadtler, D. O. Demchenko, H. Zheng, S. M. Hughes, M. Merkle, U. Dahmen, L.W.-Wang, A.P. Alivisatos. JACS 2009, 131, 5285

Comparison of morphologies produced by Ag+ and Cu+ exchange

Ag+/Cd2+ = 0.2 Ag+/Cd2+ = 0.8

Ag+ cation exchange: non-selective Ag2S nucleation followed by partial phase segregation

As Ag2S regions grow into the nanorod, ripening occurs to

Increasing Ag+/Cd2+ ratio

reduce elastic strain

Ag /Cd2 ratio

Cu+ cation exchange: selective Cu2S nucleation of low energy interfaces

Cu2S nucleates at one or both ends producing a stable configuration

Increasing Ag+/Cd2+ ratio

20 nm 2 nm

configuration

Difficult to directly exchange two divalent cations (e g Cd2+ and Pb2+)

Sequential Cation Exchange

Cu+(MeOH)

d2

Pb2+(TBP)

( )

Difficult to directly exchange two divalent cations (e.g. Cd and Pb )

PbSCu2SCdS

Cd2+(MeOH) Cu+(TBP)

100 nm 100 nm 100 nm

y (a

u)

nce

(au) PbS

Cu2SCdS

PbS

Cu2S

Inte

nsit

y

Abs

orba

n CdS Cu2S

CdS

400 800 1200 1600 2000 30 40 50 60 70

Diffraction angle (2)Wavelength (nm)

J.M. Luther, H. Zheng, B. Sadtler, A. P. Alivisatos, JACS 2009, 131, 16851

Exchange in ionic nanocrystals can lead to entirely new materials & devices that cannot be synthesized through y g

direct techniques.

CdS PbS

ITO

nanocrystal photovoltaicsvertically-aligned nanorod array

hole carrier

electron carrier200

nm h+

electron carrier

~ 2 e‐

bottom electrode

Exchange in ionic nanocrystals can lead to entirely new materials & devices that cannot be synthesized through y g

direct techniques.

Jungwon Park; Haimei Zheng; Young-wook Jun; A. Paul Alivisatos; J. Am. Chem. Soc. 2009, 131, 13943-13945.

How can we rationalize ion exchange?

The thermodynamic driving force for exchange between two cations can be controlled by the solvent and surfactant system

• In the CdSe−Ag2Se pair, the forward exchange from CdSe to Ag2Se is thermodynamically driven by the preferential solvation of Cd2+ ions relative to Ag+ in methanol (MeOH). g ( )

• The reverse exchange from Ag2Se to CdSe is favored by the addition of Cd2+, along with tributylphosphine (TBP). , g y p p ( )

• These exchange reactions can be qualitatively understood in terms of hard−soft acid−base theory:y

• The monovalent Ag+ cation is softer than the divalent Cd2+ cation. Therefore, MeOH, a hard base, preferentially binds Cd2+ cations. Therefore, MeOH, a hard base, preferentially binds Cd cations. Similarly, the soft base, TBP, binds strongly to Ag+ cations.

J.M. Luther, H. Zheng, B. Sadtler, A. P. Alivisatos, JACS 2009, 131, 16851

A brief history of Acids and BasesGreece (BCE)

•Acids: “sour-tasting” substances:•The early word for acids, “oxein”, which mutated into the Latin word for vinegar, acetum, which became anglicized to “ id”“acid”• Bases could counteract acids and felt “soapy.”•The early word for base, “alkaline” is derived the Arabic word for “roasting:” the first bases were obtained from soaps, made by

A h i (1859 1927)

g p , yroasting ashes and treating them with water and lime.

• Dissertation at University of Uppsala: proposed that chemical reactions in solution were reactions between ions

Arrhenius (1859-1927)

ions• Acids dissociate in aqueous solution to form hydrogen

ions (H+) and bases form hydroxide (OH−) ions• Awarded non since laude approbatur (equivalent to a “D”)

L i h 1903 N b l P i• Later went on to win the 1903 Nobel Prize

Bronsted & Lowry (1923)

Bronsted Acid: A proton donorBronsted Acid: A proton donor

HF(aq) + H2O(l) H3O+(aq)+F-(aq)

Bronsted Base: a proton acceptor

H2O(l) + NH3(aq)NH4+(aq)+OH-(aq)

Water is amphiprotic: can act as both a Bronsted acid and a Bronsted base

H3O+ (hydronium ion): • Participates extensively in hydrogen bonding. p y y g g

Better representation is H9O4+ (right).

• Mass spec suggests a cage of H2O molecules can condense around one H3O+ ion in a regular condense around one H O ion in a regular pentagonal dodecahedral arrangement, resulting in H+(H2O)21.

Proton Transfer & Equilibrium

The central feature of Bronsted acid-base chemistry in aqueous solution is that of rapid attainment of equilibrium in the proton

transfer reactiontransfer reaction

Proton transfer between acids and bases is fast in both directionsdirections.

HF(aq) + H2O(l) H3O+(aq)+F-(aq)

H2O(l) + NH3(aq) NH4+(aq)+OH-(aq)

Acid1 + Base2 Acid2 + Base1

Conjugate base of acid 1

Conjugate acid of base 1base2

The strengths of Bronsted AcidsThe strength of a Bronsted acid is measured by it’s acidity constant (or The strength of a Bronsted acid is measured by it s acidity constant (or

acidity ionization constant), and the strength of a Bronsted base is measured by it’s basicity constant.

HX(aq) + H2O(l) H3O+(aq)+X-(aq)

][]][[ 3

HXXOHKa

Acidity constant:

f [ ] l h [ ] b hIf Ka<<1, [HX] is large with respect to [X-] proton retention by the acid is favored

41053 xK 105.3 xKa

The strengths of Bronsted BasesThe strength of a Bronsted acid is measured by it’s acidity constant (or The strength of a Bronsted acid is measured by it s acidity constant (or

acidity ionization constant), and the strength of a Bronsted base is measured by it’s basicity constant.

B(aq) + H2O(l) HB+(aq)+OH-(aq)

[B]]][OH[HB

bKBasicity constant:

f [ ] [ ] l ll f f l lIf Kb<<1, [HB+] << [B] only a small fraction of B molecules are protenated

5108.1 xKb

Ionization Constant for Water

2H2O(l) H3O+(aq)+OH-(aq)

-141 00 10]][OHO[H KA l i -143 1.00x10]][OHO[H

wKAutoprotolysis constant:

pH=-log[H3O+] [H3O+]=10-pH

Also, KaKb=Kw for an acid and it’s conjugate base (or vice-versa), a b w j g b ( )

Recall from thermodynamics: aA+bBcC+dD

dc[D][C])]products([

miQActivity quotient

ba[B][A])]reactants([

n

j

Qy qQ=K in equilibrium:

Polyprotic AcidsPolyprotic acid: can donate more than one protonPolyprotic acid: can donate more than one proton

H2S

H2S(aq)+H2O(l) H3O+(aq)+HS-(aq)

HS ( ) H O(l) H O+( ) S2 ( )

S][H]][HSO[H

2

31

aK

]][SO[H 23

A l ti id l t i i d i

HS-(aq)+H2O(l) H3O+(aq)+S2-(aq)][HS

]][SO[H-

32 aK

A polyprotic acid loses protons in succession, and successive deprotenations are progressively less favorable (Ka2<<Ka1)

Polyprotic Acids & Distribution DiagramsThe concentration of each solute at a given pH can be The concentration of each solute at a given pH can be

calculated from the pKa values. Then, we can plot the fraction of solute present for a given pH.

If pH<pK high If pH<pKa1, high hydronium ion concentrations

If pH>pKa3, low hydronium ion concentrations

Distribution diagram for Phosphoric acid

What governs the strength of acids and bases?

Considering enthaply changes accompanying the proton transfer!

Δpg: Proton gain enthalpy: if large and negative, gas phase is a strong base

Proton gain can be thought of as three key steps:

1. Electron loss from A = - Δeg

2. Electron gain by H = - I(H)3 Combination of H and A = - B(H-A)3. Combination of H and A = - B(H-A)

Δpg = - Δeg - I(H) - B(H-A)

Periodic Table Trends

Dominant factor in proton affinity i d l ffi i across a period: electron affinity

of A

• Increases from left to right, lowering the proton affinity of

A-A

• Gas phase acidity of HA i h l i i

Acidity of the hydrides of the

increases as the electronegativityof A increases

y yelements

Periodic Table Trends

Dominant factor in proton paffinity down a group: decrease in H-A bond dissociation enthalpydissociation enthalpy

• Lowers the proton affinity f A hof A-, increasing the gas phase acidity of HA.

A idit f th h d id f th Acidity of the hydrides of the elements

Acids and bases in solution

A-(aq)+H+(aq)HA(aq)

BasesAcids

HA(aq)+H2O(l)H3O+(aq)+A-(aq) A-(aq)+H2O(l)HA(aq)+OH-(aq)( q) 2 ( ) 3 ( q) ( q)

is exothermic if the effective proton affinity of A-(aq) is lower than that

of H O(l) : less than 1130 kJ/mol

is exothermic if the effective proton affinity of A-(aq) is higher than

that of OH-(aq) : 1188 kJ/molof H2O(l) : less than 1130 kJ/mol

HA(aq) will be strongly acidic

that of OH (aq) : 1188 kJ/mol

A- will be strongly basic( q) g y

Usually cannot ignore entropy in solution!

Simple cycle for HCl

½ Cl2(g)Cl (g):

Dissociation energy (106 kJ/mol)

H(g)H+(g):

Ionization energy (1312 kJ/mol)Ionization energy (1312 kJ/mol)

½ H2(g)H(g):

Dissociation energy (218 kJ/mol)

H+(aq)½ H (g): Gibb’s energy of H (aq)½ H2(g): Gibb s energy of formation

(g)(aq): Energy of solvation

The Born Equation: “Hydrations” of Ions

The energy of solvation of an ion (ΔsolvG = ΔGm) :

Energy involved in transferring the anion from a vacuum into a solvent of

relative permittivity εr

The Born Equation: Derivation

Starting from the energy u of an electric field:

Using the expression for the electric field E at a distance r from an ion of Using the expression for the electric field E at a distance r from an ion of charge ze and radius ri, we have:

Therefore:

Highly charged anions are stabilized in polar solvents!

• A large, negative value of ΔsolvGfavors the formation of ions in solution compared with the gas phase

• The interaction of the charged ion with the polar solvent

l l bili h molecules stabilizes the conjugate base A- relative to the parent acid HA

• The acidity of HA is enhanced by the polar solvent

=Z2/r