Lecture 12Lecture 12

Oxidation & Reduction II

Suggested reading: Chapter 5

Recall from Last time: Redox Potentials

QRTEE l0The Nernst equation: Q

FEEcell ln0

Cell Potential and pH

For the H+/H couple at 1 bar and 25oC:For the H /H2 couple at 1 bar and 25oC:

pHpHRTE -59 15mV10ln pHpHF

Ecell -59.15mV

In general for aOx+ν e-+ν H+a’RedIn general, for aOx+νee +νHH a Red

pHEpHRT

EE HH )V0590(

10ln '' pHEpH

FEE

eecell )V059.0(

aRT ]Red[ '

Th i l d (b i i ) h

ae xF

RTEE]O[]Red[ln0'

The potential decreases (becoming more negative) as the pH increases and the solution becomes more basic

Redox stabilities

When assessing the thermodynamic stability of a i i l i id ll ibl species in solution, we must consider all possible

reactants:

• the species itself• the solvent

• other solutes• dissolved O2

Redox Chemistry of Water

What is in pure water? )(),(),( 2 lOHaqOHaqH

Water can act as an oxidizing agent, when it is reduced to H2:

(aq)OH(g)H21eO(l)H 22

For the equivalent reduction of hydronium ions in water:

1 (59 V) HE

Water’s oxidation power increases with decreasing pH

(g)H21e(aq)H 2 (59mV)pH

/2HH

E

Water s oxidation power increases with decreasing pH.

Redox Chemistry of Water

Water can also act as a reducing agent, when it is oxidized to O2:

O(l)2H4e(aq)4H(g)O O(l)2H4e(aq)4H(g)O 22

When the partial pressure of O2 is 1 bar, the Nernst equation gives:p p 2 b , q g

pH0.059V1.23V]H[

1ln4 4

0 FRTEE

]H[4F

Oxidation by Water

For metals with large negative standard potentials reaction For metals with large, negative standard potentials, reaction with aqueous acid will occur

Oxidation of the metal by water or hydrogen ions

The overall reaction occurs via one of the following two processes:

(aq)OH(g)H21(aq)MO(l)HM(s) 22

(g)H21(aq)M(aq)HM(s) 2

These reactions are thermodynamically favorable when M is an s-block metal of a 3d series metal (i.e., Ti, Cr, Al, Ni, etc)

(g)H3(aq)2M(aq)H62Sc(s) 23

Oxidation by atmospheric oxygen

•Reactions of Al, Ti metal with moist air are spontaneous but moist air are spontaneous, but they can be used for many years in the presence of water y pand oxygen.

h h f b•Why?: Their surfaces become passivated by an oxide film

•ie: aluminum oxide, titanium oxide, also oxides of Cu, Fe, Zn, , ,

Copper carbonate on the roofs of the Chateau Frontenac in Quebec

Cu Oxidation

R d h lf iRedox half reactions:

O(l)2H4e(aq)H4(g)O 2-

2 pH0.059V1.23V E( )( q)(g) 22

Cu(s)e2(aq)Cu -2

pH0.059V1.23VE

V34.0E

Full Reaction:

O(l)2H(aq)2Cu(aq)H4(g)O2Cu(s) 22

2

pH0.059VV89.0 E p

Since E>0 in neutral and acidic environments atmospheric oxidation Since E>0 in neutral and acidic environments, atmospheric oxidation is spontaneous (E=0.48V at pH=7)

Reduction by water

The positive potential of the O2, H+/H2 couple is large:

pH0.059V1.23V E pH0.059V1.23VE

Acidified water is a poor reducing agent (i.e., a poor electron li ) d idi i supplier) except toward even stronger oxidizing agents

23 (aq)4H(g)O4CoO(l)2H(aq)4Co 22

23

1.92VE .9 V

(Lowering acidity favors the reaction)

Standard potentials at 298KOnly a few redox couples have standard potentials greater than

h 1 23V greater than 1.23V.

Water splitting & Photosynthesis

(g)O(g)2H2eO(l)2H 222

Easy with metals

(aq)OH(g)H2eO(l)2H 22

4eO(l)2H(g)O4OH 22

Hard in general: barrier is kinetic• transfer 4 electrons, form O=O

PhotosynthesisNature uses a metal-oxide cluster containing 4 Mn atoms and 1 Ca g

atom that is located in photosystem II for O2 evolution

The Porphyrin Porphine Chlorophyll-a (located in giant proteins known as “light

harvesting antennae”harvesting antennae

Photosynthesis

A li h A light harvesting complexp

Reduction of CO to

hvP* CO2CH2O

e- (in 1 ps)

Reduction of CO2 to carbohydrates via

reduction of NADP+ to NADPH

Ch d ti t P+

Charged reaction center chlorophyll, reduced

back to it’s ground state P

In PSII, this electron comes from oxidation of water into O and by accepting an electron

e-

of water into O2 and H+

O2 evolution catalyst

Various hypotheses for O2 evolution:) l d d d d l l1) As Mn sites are progressively oxidized, coordinated H2O molecules

become increasingly polarized and lose protonsH2OOH-O2

2-2 2

2) Since Mn(IV) and Mn(V)=O are equivalent to Mn(II)-[O] and Mn(III)-[O], if two [O] atoms are close together, and O2 molecule

may formmay form3) Presence of Ca2+ is essential: remains in 2+ state and provides a fast

binding site for H2O

Dis & co-proportionation

DisproportionationDisproportionationA redox reaction in which the oxidation number of element is simultaneously raised and lowered.

Example: Cu+VsCueaqCua

sCuaqCuaqCuba520)()(:)

)()()(2:)) 2

VEVaqCueaqCub

VsCueaqCua

36.016.052.016.0),()(:)

52.0),()(:)

0

2

FFF )(3)()(2 23

VFFVaqFeeaqFe

aqFesFeaqFe

450)(2)(77.0),()()(3)()(2

2

23

23

CoproportionationThe reverse of disproportionation.

VEVsFeeaqFe

22.1)45.0(77.045.0),(2)(

0

2

Example Fe3+ and Fe

Redox Reactions in Biology: Neuroscience

http://en.wikipedia.org/wiki/Neuron

The Soma Membrane

Cl-

http://www.nicerweb.com/bio1152/Locked/media/ch48/resting_potential.html

Re-deriving the Nernst Equation

The Nernst equation specifies the voltage that will result from maintenance of a given concentration difference.

Diff i fl Th b f h (i ) i

Flux due to drift and diffusion

“Fick’s First Law”xdCDJ )(

Diffusion flux: The net number of charges (ions) crossing some position per unit time per unit area, Γ is:

“Fick’s First Law”dx

DJdiff

D = diffusion coefficient of charges = l2/τ

dC/dx = charge concentration gradient

Drift flux: Ions will drift with a velocity proportional to their mobility mu, charge, and the strength of the E field:

xdrift xCqJ E)(xdrift q Ev

(Assuming single charged ions, so coefficient of q=1)

xdC )(Total Flux

dxxdCDxCqJ xtot)()( E

kTD Einstein relation

In equilibrium, J=0

CdCkTdxx

EC

out

V din

V dxxE

Membrane Potential

))](ln())([ln(Vout

i

outCinCqkTdxx

E

in q

)()( inCinCkT)(

)(ln25mV)(

)(lnVoutCinC

outCinC

qkT

(Recall: R=Nak, F=qNa)

[Ki+]:[K +]=10:1

ΔV=-58mV resting l f

[Kin ]:[Kout ] 10:1potential of neuron

Action potentialsIn the resting state of a nerve cell, sodium mobility across the membrane is much lower than

potassium and the cell maintains a negative voltage When a nerve or muscle cell is potassium, and the cell maintains a negative voltage. When a nerve or muscle cell is stimulated by synaptic transmission, the mobility (or channel conductance, or permeability)

for sodium transiently increases to a value greater than that for potassium and the cell internal voltage "spikes" above zero volts for about a millisecond.

Clark, Nature Neuroscience 8 (2005)http://www.brown.edu/Departments/Engineering/Courses/En123//Lectures/electroN.htm

Electrode : Solution Interactions

Cations

Outer

Cationssurrounded by solvent particles Specifically Primary solvent Outer

Helmholtz plane

p(solvated cations)

Specifically adsorbed

anionsElectrolytic

solution

ylayer (acting as a

dielectric)

Inner H l h l

Metal planeMetal (with negative

h )Helmholtz plane

charge)

Electrical Double Layer

T d i h To derive the potential ψ, start

with Poisson’s

Negatively charged particle

equation:

/2

ρ: charge density = ρ(x)

Boundary conditions:

“slipping ψ

ψ(0)=ψo

ψ(∞)=0pp g

plane”

Pot

entia

l, P

Electrical Double Layer

A h i b B l di ib i ( b bili i Assume the ions obey a Boltzmann distribution (probability an ion having a local potential ψ ):

kTqz

i

i ienn /

#ions/vol valencei

iiqnz

#ions/vol

i

iiq

kTqd /2

2

i

kTqzii

ienzqdxd /

22

Poisson-Boltzman equation

Electrical Double Layer: Huckel approximation

P i B l i h l l iPoisson-Boltzman equation has no general solution.

kTAssume:

kTqzi

mV7.25~kT T=300KmV7.25q

(Low surface potential approximation)

d 2

Expand exponential into a power series

i

iii kT

qznzqdxd )1(2

2

At infinity, electrical neutrality – all charges cancel0

Electrical Double Layer: Huckel approximation

d 222 1

i

ii

kTnqz

dxd 2

2

2 1

ii nzkTq 2

22

ikT

22

d xe 2 dx oe

κ: Double layer thickness (typically 1-3 nm)y ( yp y )

Beyond the Huckle approximation: Gouy-Chapman-Stern:

kTzqkTni

o 2sinh8