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Electromotive Force (電動勢 )
(C) charge
(J)work (V) difference potentialemf
1 joule of work is produced or required when 1 coulomb of charge is transferred between two points in the circuit that differ by a potential of 1 volt.
Galvanic Cells (Voltaic Cells )
Galvanic cell - an electric cell that generates an electromotive force by an irreversible conversion of chemical to electrical energy; cannot be recharged.
The electron flow from the anode to the cathode is what creates electricity.
In a galvanic cell, the cathode is positive while the anode is negative, while in a electrolytic cell, the cathode is negative while the anode is positive.
Standard Hydrogen Electrode
2H+(aq)+Zn(s) →Zn+2(aq)+H2(g)
Oxidation half-reaction
Zn(s) →Zn+2(aq)+2e-
Standard hydrogen electrode
2H+(aq)+2e-→H2(g)
The cathode consists of a platinum electrode in contact
with 1 M H+ ions and bath by hydrogen gas at 1 atm. We
assign the reaction having a potential of exactly 0 volts.
)(76.076.000002
2VEEE
ZnZnHHcell
The Cell Potentials
E0cell=E0(cathode)-E0 (anode)
The value of E0 is not changed when a half reaction is multiplied by an integer.2Fe+3+2e- →2Fe+2 E0(cathode)=0.77 VCu →Cu+2+2e- -E0 (anode)=-0.34 VCu+2Fe+3 →2Fe+2+Cu+
E0cell=E0(cathode)-E0 (anode)=0.43 V
oxidationreduction
Cell Diagrams
For a copper-zinc voltaic cells
Cu’ Zn ZnSO4(aq) CuSO4(aq) Cu
1. A vertical line indicates a phase boundary.
2. A dashed vertical line indicates the phase boundary between two miscible liquid.
Dashed line
PtL| H2(g)|HCl(aq)|AgCl(s)|Ag| PtR
Anode: H2(g)=2H++2e-(PtL)
Cathode: [AgCl(s)+e-(PtR)=Ag+Cl-] ×2
Overall: 2AgCl(s)+ H2(g)=2Ag+ 2H++2Cl-
CuL|Cd(s)|CdCl2(0.1M)|AgCl(s)|Ag(s) |CuR
Anode: Cd=Cd+2+2e-
Cathode: [AgCl+e-=Ag++Cl-] ×2
Overall: Cd+2AgCl=2Ag+Cd+2+2Cl-
Nernst Equation
E0: standard reduction potentialn: moles of electronsF: Faraday constant 96485 C/mol
QnF
RTEEcell ln0
Thermodynamic-Free Energy
The maximum cell potential is directly related to the free energy difference between the reactants and the products in the cell.
max
maxmax
nFEG
nFq
qEGW
Calculation of Equilibrium Constants for Redox Reactions
0000
0000
0
ln
lnln
0
ln
KRTG-nFEG
RT
nFEKK
nF
RTE
K, Ewhen Q
QnF
RTEE
cell
cell
Reaction Quotient (Q)
Q
K
nF
RTQ
nF
RTK
nF
RTE
KnF
RT
nF
GE-nFEG
QnF
RTEE
00
00
000
0
lnlnln
ln
ln
The positive E (R>L ) means that Q<K0. As Q increases toward K0, the cell emf decreases, reaching zero when Q=K0
The Equilibrium Constant of a Cu-Zn Cell
Zn+Cu+2(aq)=Zn+2(aq)+Cu
E0=0.34V-(-0.76V)=1.10V
KJ/mol 212
101.5K
85.6K) )(298K mol J (8.314
)C J )(1.1mol C 2(96485lnK
0
370
1-1-
-1-10
G
V..
..
C
C
nF
RTEE
QnF
RTEE
R
L 0591001
10ln
964851
2983148 ln0
ln
0
0
AgL Ag+(0.1M) Ag+(1M) AgR
PtL Cl2(PL) HCl(aq) Cl2(PR) PtR
R
L
P
P
F
RTE ln
2
Liquid Junction Potential
Liquid junction: the interface between two miscible electrolyte solutions.
Liquid-junction potential: A potential difference between two solutions of different compositions separated by a membrane type separator.
The salt will diffuse from the higher concentration side to the lower concentration side.
Liquid Junction Potential The diffusion rate of the cation and the anion of the
salt will very seldom be exactly the same. Assume the cations move faster; consequently, an
excess positive charge will accumulate on the low concentration side, while an excess negative charge will accumulate on the high concentration side of the junction due to the slow moving anions.
When the cell has a liquid junction, the observed cell emf includes the additional potential difference between the two electrolyte solutions.
How to Solve the Liquid Junction Potential
Liquid junction potentials are generally small, but they certainly cannot be neglected in accurate work.
By connecting the two electrolyte solutions with a salt bridge, the junction potential can be minimized.
A salt bridge consist of a gel made by adding agar to a concentrated aqueous KCl solution.
A Cell Diagrams Containing a Salt Bridge
For a copper-zinc voltaic cells
Cu’ Zn ZnSO4(aq) CuSO4(aq) Cu
A salt bridge is symbolized by two vertical dashed lines.
Estimate the Liquid Junction Potential from EMF Measurement
Ag AgCl(s) LiCl(m) NaCl(m) AgCl(s) Ag
m(LiCl)=m(NaCl), E0=0
Anode: Ag+Cl- (in LiCl(aq))=AgCl+e-
Cathode: AgCl+e-=Ag+Cl- (in NaCl(aq))
Estimate the Liquid Junction Potential from EMF Measurement
J
J
EE
l in aq.LiCCll in aq.NaCCl
alities At low mol
l in aq.LiCCl
l in aq.NaCCl
nF
RTEEE
][][
][
][ln0
Determination of pH
Pt H2(g) soln. X KCl(sat.) Hg2Cl2(s) Hg Pt’
1/2H2(g)+1/2Hg2Cl2=Hg(l)+H+(aq,X)+Cl-(aq)The cell reaction and emf Ex:
2/100
, )/(
)()(ln
PP
ClaHa
F
RTEEE X
XJX
Junction potential between X and the saturated KCl solution
If a second cell is set up to except that solution
X is replaced by solution S, the emf Es of this
cell will be:
2/100
, )/(
)()(ln
PP
ClaHa
F
RTEEE S
SJS
)( 10ln
)()(
10ln10ln)()(
)](log)(log[10ln
)()()(
)(ln
)(
)(ln
,,1
1,,
1
,,
,,
,,
XJSJSX
XJSJSXSX
XJSJSXSX
SXSJXJS
X
S
XSJXJSX
EERTF
EESpHXpH
RTF
EE
RTF
EEHpaHpa
EEEEHaHaF
RT
EEEEHa
Ha
F
RT
Ha
Ha
F
RTEEEE
Reference electrode:saturated calomel electrode (SCE)
Hg2Cl2(s)+2e- 2Hg(l)+2Cl-
Sensing electrode:Ion Selective Electrode (ISE)
Pt Ag AgCl(s) HCl(aq) glass soln. X KCl(sat.) Hg2Cl2(s) Hg Pt’
Ag(s)+Cl- AgCl(s)+e-
Determine the pH of a Solution by a pH Meter
When the glass electrode is immersed in solution X, an equilibrium between H+ ions in solution and H+ ions in the glass surface is set up.
This charge transfer between glass and solution produces a potential difference between the glass and solution.
Ion Selective Electrodes (ISE) for PH Meter An ion selective electrode contains a glass,
crystalline, or liquid membrane whose nature is such that the potential difference between the membrane and an electrolyte solution it is in contact with is determined by the activity of one particular ion.
It is dependent on the concentration of an ionic species in the test solution and is used for electro-analysis.
Marcus theory for Electron transfer reactionsRudolph A. Marcus was awarded the 1992 Nobel Prize in chemistry
Membrane Equilibrium
ii
ni,ionZ+
Phase α Phase β
ii
ni,ionZ+
Phase α Phase β
ii
ni,ionZ+
Phase α Phase β In a closed electrochemical system, the phase equilibrium condition for two phases and
C
C
nF
RTEEE
EquationNerst
ln
Free-energy change during proton movement across a concentration gradient
The movement of protons from the cytoplasm into the matrix of the mitochondrion.
pHRTG
pHpHRTRTG
RTRTEnFG
nF
RTEEE
outin
inout
303.2
)(303.2])Hlog[]H(log[303.2
]H[
]H[log303.2
]H[
]H[ln
]H[
]H[ln
HH
outin
out
in
out
in
out
in
inout
Proton Pumping
Proton pumping maintains a pH gradient of 1.4 units, then pH = + 1.4
G = -2.303RTΔpH =- 2.303 (8.315 × 10-3 kJ/mol)(298K)(1.4) = - 7.99 kJ/mol Proton concentration gradient
Free-energy change during solute movement across a voltage gradient
In mitochondria, electron transport drives proton pumping from the matrix into the intermembrane space.
There is no compensating movement of other charged ions, so pumping creates both a concentration gradient and a voltage gradient.
This voltage component makes the proton gradient an even more powerful energy source.
Proton-motive force
Proton-motive force (P) is a that combines the concentration and voltage effects of a proton gradient.
G=-nFP = - 2.303 RT pH + nFm
=(-7.99 kJ/mol)+( - 13.5 kJ/mol)
= -21.5 kJ/mol
ATP synthesis
Mitochondrial proton gradient as a source of energy for ATP synthesis
Estimated consumption of the proton gradient by ATP synthesis is about 3 moles protons per mole ATP.
G = 50 kJ/mol for ATP synthesis G = 50 + 3(- 21.5) = - 14.5 kJ/mol The synthesis of ATP is spontaneous under
mitochondrial conditions.
Potential for a resting nerve cell Goldman-Hodgkin-Katz equation
P: permeability (穿透率 )D: diffusion coefficient (擴散係數 ): thickness of membrane (薄膜厚度 )
τ
DP
)][ClP][NaP][KP
][ClP][NaP][KPln(
F
RTΔE
potential anetransmembr
ext
Cl
int
Na
int
K
int
Cl
ext
Na
ext
Kextint
Resting Nerve Cell of a Squid
Concentrations cell
△(K+)=-95 mV
△(Na+)=+57 mV
△(Cl-)=-67 mV
(mmol/dm3)
K+ Na+ Cl-
int 410 49 40
ext 10 460 540
P(K+) /P(Cl-)=2P(K+)/P(Na+)=25
The observed potential for a resting squid nerve cell is about-70 mV at 25oC.
Resting Nerve Cell of a Squid
The observed potential for a resting squid nerve cell is about -70 mV at 25oC.
Hence Cl- is in electrochemical equilibrium, but K+ and Na+ are not.
Na+ continuously flows spontaneously into the cell and K+ flows spontaneously out.
Na+-K+ pump
Batteries
Secondary batteries: Voltaic cells whose electrochemical reactions can be reversed by a current of electrons running through the battery after the discharge of an electrical current.
A secondary battery can be restored to nearly the same voltage after a power discharge.
Lead Storage battery
Anode reaction
Pb+HSO4-→ PbSO4+H++2e-
Cathode reaction
PbO2+HSO4-+3H++2e- → PbSO4+2H2O
Cell reaction
Pb+PbO2+ 2H++2HSO4-→ 2PbSO4+2H2O
Dry Cell Battery
Anode reaction
Zn→ Zn2++2e-
Cathode reaction
2NH4++2MnO2+2e- → Mn2O3+2NH3+H2O
Cell reaction
2MnO2+2NH4Cl+Zn→ Zn(NH3)2Cl2 + Mn2O3
+H2O
Alkaline Dry Cell
Anode reaction
Zn+2OH- → ZnO+H2O+2e-
Cathode reaction
MnO2+2H2O+2e- → Mn2O3+2OH-
Cell reaction
MnO2+H2O+Zn→ Mn2O3+ZnO
燃料電池工作原理
Anode reaction
2H2+4OH-→4H2O+4e-
Cathode reaction
4e-+O2+2H2O →4OH-
Cell reaction
2H2+O2 → 2H2O
Anodic Region
Fe→Fe+2+2e-
Cathodic Region
O2+2H2O+4e- →4OH-
Overall Reaction
4Fe+2(aq)+O2(g)+(4+2n) H2O(l)
→2Fe2O3‧nH2O(s)+8H+(aq)
Electrolysis
Electrolytic Cell: use electrical energy to produce chemical change
The process of electrolysis involves forcing a current through a cell to produce a chemical change for which the cell potential is negative.
Electrolysis of Water
Anode reaction: 2H2O→O2+4H++4e-
Cathode reaction: 4H2O+4e-→2H2+4OH-
2H2O →2H2+O2 E0=-2.06V
Electrolysis of Mixture of Ions
A solution in an electrolytic cell contains the ions Cu+2, Ag+ and Zn+2.
The more positive the E0 value, the more the reaction has a tendency to proceed in the direction indicated.
Ag+ > Cu+2 > Zn+2
Electrolysis of NaCl/H2O System
Anode reaction:
2H2O→O2+4H++4e- -E0=-1.23 V
2Cl-→Cl2+2e- -E0=-1.36 VThe Cl- ion is first to be oxidized. A much higher potential than expected is required to oxidized water. The voltage required in excess of the excepted (overvoltage) is much greater for the
production of O2 than for Cl2.