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Electrochemistry and the
Nernst Equation
Experiment 13
#13 Electrochemistry and the Nernst Equation
Goals:
To determine reduction potentials of metals
To measure the effect of concentration on
reduction potential
To prepare a Nernst plot to find solubility of
silver halides (AgX)
Method:
Use an electrochemical cell and voltmeter
Redox Chemistry/Electrochemistry
e ZnZn 2
Thermodynamics of redox reactions
Chemical / electrical work interchange
Involves transfer of electrons or electron density
Oxidation:
Loss of electrons
Reduction:
Gain of electrons Cu eCu 22
Redox reactions and spontaneity
Spontaneity is determined by thermodynamics
Ex. Cu/Cu2+ // Zn/Zn2+ system
What will be oxidized (lose e-)? Cu or Zn
What will be reduced (gain e-)? Cu2+ or Zn2+
Will e- flow from Zn to Cu2+ or from Cu to Zn2+?
What will the energy change be?
Current:
“Flow” of e-
System’s attempt to attain equilibrium
(minimum energy state)
Zn (s) + Cu2+
(aq) Cu (s) + Zn2+
(aq)
2e-
Electrochemistry/Electrochemical Cells
Redox reaction produces or uses electrical energy
Voltaic (galvanic) cell:
spontaneous reaction generates electrical energy
(battery)
Electrolytic cell:
absorbs energy from an electrical source to drive
nonspontaneous reaction (recharge)
Cell Components
Electrodes:
conduct electricity between cell and surroundings
Anode: oxidation site “AO”, “an ox”
Cathode: reduction site “CR”, “red cat”
Electrolyte:
ion mixture involved in reaction or carrying charge
Salt bridge:
completes circuit (provides charge balance)
Experimental Set-up
Electrochemical cell
Separated ½ reactions
(ox and red)
“Driving force” for
electron transfer is
measurable
What is +1.10?
Electrochemical Cell Set-up
e –
Mox(s)
Cathode
Ions are reduced
My+(aq) + y e- M(s)
My+
Oxidizing
agent
Mred(s) e – e –
e –
voltmeter
Salt Bridge (KNO3)
Mx+
Reducing
agent
Anode
Electrode is oxidized
M(s) Mx+(aq) + x e-
Example Set-up
e –
Zn(s)
Cathode
Ions are reduced
Cu2+(aq) + 2e- Cu(s)
Cu2
+
Oxidizing
agent
Cu(s) e – e –
e –
+1.10V
Salt Bridge (KNO3)
Zn2+
Reducing
agent
Anode
Electrode is oxidized
Zn(s) Zn2+(aq) + 2e-
Zn (s) + Cu2+
(aq) Cu (s) + Zn2+
(aq)
Zn gives up e- to Cu spontaneously
Zn “pushes harder” on e-
e- on Zn – greater potential energy
– greater electrical potential
+1.10 V is a measure of this
Electrochemical potential – measured voltage
Voltage
difference in energy of the e- on the metals or
relative difference in metals’ abilities to give e-
different metals → different e- energy
→ different “push” on e-
Electromotive force (EMF; cell potential), Ecell
Driving force on electrons
Measured voltage = potential difference
Higher Ecell = larger “drive”
VC
J
movedhargeunit of c
nergyotential eectrical pwork or elEcell
Thermoelectric bridge: work and e- flow
DG0: free energy change (available work)
E0: standard cell potential
n: number of moles of e- transferred
F: Faraday’s constant
00
max nFEΔGw
emol
CF
96485
Energy, E0, and Spontaneity
Cell potential Free Energy Spontaneity
Positive E0cell DG0 < 0 Spontaneous
Negative E0cell DG0 > 0 Not
Zero E0cell DG0 = 0 Equilibrium
DG0: free energy of change
amount of available (electrical) work
Standard Reduction Potentials, E0
E0cell cell potential under standard conditions
(reference tables)
elements in standard states: s, l, g
solutions: 1 M
gases: 1 atm
Relative to standard hydrogen electrode, “SHE”
2H+(aq) + 2 e- H2(g) E0
cell = 0.00 V
Overall E0cell: combine E0’s for half-reactions
Example E0 values
Reduction reaction E0
Mg2+ + 2e- Mg −2.30 V
Zn2+ + 2e- Zn −0.76 V
Ni2+ + 2e- Ni −0.23 V
2H2+ + 2e- H2 0.00 V
Cu2+ + 2e- Cu +0.34 V
Ag+ + e- Ag +0.80 V
Au3++ 3e- Au +1.50 V
More positive E0 = greater reduction potential
The push on e- relative to H2/2H+
E0 values
More positive:
Stronger oxidizing agent
Easier to reduce
More readily accepts e-
More negative:
Stronger reducing agent
More easily oxidized
More readily gives e-
In a spontaneous reaction
Stronger R.A. + O.A. Weaker R.A. + O.A.
Calculating E0cell
Reaction: Zn (s) + Cu2+
(aq) Cu (s) + Zn2+
(aq)
red. Zn(s) Zn2+(aq) + 2 e- E0 = +0.76 V
ox. Cu2+(aq) + 2 e- Cu(s) E0 = +0.34 V
Zn (s)+ Cu2+
(aq) Cu(s)+ Zn2+(aq) E0 = +1.10 V
Assumes 1 M Cu2+ and Zn2+ solutions under standard conditions
Connection to work: DG0, E0, and K
0ln nFEKRT
nF
KlnRTE0
At equilibrium: DG0 = 0 and Keq = Q
]M[
]M[log
n
V.
]tstanreac[
]products[log
n
V.E
y
red
x
oxcell
05910059100
KRTΔG ln0
00 nFEΔG
From thermodynamics:
From electrochemistry:
So:
So:
n = #moles of e- transferred
Nernst Equation
Nonstandard conditions: QRTnFEnFE
QRTΔGΔG
ln
ln
0
0
QnF
RTEEcell ln0
]M[
]M[log
n
V.EE
y
red
x
oxcellcell
059100
Q, reaction quotient: coeff
coeff
][reactants
[products]Q
Cell potential298K:
So:
Summary of Key Equations
Remember: Ecell is proportional to DG
Standard Conditions and at Equilibrium:
s'E'reactionshalfofcombo]M[
]M[log
n
V.E
y
red
x
oxcell
00 05910
]M[
]M[log
n
V.EE
y
red
x
oxcellcell
059100
Non-standard conditions:298K:
Concentration Dependence
]Cu[
]Zn[Q
2
2
Q
Electrical potentials depend on:
type of metal
solution concentration
For: Zn (s) + Cu2+(aq) Cu (s) + Zn2+(aq)
Qlogn
V.EE cellcell
059100
Example
Gold will plate onto silver (not vice versa) – why?
Ag+(aq)
Au3+(aq)
No reaction 3Ag + Au3+ 3Ag+ + Au
e-
Au(s)
Ag+(aq)
Ag(s) Au(s)
Example – Au plating on Ag
][Au
][Aglog
n
.EEcell
3
30 05910Spontaneous reaction:
3Ag + Au3+ 3Ag+ + Au
Given (tables):
Ag+ + e- Ag E0 = +0.80 V
Au3++ 3e- Au E0 = +1.50 V
V.E
)V.(V.E
700
800501
0
0
Experimental Parts and Key Ecell Equation
]M[
]M[log
n
V.EE
y
red
x
oxcellcell
059100
Part 1 Parts 2 and 3
Experimental Overview
1. Dependence of potential on metal type
Metal1 Metal2
c1 = c2
Use 0.1 M solutions and electrodes of different metals
Measure Ecell for each (= E0cell)
Compare experimental vs. literature values
0
y
red
x
ox0
cell E]M[
]M[log
n
0591.0EE
0
Overview
2. Dependence of potential on concentration
Metal1 = Metal2
c1 c2
Use 0.1 M solution with 110-5 to 110-1 M solutions
Measure Ecell for each
Plot Ecell vs. log(cdil/cconc)
Compare slope to Nernst equation
]c[
]c[log
n
0591.0EE
edconcentrat
dilute0
cell
0
Overview
3. Ksp Determination:
AgX(s) Ag+(aq) + X-
(aq) Ksp = [Ag+][X-]
Met1 = Met2
c1 c2
Use 0.1 M Ag+ with sat’d AgX (0.1M Ag+ + 0.2M KX)
Measure Ecell
Part 2 plot gives:
So:
slopeE
concdil
cell
10]Ag[]Ag[
]X][Ag[K dilsp
Part 1 Notes: Ecell Dependence on type of metal
Measure Ecell for metal pairs
0.1 M Solutions (eliminates conc. dependence)
TA will demonstrate cell set-up
Each cell: vial 2/3 full of solution
liquids MUST be at equal levels
Salt bridge: filter paper soaked in 1.0 M KNO3
don’t let tweezers touch solutions in vials
Voltmeter: Clip leads to metal strips (electrodes)
Insert into solutions
Part 1 Notes: Ecell Dependence on type of metal
Measure cell voltage, Ecell
Measure 2 or 3 metal relative to Cu
Measure 2 or 3 metals relative to each other
Calculate “E0cell” values
Compare to literature
0
y
red
x
ox0
cell E]M[
]M[log
n
0591.0EE
0
Electrochemical Cell Set-up
e –
Pb(s)
Cathode
Cu2+
Cu(s) e – e –
e –
+0.47
Salt Bridge (KNO3)
Pb2+
Anode
Spontaneous when Pb is oxidized and Cu2+ is reduced
Part 1 Examples
Copper and Lead:
Pb Pb2+ Cu2+ Cu
oxidation: Pb metal/solution
reduction: Cu metal/solution
Reduction potentials (table)
Pb2+(aq) + 2 e- Pb(s) E0 = –0.13 V
Cu2+(aq) + 2 e- Cu(s) E0 = +0.34 V
For spontaneous reaction, E0 > 0 so calculated E0 is
Pb (s)+ Cu2+
(aq) Cu(s)+ Pb2+(aq) E0 = +0.47 V
Example Part 1 Data
Measured vs.
Calculated Ecell
Theoretical values given to
the right→
Ecell =
Ecathode + ( Eanode)
Calculated
Cu2+
/Cu cathode anode
Zn2+
/Zn 1.10 Cu2+
/Cu Zn2+
/Zn
Ni2+
/Ni 0.57 Cu2+
/Cu Ni2+
/Ni
Pb2+
/Pb 0.47 Cu2+
/Cu Pb2+
/Pb
Mg2+
/Mg 2.64 Cu2+
/Cu Mg2+
/Mg
Zn2+
/Zn cathode anode
Cu2+
/Cu 1.10 Cu2+
/Cu Zn2+
/Zn
Ni2+
/Ni 0.53 Ni2+
/Ni Zn2+
/Zn
Pb2+
/Pb 0.63 Pb2+
/Pb Zn2+
/Zn
Mg2+
/Mg 1.54 Zn2+
/Zn Mg2+
/Mg
Ni2+
/Ni cathode anode
Zn2+
/Zn 0.53 Ni2+
/Ni Zn2+
/Zn
Cu2+
/Cu 0.57 Cu2+
/Cu Ni2+
/Ni
Pb2+
/Pb 0.10 Pb2+
/Pb Ni2+
/Ni
Mg2+
/Mg 2.07 Ni2+
/Ni Mg2+
/Mg
Part 2 Notes: Ecell dependence on concentration
Cells: same metal/metal ion solution
TA will demonstrate cell set-up
Measure Ecell (E0 = 0)
Concentrations: 0.1 to 110-5 vs. 0.1 M
Plot Ecell vs. log(cdil/cconc)
Compare slope to Nernst equation (-2.303RT/nF)
Ag(s) + Ag+(aq, conc) Ag(s) + Ag+
(aq, dil)
bxmy
E]Ag[
]Ag[log
1
0591.0E 0
edconcentrat
dilutecell
Example Part 2 Data
Plot Ecell msd vs. log(A/B)
Theoretical Slope =
2.303RT/nF
B Ag+
conc A Ag+
dilute Calculated Measured %error
0.1 0.1 0.000 0.000 ---
0.1 0.01 0.0591 0.054 8.6
0.1 0.001 0.1182 0.110 6.9
0.1 0.0001 0.1773 0.170 4.1
0.1 0.00001 0.2364 0.222 6.1
Measured log(A/B)
0.000 0.000
0.056 -1.000
0.117 -2.000
0.177 -3.000
0.234 -4.000
T(K) 296
Theor. m 0.0587
%error 0.24
Ecell vs. log(A/B)
y = -0.0586x
R2 = 0.9997
0.000
0.050
0.100
0.150
0.200
0.250
-4.000 -3.000 -2.000 -1.000 0.000
log(A/B)
Ece
ll
Part 3 Notes: Silver Halides’ Ksp
cell 1: 0.1 M Ag+Ag electrode
cell 2: saturated AgX solution (KCl/AgNO3)
Measure Ecell
Determine [Ag+dilute]
Find Ksp = [Ag+][X-]
[X-]: ~unchanged
[Ag+]: Ecell /Part 2
Find DG0 = -RTlnKsp
slopeE
concdil
cell
10]Ag[]Ag[
]X][Ag[K dilsp
]Ag[
]Ag[logslopeE
conc
dilmeasured,cell
~0.2M
Electrochemical Ksp and DG0 Determination
Experimental voltages: good <5% error
Experimental Ksp: good – high ~20% error
X- [X-] [Ag+]conc Trial 1 Trial 2 Trial 3 Average Calculated %error
Cl- 0.2 0.1 0.470 0.464 0.468 0.467 0.473 1.1
Br- 0.2 0.1 0.617 0.620 0.608 0.615 0.621 1.0
I- 0.2 0.1 0.839 0.837 0.841 0.839 0.845 0.7
Ecell, V
AgX(s) Ecell, V [Ag+]dil, ex p [Ag+]dil, lit Exp.Ksp Lit.Ksp %error G0(kJ/mol), exp
AgCl(s) 0.467 1.24E-09 9.00E-10 2.5E-10 1.8E-10 37.5 55
AgBr(s) 0.615 3.93E-12 2.65E-12 7.9E-13 5.3E-13 48.1 69
AgI(s) 0.839 6.36E-16 4.15E-16 1.3E-16 8.3E-17 53.3 91
Report
Abstract
Sample calculations including:
Reduction potentials for metals
E0cell for cells without Cu
log ([Ag+dilute]/[Ag+
conc])
[Ag+dilute], Ksp, DG0
Results
Ecell, msr’d for all cells
Reduction potentials for metals
E0cell for metals
concentrations, Emeasured, slopes, graph
Ecell, msr’d, [Ag+dilute], Ksp, DG0
Discussion/review questions
