Download Electrochemistry questions for midterm or semi-final exam

Activity, mean activity, activity coefficient
Preparation for test writing
1.Activity, the value of activity coefficient at infinite dilution.
1a. Activity of a molecule or ion is the effective concentration which depend on the
composition of solution, the interaction between solvent and solute components.
m
a i
m0
The magnitude of activity is given properly, if the applied concentration unit is also
known. On diluting the solution, i.e.
c→0
γ→1
then a = c
activity becomes equal to the concentration. In very dilute solution interactions are
insignificant and concentration and effective concentration are the same.
2. Characterize a dilute solution of a one to one electrolyte by thermodynamic
quantity!
2a. The chemical potential of a 1:1electrolyte can be given for positive and negative
ions separately
0
salt
 RT ln asalt   0   0  RT ln m   m 
but in this form a salt can not be calculated, because γ+, and γ-can not be
2








determined separately. Defining the mean activity coefficient
which says that equal amount of “activity coefficient property” is divided to
positive and negativ ions. Inroducing mean activity coefficient an equation can be
constructed
0
salt
 0  0
RT ln asalt  RT ln m 2  m
and m  m  m
therefore asalt  m   .
2
2
1
3. Relationship between Ka and Km.in the case of dissociation equilibrium, HA →
H+ + A-.
a a
m m
1
3a. The equilibrium constant of the reaction, Ka         
o
aHA
mHA   HA m
Knowing:
   
2
 and
m+ = m- = m
a a
m2   2
Ka 

aHA mo  mHA   HA the ratio is
also given by concentration ratio times activity coefficient ratio.
Ka  Kc  K where
 2
K 
 HA
m2
Kc  o
m  mHA
The equilibrium constants given in terms of molality and activity coefficient.
Ka = f(T,p) but independent of molalities. Ka has no unit.
4. Give the activity of salt: KCl
4a. The actual form of the geometric mean depends on the number of ions produced
by the salt. We define for KCl, a one to one electrolyte,
   
2

     
1
2
or
It is true that activity coefficients equals
activity of salt is,
 
     . It was our assumption. The
asalt  m  m 2
But for a KCl solution of molality, m, we have m+ = m and m− = m so that
asalt  m2 2
5. Ionic strength and its use.
2
I
5a. Ionic strength, I, defined as
1
mi zi2

2 i
where zi is the charge on ion i, and mi is the molality of ion i. The ionic strength of
a solution is a measure the amount of ions present. Otherwise, the ionic strength is
a measure of the total concentration of charge in the solution. A divalent ion (a 2+
2+
or 2- ion, like Ca ) does more to make the solution ionic than a monovalent ion
+
(e.g., Na ). The ionic strength, emphasizes the charges of ions because the charge
numbers occur as their squares.
6. Give the activity of salt: BaCl2. The dissociation of divalent anion is complete.
6a. BaCl2 dissociates to 3 ions: BaCl2 → Ba2+ + 2 Cl−
The chemical potential of salt:
0
salt
 RT ln asalt   Ba0  RT ln mBa    2 Cl0  2 RT ln mCl  
(Do not forget factor two multiplayer before chloride term.)
RT ln asalt   RT ln m   m2 2 so
asalt  m m2   2   m m2   3
The molality of BaCl2, ions: m+ = m and m− = 2m
m2  (2m)2  4m2
Finally we get for the activity of salt
asalt  m  2m2   3  4m3 3
2
2


7. Give the activity of salt: FeCl3. The dissociation of trivalent cation is complete.
7a. FeCl3 dissociates to 4 ions: FeCl3 → Fe3+ + 3 Cl−
The chemical potential of salt:
0
salt
 RT ln asalt   Fe0  RT ln mFe    3Cl0  3RT ln mCl  
(Do not forget factor three multiplayer before chloride term.)
RT ln asalt   RT ln m   m3 3 so
asalt  m m3   3   m m3   4
The molality of FeCl3, ions: m+ = m and m− = 3m
m2  (3m)3  27m3
Finally we get for the activity of salt
3
asalt  m  3m   4  27 m4 4
3
3

3

8. What is the difference between Debye Hückel limiting law (DHL) and the
extended DH law (EDH)?
8.a Both DHL and EDH gives   from theoretical calculations using ionic strength
(a measure of the amount of ions present), temperature and solvent parameters.
DH limiting law.
lg    0.509  z  z  I 1/ 2
 0.511  z   z  I 1 / 2
Extended DH law. lg   
1  b  I 1/ 2
DHL gives a good estimation for small concentrations (small I) while EDH
describes the situation for higher concentrations. When I is small enough, 1+bI1/2
approximates one, and EDH transforms to DHL.
9. Calculate I for a solution that is 0.4 molal in KCl and 0.6 molal in K2Cr2O7.
9a. The molality of chloride comes from KCl exclusively: 0,4 mol/kg. The molality
of potassium comes from both KCl and chromate: 0.4+2*0.6=1.6 mol/kg. The
molality of chromate is 0.6 mol/kg.


1
2
2
I   mK 12  mCl    1  mCr O   2
2
mK  mKCl  2  mK Cr O
mol/kg


2
2
2
7
7
I  0.5  1.6  0.4  2.4  2.2
Conductivity, Ionic Mobilities, Transport Number
Preparation for test writing
1.Electric resistance, e. conductance, e. conductivity, e. molar conductivity.
1a. The definition of electric resistance is based on a solid state model. An equation
for a wire with length l, cross sectional area A and a material constant specific
l
resistivity  takes the form R   . Where R is the ohmic resistance of that piece
A
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of wire. The greater the length and smaller the cross sectional area the higher the
resistance of the wire. Conductance and conductivity can be derived easily from
1 1 A
1
G    . where conductance G is proportional conductivity    Turning
R  l

to the property of solutions, as conductivity is divided by concentration, molar
conductivity: Λm 

we get.
c
2. Characterize weak and strong electrolytes with Λm vs. c1/2 function!
2a. At a concentration range strong electrolytes have higher conductivity than weak
ones. Strong electrolyte is characterized a long straight line section in the Λm
vs. c1/2 range studied. Reducing concentration to zero by fitting a straight line,
0
0
from intercept Λm can be red. The limiting molar conductivity Λm is independent of
concentration and interactions in the bulk of solution.
For weak electrolytes (i.e. incompletely dissociated electrolytes), however, the
molar conductivity strongly depends on concentration: The more dilute a solution,
the greater its molar conductivity, due to increased ionic dissociation.
3. Strong electrolite: Kohlrausch’s law ( Λm  f (c) . Use figure for explanation.
3a. It is a square-root law: Λm  Λm0  k  c1/ 2 . It is applicable for strong electrolytes,
and from this equation the value of limiting molar conductivity, Λm0 can be
determined by using the graph. Fitting a straight line to the graph from intercept the
limiting molar conductivityis determined. k depends principally on the
stoichiometry of salt, rather than specific identity.
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4. The condition for mechanical equilibrium of transporting ion, ionic mobility.
4a. The condition for mechanical equilibrium of transporting ion,
F friction  F field In a short time after the electric field has been switched
on, the ions, e.g. the cations migrate with a constant speed, s toward the negative
electrode. F friction  s  6   r 
F field  zeE  ze

l
A potential difference Δφ at a distance l produces E electric field which make
spherical ions with radius, r move against friction, that is caused mainly by solvent
molecules, z is the charge number.
When net force is zero (see Eq. 1.) the speed, s, at a migrating ion travels can be
given as
zeE
s
6r
As η, the viscosity of liquid or the radius of migrating ion increases the speed
lowers.
5.Independent migration
5a.
All ionic solutions contain at least two kinds of ions (a cation and an anion), but may contain others as
well. In the late 1870's, Friedrich Kohlrausch noticed that the limiting equivalent conductivities of salts
that share a common ion exhibit constant differences.
These differences represent the differences in the conductivities of the ions that are not shared between the
two salts. The fact that these differences are identical for two pairs of salts such as KCl/LiCl and
KNO3 /LiNO3 tells us that the mobilities of the non-common ions K+ and LI+ are not affected by the
accompanying anions.
6. The hydrodynamic radius
6a. Not only the ionic radius counts for transporting ions. For alkali metal ions (Li
– Cs) the hydrodynamic radius of Li+ is the greatest, though its radius without
hydration shell is the smallest. The surface charge density of Li + is the greatest in
the first column of periodic system.
Migration speed can be referred to unit field:
u
s
ze

E 6r
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the quantity u is called ionic mobility. The ion mobility is independent of the
magnitude of electric field.
7. The ion flux, and its unit
7a.
N
J ion 
A  t
The number of ions, N pass through area, A at a time Δt producing ion flux.
Each of the positive or negative ion concentration is chosen the same flux can be
observed (electroneutrality).
Unit: m-2s-1
Electrode, galvanic cell
Preparation for test writing
1.Anode, cathode, liquid-liquid junction – their description and working principle.
1a Electrode an electronic conductor (charge carriers are electrons), the electrode
metal and an ionic conductor, electrolyte solution form an interface at which the
electrode process takes place. This two or more phase system is called electrode.
An electrohemical cell contains two electrodes anode and cathode. In general, a
liquid liquid junction separates the two electrodes.
The anode is the electrode where oxidation occurs.
The cathode is the electrode where reduction occurs.
In an actual cell, the identity of the electrodes (anode or cathode) depends on the
direction in which the net cell reaction is occurring.
Liquid liquid junction: (llj)
Serves as a galvanic contact between the electrodes. Llj can be a porous membrane
or a salt bridge.
Salt bridge is an intermediate compartment filled e.g. saturated solution of KCl and
fitted with porous barrier at each end. The two solutions are joined by a salt bridge,
which consists of an inverted U-shaped glass tube filled with a saturated solution of
a salt (for technical reasons, usually KCl) that is thickened with a gel such as agar
(the salt solution should remain in the U-tube).
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2.Galvanic cell, electrolisys cell –the thermodynamic direction of electrode
processes.
2a Galvanic cell. A galvanic cell contains two electrodes which are separated by a
llj., therefore the electrode reactions are also separated.
In a galvanic cell the electrochemical reaction proceeds spontaneously. (That can
be used as energy sources.) The Gibbs free energy of cell reaction is negative,
 r G  0 .Work is done by the system.
Electrolysis cell
Non-spontaneous reaction is driven by an external source of current, e.g. a battery
is charged.  r G  0 Work is done on the system.
3. Cell diagram using Daniell cell as example cell. How to make sure the cell
reaction potential to be positive?
3a. The cell diagram, sign convention
The cell diagram involves instructions for setting the cell and should be in conform
with the cell reaction. The sign of cell reaction potential, Ecell should always be
positive. Cell diagram is constructed to show the cell reaction running in
spontaneous direction, i.e. the positive ion drifts from left to right.
If electrons flow from the left electrode (Zn/Zn2+) to the right electrode (Cu/Cu2+)
in metal leads when the cell operates in its spontaneous direction, the potential of
electrode on the right will be higher than that of the left.
Zn(s) │ ZnSO4(aq) ¦ CuSO4(aq) │ Cu(s)
In the cell diagram components are marked with their phases, vertical bars
symbolize the phase boundaries.
Dashed vertical line ¦ for liquid junction means that diffusion potential is not
eliminated.
Zn(s) │ ZnSO4(aq) ║ CuSO4(aq) │ Cu(s)
Double vertical line for liquid junction: ║, means that diffusion potential has been
eliminated.
Cell reaction potential
 zFE cell   r G
Ecell, the cell reaction potential is the potential difference between electrodes, and
zFEcell is the maximum work can be done by the cell.
The thermodynamic sign convention for spontaneous (natural) processes:
 r G  0 thus
Ecell ≥ 0.
That is why we place positive electrode on the right. Subtracting from positive
potential the negative one Ecell becomes positive.
4.Cell reaction
8
4a Cell reaction. The cell reaction is the sum of half cell reactions writing in
spontaneous direction.
Cu2+(aq) + 2e → Cu(s)
Zn(s) → Zn2+(aq) + 2eAdding the two processes up the result is the cell reaction.
Zn + Cu2+ → Cu + Zn2+
Using the sign convention the potential difference
 Cu   Zn  Ecell and Ecell  0
In general, the electrode placed on the right in the cell diagram should be the
cathode, than subtraction
Ecell   Right    Left 
3a.
will give positive result. The real spontaneous direction depends on the actual
concentration/activity values in the cell. The cell reaction can change its direction
and consequently Ecell its sign. The proper sign can be determined by polarity
measurement, by using high input resistance voltmeter.
5. The Nernst equation – the activity dependence of Ecell .
5a.
 r G   r G 0  RT ln( Q)
 r G 0 standard reaction Gibbs free energy
Q reaction quotient
Dividing both sides by -zF
F = 96500 C mol-1
z reaction charge number. ( z(Daniell cell) = 2))
(The number of transported electrons / electrode reaction in the given galvanic
cell.)
By definition of Eq. 1.
 r G 0 RT
Ecell  

ln( Q)
zF
zF
rG0
0
, the standard cell reaction potential

 Ecell
zF
0
Ecell  Ecell,1

RT
ln(Q )
zF
For the cell reaction Zn + Cu2+ → Cu + Zn2+ in Daniell cell reaction quotient can be
given,
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aCu aZn
,
aZn aCu
for pure and homogeneous phases aCu = constant and aZn = constant, thus they are
involved in standard term
Q
2
2
RT aCu
ln( )
zF
aZn
aZn 2
RT

ln(
)
zF
aCu 2
0
0
Ecell
 Ecell,1

0
Ecell  Ecell
7.
At conditions dT = 0 and dp = 0 the Nernst equation gives the relationship between
Ecell and the activity ratio of electroactive components.
0
When activity values in a galvanic cell are set as Q = 1, than Ecell  Ecell , the
standard cell reaction potential.
6. . The structure of electric double layer.
6a.
The electrical double layer forms at the boundary of electrode metal and electrolyte
solution. The density of ions differ to that of in the bulk of solution. If there is no
electrochemical reaction present a potential difference between the metal and the
bulk of solution arises. The potential difference formed E = φM – φS is the metal
solution potential difference which can not be determined direct potential
measurements.
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7. Ion – ion (redox) electrode: half cell diagram, the half cell reaction, Nernst
equation
7a. Ion – ion (redox) electrode. A single liquid phase contains both the oxidized
and reduced forms of electrode reaction. A noble metal electrode, e.g. Pt senses the
potential difference between the bulk of solution and the metal. The electron
exchange occurs in the liquid phase.
The electrochemical process which determines the electrode potential of
redox electrode
Pt(s)│cFe2+(aq), cFe3+(aq)
Fe3+ + e = Fe2+
0
 Fe2  / Fe3   Fe

2
/ Fe3
RT aFe2 
ln
F
aa 3
Fe
3
a( Fe )
RT a( Fe3 )
If
→
1
ln(
)0
zF
a( Fe2 )
a( Fe2 )
The electrode potential is identical to the standard potential.
0
 Fe2 / Fe3   Fe
2
/ Fe3
0
 Fe
 0.771 V at T = 293 K.
2
/ Fe3
If
a ( Fe3 )
1
2
a ( Fe )
→
RT
a( Fe3 )
ln(
)0
2

zF
a( Fe )
The electrode potential is less than the standard potential.
0
 Fe2 / Fe3   Fe
2
/ Fe3
8. Cell reaction potential, electromotive force – their definitions, conditions of
measurement Ecell.
8a. Cell reaction potential
 zFE cell   r G
Ecell, the cell reaction potential is the potential difference between electrodes, and
zFEcell is the maximum work can be done by the cell. The thermodynamic sign
convention for spontaneous (natural) processes:
 r G  0 thus
Ecell ≥ 0.
That is why we place positive electrode on the right. Subtracting from positive
potential the negative one Ecell becomes positive.
11
The conditions of Ecell measurement,
 1. Current flowing between electrodes approximates zero I → 0 in the
measuring electric circuit, so system does not do any work on surroundings.
 2. diffusion potential, φd has been eliminated
 3. cell reaction is reversible.
At the conditions given Ecell is a measure of maximum work the cell could do. From
the measured Ecell, knowing the cell reaction itself, the reaction Gibbs free energy
can be calculated. If diffusion current should be taken into account
EMF  Ecell   d .
electromotive force EMF is measured instead of Ecell. In this case a nonthermodynamic quantity is added to Ecell.
In many case  d can be minimized down to several milli-volts by the application of
a salt bridge, and Ecell and EMF can be taken equal.
When the cell reaction is in chemical equilibrium (at dT = 0, dp = 0)
 r G  0 and Ecell  0
System is incapable to do any work.
9.Electrode potentials, possibility of determination of individual electrode
potentials
9a. Electrode potentials., E, in chemistry or electrochemistry, according to
a IUPAC definition,[1] is the electromotive force of a cell built of two electrodes:
on the left-hand side is the standard hydrogen electrode, and on the right-hand side
is the electrode the potential of which is being defined.
By convention:
ECell = ECathode − EAnode
From the above, for the cell with the standard hydrogen electrode (potential of 0 by
convention), one obtains:
ECell = ERight − 0 = EElectrode
The left-right convention is consistent with the international agreement that redox
potentials be given for reactions written in the form of reduction half-reactions.
Electrode potential is measured in volts (V).
Ecell can be given as the difference of electrode potentials (see Eq. 3.):
RT
RT
Ecell  Cu 2  Zn 2  0Cu 2 
ln aCu 2  (0Zn 2 
ln aZn 2 )
8.
zF
zF
Individual electrode potentials can not be measured, owing to formation of double
layer at the interface.
12
0
10. . Eqilibrium constant determination from Ecell
data.
10a.Equation 6. Ecell  Ecell,1 
RT
ln(Q )
zF
At equilibrium from Eq. 6.
Q = Ka
0
and
rG  0 ,
therefore
 zFE cell  0
RT
ln K a
zF
0
zFEcell
ln Ka 
RT
0
0  Ecell

9.
0
The measured data for Ecell
at a given temperature serves for the calculation of
equilibrium constant.
11.Electrolyte concentration cells: the cell diagram, the cell reaction, Nernst
equation.
11.a We set a cell from two identical metal electrode (Me) and an electrolyte from
a soluble salt of this metal (Me+). The Me+ activities of compartments (in the two
half cells) are different, a1 and a2.
Me │ Me+(aq), a1 ║ Me+(aq), a2 │ Me
When inequality a2 > a1 holds, Me+ in the right side electrode has a greater
tendency to reduce, the spontaneous processes are:
Reduction (cathodic)
Me+(a2) + e → Me
Oxidation (anodic)
Me → Me+(a1) + e
reaction:
Me+(a2) → Me+(a1)
RT a1
Nernst equation:
Ecell  
ln( )
F
a2
The standard cell reaction potential is zero.
RT a1
If a1 = a2 than 
ln( )  0 , there is no driving force of the process, and
F
a2
system is in chemical equilibrium: Ecell = 0.
0
 0.
From Nernst equation Ecell
a1
a
→
1
ln 1  0
a2
a2
and Ecell > 0 as it should be.
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Electrochemical Kinetics
Preparation for test writing
1.The rate of reactions at phase boundary.
1a. The current density is proportional to the rate at a phase boundary.The rate of a
homogeneous reaction, vr:
vr 
1 dn
 dt
where n and ν are the amount of material and stoichiometric number of a reactant
or product. The unit for vr is mol s-1. Taking stoichiometric number to be one,
vr 
dn
dt
The reaction rate of a heterogeneous process (e.g., an electrode process ) depends
on the surface of the electrode at constant polarization potential. The rate v refers to
unit surface area
v 
1 dn
A dt
The unit for v is mol dm-2 s-1.The rate of an electrode process is proportional to the
current density
j
1 dq
A dt
The current density is proportional to rate of an electrochemical reaction and it
makes rate independent of the area of electrode.
An infinitesimal amount of charge dq is proportional to the amount of material
passed through the interface dq  zF  dn .
zF dn
j
A dt
From equations 1. and 2. we get
j  zF  v
The reaction rate of a unit surface electrode is proportional to current density.
2. Polarization, overvoltage, exchange current density.
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2a. Polarization, overvoltage. Polarization: the shift in the voltage across a cell
caused by the passage of current, departure of the cell potential from the reversible
(or equilibrium or nernstian) potential.
For a simple reversible redox reaction
Mz  ze-  M
the cathodic process is a reduction at a rate jc, cathodic current density, while the
anodic process is an oxidation at a rate ja, anodic current density.
At equilibrium a rest or equilibrium potential εe is measured against a proper
reference electrode. When electrochemical equilibrium is established
jc  j a  j0
the anodic and cathodic current densities are the same and equals to exchange
current density.
Increasing the negative potential:
jc  j a
The portion of potential differs from equilibrium potential is called overvoltage, η.
   pol   e
3. Anodic and cathodic processes at electrodes
3a. The rate constant of forward reaction, kf is characteristic to the cathodic
reduction process. The higher the negative polarization potential, the greater the
rate of cathodic reaction.
Heterogeneous process at the electrode surface.
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