Concentration and activity

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CHEM 12032Concentration and activity
Dr. K.A.S Pathiratne Head of the Department of
chemistry University of Kelaniya, Sri Lanka
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- Like charges repel -
Unlike charges attract Availability for e.g.
Ability for participation in reactions is
altered. Decreases mostly or increases under
certain circumstances.
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Meaning True or effective concentration is
different from the molar concentration.
Activity The concentration corrected
taking into account ion ion interactions
(attractions repulsions) is called the activity
a. a is obtained by multiplying molar
concentration, C with mean activity coefficient (
? or f).
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Mean Activity coefficient (?)
This can be calculated using equations developed
by Debye Huckel (Debye- Huckel Theory for mean
activity coefficients) or experimentally
determined. a ? . C
and several other
relationships.
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Debye-Huckel Theory

• Assumptions
• The model for a very weak electrolytic solutions
• Major assumptions
• The ions are hard spheres
• Solvents have no structures
• The dielectric constants of solvent remain the
  same throughout solution
• Ion-Ion interactions are purely columbic
• Thermal energies of ion are much larger than
  columbic interaction energies.

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Debye-Huckel Limiting Law

• When point charge approximation is used.
• i.e. the central ion is a point charge. It has no
  volume.

Where A Debye-Huckel const
0.503 mol½dm3/2 , at 250C.
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Z and Z- are charges of the cation and
anion respectively. I Ionic strength

Ci concentration of the ith ion Zi charge of
the ith ion.
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Debye-Hukel General Law

• When the point charge approximation is
  abandoned.

Where, B A constant depends on the
solvent and temperature. a
size parameter
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e.g. Calculate the mean activity coefficient
(?), the mean activity ,a, for 0.01moldm-3 NaCl
solution present in a. 0.1moldm-3 KNO3 medium at
250C, using both limiting and general expressions
of Debye-Huckel Law for mean activity
coefficients of electrolytes.
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Electrode Potentials Nernst Equation
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Charge separation between the metal surface
the nearby solution layer due to the
equilibrium oxidation and reduction reactions
given below. Mn(aq) ne
M(S) develop an electric potential
E, at the interface, given by the equation
Known as Nernst Equation
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Where, E0Mn(aq)/M(S) is called the standard
electrode potential of the electrode R,T,n F
have their usual meanings. aMn(aq) the
activity of Mn(aq) ions the solution aM(S)
the activity of the metal M of the solid
state 1.
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Where, E0 formal potential of the
Mn(aq) /M(s) electrode.
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Gas Electrodes

• e.g. Cl2 electrode
• Equilibrium reaction
• Cl2(g)2e 2Cl-(aq)
• Nernst Equation

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Redox electrodes

• Elements (metals) with multiple valencies.
• (e.g. Transition metal Co, Ce, Fe, Sn, etc.)

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• Note
• Inert metal Pt, Pd Au does not participate in
  
• oxidation or reduction (only a conductor)
• (2) Both oxidized reduced forms of ions are
  present
• in the solution.

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Liquid Junction Potential
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At the beginning, no Cu2 in R.H.S. and no Zn2
in L.H.S. also, ?Cu2
? ?Zn2 Assume ?Cu2 gt ?Zn2 Result more
() ions in R.H.S compared to L.H.S. Right side
more ()ve than left side An equilibrium is
achieved and under that condition
?Cu2 ?Zn2
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The charge separation develops an electric
potential called liquid junction potential, E L.J

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Hydrogen Scale of Electrode potentials
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By convention the potential of 0.0 V has been
assigned to the hydrogen electrode at the
standard state.
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Standard Electrode Potentials

• The potential of other electrodes have been
  determined with respect to the standard hydrogen
  electrode.
• Note
• The magnitude of the electrode potential
  of the unknown electrode is the e.m.f. the cell
  constructed with the std hydrogen electrode and
  the electrode under measurement.

1.
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• Sign of the standard electrode potential is
  the polarity of the unknown electrode of the
  cell constructed with the std. hydrogen
  electrode.
• The standard electrode potential are
  represented in the form
• E0ox / red

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Secondary Reference Electrodes

• Construction and maintainace of std.
  hydrogen electrodes are difficult. Alternative
  subsidiaries are available.
• 1. Calomel electrode
• Hg(l)/Hg2Cl2(s)/Cl-(aq)
• 2. Silver/ Silver chloride
  electrode
• Ag(s)/AgCl(s)/Cl-(aq)

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Calomel Electrode

• Hg2Cl2 (s) 2e 2Hg
  (l) 2Cl-(aq)

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At a given temperature E depends on Cl-. So
maintaining a constant concentration in Cl-,an
electrode with a constant potential can be
prepared. SCE Saturated calomel electrode.
The KCl solution is saturated
solution.
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A Lab Made Calomel Electrode
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Calomel Electrode
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Silver/Silver Chloride electrode
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E, therefore depends on Cl- for a given
temperature
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Block diagrams Ag/AgCl reference electrode
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Cell Thermodynamics
Determination of thermodynamic parameters ?G, ?H
and ?S for a chemical reaction using cell e.m.f
measurements.

• The relationship between the free energy change,
  ?G of an electrochemical cell and the cell e.m.f
  ,E is given by

?G -nEF
n and F have their usual meanings

• The energy provided to external load during a
  discharge of a cell equals to the decrease in
  free energy of the cell.

• We can determine ?G, ?H and ?S ,if we design a
  cell in which the required reaction occurs during
  the discharge the cell designed.

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?G ?H - T ?S.(01) ?G V ?P- S
?T..(02)? (? ?G / ?T)P - S.(03) -( ?
nFE/ ?T)P - S.(04) ?H - nFE T (? ?G /
?T)P
? ?H - nFE nFT(? E / ?T)P
and
?S nF(? E / ?T)P

• Results obtained are approximate compared to
  those obtained from thermodynamic measurements.

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Concentration Cells
Ag (s) / AgNO3 (a1) // AgNO3 (a2) / Ag (s)
E LHS EO Ag (RT/F) ln a1
E RHS EO Ag (RT/F) ln a2
Cell emf , E E RHS - E LHS
E (RT/F) ln (a1/ a2)

• ?The e.m.f of the cell depends on activities Ag
  in the two compartments (concentrations) of the
  oxidizing / reducing components in the cell.

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Measurement of Cell e.m.f. Basis of
Potentiometry

• Potentiometer Circuit

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• Two information related to an unknown cell can be
  derived from a potentiometric experiment.
• Polarity of the electrodes of unknown cell
• e.m.f. of the unknown cell

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Electrodes of different activities in the same
solution cells with no liquid junctione.g Two
gas electrodes at different pressuresPtCl2HClC
l2Pt (P1) (P2)Equilibrium at
each electrode is given by, Cl2(g) 2e
2Cl-(aq)

• Concentration cells continued

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Redox Systems
Elements with multi-valences e.g. Transition
elements Co , Ce, Sn ,Fe, ect , exhibit
this behavior.
Ce4(aq) e Ce3 (aq)
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Redox systems (contd)

• Oxidizing and Reducing Powers of Redox
  electrodes.
• Consider,
• Ox ne Red

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If equilibrium is more towards right to form
reduced ion electrons have to be supplied from
the inert conductor, leaving it with an electron
deficient state acquiring a positive charge. The
more the reaction to the right more will be the
() character on the inert electrode. This gives
more () ve standard electrode potential to the
electrode. Then this electrode tends to pull
electrons from other electrodes which are less
()ve than this particular electrode. This
results an oxidation at the second electrode.
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On the other hand if the Ox ne
Red reaction is more towards left more
oxidized species will be formed in the
solution. The electron liberated from Red
species producing Ox species will be
accumulated on the inert metal building (-) ve
charges on the inert metal. The more the reaction
towards the left more (-)ve will be the charge on
the inert metal and more (-)ve will be the
standard electrode potential of the couple. When
other electrode with a lesser (-) ve potential is
connected to the particular electrode electron
will be donated to the previous electrode. i.e.
The more (-) ve the standard electrode potential
of a given electrode more will be the reducing
power of the redox couple.
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Redox Potentials

• Std. Electrode potentials of several selected
  redox electrodes at 250C

Increasing oxidizing power
Increasing reducing power
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Consider the std cell given below
Salt bridge
E0Fe3/Fe2 0.771V E0Sn4/Sn2
0.15V Fe3/Fe2 couples (E0 0.771V) is more
() than Sn4 /Sn2 couple (E0 0.15V)
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Therefore when the switch s is closed electron
from the Sn4 /Sn2 couple through the inert
platinum wire passes to the Pt wire immersed in
Fe3 , Fe2 solution.
The result is that Fe3 will be converted to Fe2
in the Fe3/Fe2 couple The electron required in
this situation is now supplies from Sn2 in the
Sn4/Sn2 redox system. More Sn4 will be formed
from Sn2.
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Standard Electrode Potentials And Equilibrium
Constants
(aq)
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Consider the mixing of 2 redox systems, Fe3/Fe2
and Sn4/Sn2 systems and the potential ESn of
the tin system according to Nernst equation are
given below.
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The decrease of Fe3 increases of Fe2,
decreases the value of EFe continuously. Also
increase of Sn4 and decrease of Sn2
increases the value of ESn. As reaction
continuous the potential of EFe continuous to
reduce and that of ESn continues to increase.
When EFe ESn become equal i.e., EFe Esn The
reaction reaches the state of equilibrium and no
net reaction occurs.
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Generalized Equation
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Redox Titrations
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The above reaction is an equilibrium reaction.
Fe2 Ce4 Fe3
Ce3 Even using an equilibrium reaction (e.g. the
above reaction) still a titration can be carried
out and unknown can be determined with a required
accuracy depending on the extent of progress of
the reaction to the right. Suppose using the
above reaction only 99.9 of total Fe2 can be
converted to Fe3 leaving behind 0.1 of
Fe2. That is ,the reaction goes to 99.9
completion.
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CALCULATION OF THE POTENTAL AT THE EQUIVALANCE
POINT
For example of 99.9 completion occurs
And
The makes
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Application of cell e.m.f. Measurements

• Determination of solubility product of
  sparingly soluble salts.
• e.g. Solubility product of AgCl, KAgCl
• Usual approach
• A cell must be constructed. The potential of one
  half cell (i.e. an electrode) must be known e.g.
  a reference electrode can be used used for this.
• The other half cell must have a saturated
  solution of the salt (in the case, a saturated
  solution of AgCl) as one of the components in it.
  

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Sketch of a suitable cell made in the lab
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Cl- Concentration of Cl- in the solution,
i.e. the concentration of KCl in the beaker
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ELHS a constant and known (available in
text) See in previous notes for the equilibrium
reaction and Nernst equation for this. The cell
e.m.f. is measured using a potentiometer is .
It is known Celle.m.f.
EAg ESCE EAg is known since all the termes in
the equation other than KAgCl are known, KAgCl
can be calculated.
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(b) An alternative approach, which does not
require EoAg, value.
The only unknown kAgCl can be calculated.
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(c) A third alternative A cell without a liquid
function
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Ag(s) /AgCl(s) /HCl(x M) /Cl2 Pt ECell ECl 2
EAg
After rearrangement
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Determination of Thermodynamic Parameters

• e.g. ?G, ?H and ?S for the reaction.
• H2(g) Cl2(g) 2 HCl(aq)
• At room temperature,
• Construct a cell in such a way, when the cell
  discharges, the above reaction occurs as the net
  cell reaction.

(1)
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?G -nFEcell For the present reaction
?G -2 x F x Ecell ?H, and ?S then using the
relevant formula can be calculated. Note If
HCl 1M , PH2 PCl2 1atm Cell
e.m.f. E0cell
?G ?G0 ?H ?H0 ?S ?S0
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Application of e.m.f. measurement

• (3) Determination of concentration of some
  ions e.g. concentration of Cu2 ions in a given
  solution.

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The equilibrium given below will be established
is Cu2(aq) 2e
Cu(s) Nernst equation for the equilibrium is
Cu(s) 1, Cu2 ? E0, RT F are
constant. If ECu is known (Cu2) can be
calculated.
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For measuring ECu, another electrode is
needed. A convenient the correct electrode is a
reference electrode where, the potential of it
remains constant irrespective of where it is
immersed. A correct assembly, with a
potentiometer to measure potential between the Cu
reference electrode is represented below.
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The potentiometer reading, is the cell e.m.f., E
represented by the equation
E ECu ERE Since ERE is known, ECu can be
calculated hence the Cu2. Cu belongs to an
element which represent a metal electrode of the
first kind. Accuracy of the Cu2 obtained here
however is low due to several reasons beyond
discussions here.
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Membrane electrodes are another very important
range of electrodes used to measure concentration
of ions/ molecules in a medium (liquids or
moisture vapors). Ion selective electrodes are
one type belong to this category.
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THE END