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Spontaneity of redox reactions
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-Any reaction that can occur in a voltaic cell to produce a positive
e.m.f must be spontaneous.
Eo=Eored(reduction process)Eored(oxidation process)
We can now make a general statement about the spontaneity of a
reaction and its associated emf, E: a positive value of E indicates a
spontaneous process and a negative value of E indicates anonspontaneous one.
So E indicates non standard condition
Eoindicates stand condition
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Gibbs free energy, G is a measure of the spontaneity of a
process that occur at the contant pressure and temperature
When a reaction takes place in a voltaic cell, it performs
work.
We can think of this electrical work as the work producedby electrical charges in motion.
The total work done = cell voltage x the number of moles of
electrons (n) transferred between electrodes x the electric
charge per mole of electrons (1 Faraday = 96 485coulombs per mole)
welec = Ecellx n x F
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The maximum electrical workcan expressed by the
following equation:
Wmax= Welectrical=nF x Ecell
where work is defined as positive into the system and
negative by the system.
Since the free energy is the maximum amountof work that
can be extracted from a system, one can write:
G = nF x Ecell
where G is Gibbs free energy.
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A positive cell potentialgives a negative changein
Gibbs free energy. That mean when E is positive G isnegative and the reaction is spontaneous.
This is consistent with the cell production of an electric
current flowing from the cathode to the anode through theexternal circuit(e flow from anode to cathode). If the current
is driven in the opposite direction by imposing an external
potential, then work is done on the cell to drive electrolysis.
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The relation between the equilibrium constant, K, and the Gibbs free
energy for an electrochemical cell is expressed as follows:
G =RT ln(Keq)
=nF x Ecell
Rearranging to express the relation between standard potential and
equilibrium constant yields
where R is the gas constant (8.3145Jmol-1K-1), T is the Kelvin
temperature, n the no. of moles of electrons involved in the
reaction and F the Faraday constant
Nernst Equations
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Example:
Calculate the values ofGoand Keqat 25oC for the reaction
Cu(s) + 2Ag+(aq) Cu2+(aq) + 2Ag(s)
Given Eocell= 0.460V (see following slide)
Solution:
Go= -n x F x Eocell
= -2 mole e x 96 485 C/mol e x 0.460V
= -8.88 x 104J
Eocell=
ln Keq= =
Keq = 4 x 1015
0.025693V
nLn Keq
2 x 0.460V
0.025693V 35.8
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Spontanity
Will copper metal displace silver ion from aqueous solution? That is, does
this reaction occur spontaneously from left to right given EoAg+/Ag= 0.800
and EoCu2+/Cu= 0.340?
Cu(s) + 2Ag+(aq) Cu2+(aq) + 2Ag(s)
Solution:
Reduction: 2Ag+(aq) + 2e 2Ag(s) Eo= 0.800V
Oxidation Cu(s) Cu2+(aq) + 2e Eo= 0.340V
Eocell= Eo(reduction)Eo(oxidation)
= 0.800V0.340V
= 0.460V
Eocellis positive, the forward direction should be the direction of
spontaneous change. Copper metal should displace silver ions from
solution.
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To determine if a redox reaction is spontaneous, you
should compute the voltage of the reaction.
If the voltage is positive, the reaction is spontaneous
If the voltage is negative, the reaction is not spontaneousExample:Is the reaction below spontaneous?
Cu(s) + 2Fe3+(aq) --> Cu2+(aq) + 2Fe2+(aq)
Solution:To determine spontaneity, we need to determinethe voltage. Break the reaction up into two half reactions and
check the voltages of each
Cu(s) --> Cu2+ + 2e- Eox= -0.339 V
Fe3+(aq) +e - -> Fe2+(aq) Ered = +0.769 V
The cell voltage is thus Ecell= Ered- Eox
= 0.769(-0.339)
= +0. V.
Since E is positive, the reaction is spontaneous.
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Exercise:
1. Calculate the values ofGoand Keqat 25oC for the
reaction that follows
3Mg(s) + 2Al3+(1M) 3Mg2+(1M) + 2Al(s)
2. Determine Keqfor the reaction of silver metal with nitricacid. The silver is oxidized to Ag+(aq) and nitrate ion is
reduced to NO(g).
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Criteria for spontaneous change in redox reactions
1. If Ecellis positive, the reaction in the forwarddirection (from left to right) is spontaneous.
2. If Ecellis negative, the reaction in the forward
direction is nonspontaneous.
3. If Ecell= 0, the system is at equilibrium.
4. When a cell reaction is reversed, EcellandG
change signs.
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The effect of concentration on cell
EMF (The Nernst Equation)
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Effect of concentration on cell EMF
A voltaic cell is discharged, the reactant of the reaction are consumed
and products are generated, so the concentration of these substanceschanges.
The emf progressively drops until E=0, at which point we said the cell
is dead.
At the point the [ ] of the reactant and products cease to change; they
are at equilibrium.
The emf generated under nonstandard condition can be calculated by
using the Nernst equation.
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In the late 19th century, Gibbs had formulated a theory to
predict whether a chemical reaction is spontaneous
based on the free energyG = G + RTx ln(Q)
Here Gis change in Gibbs free energy, Tis absolute
temperature, Ris the gas constant and Qis reactionquotient.
Gibbs' key contribution was to formalize the understanding
of the effect of reactant concentration on spontaneity.
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Based on Gibbs' work, Nernst extended the theory to include the
contribution from electric potential on charged species. The
change in Gibbs free energy for an electrochemical cell can be related
to the cell potential. Thus, Gibbs' theory becomes
nFE = nFERT ln(Q)
Here nis the number of electrons/mole product, Fis the Faraday
constant (coulombs/mole), andE
is cell potential.Finally, Nernst divided through by the amount of charge transferred to
arrive at a new equation which now bears his name:
E = E(RT/nF)ln(Q)
E = E(2.303RT/nF)logQ
Assuming standard conditions (T = 25 C) and R = 8.3145 J/(Kmol),
the equation above can be expressed on base 10 log.
At T=298K the quantity 2.303RT/nF equals 0.0592V, so equation
simplifiers to:
E = E(0.0592/n) log Q
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In general, if the concentrations of reactants increase
relative to those of products, the cell reaction becomes more
spontaneous and the emf increase. Conversely, if theconcentrations of products increase relative to reactants, the
emf decrease.
As voltaic cell operates, reactants are converted intoproducts, which increase the value of Q and causes the emf
to decrease.
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Concentration cells
A concentration cell is an electrochemical cell where the two
electrodes are the same material, the electrolytes on the two half-cells
involve the same ions, but the electrolyte concentration differs betweenthe two half-cells.
For example an electrochemical cell, where two copper electrodes are
submerged in two copper(II) sulphate solutions, whose concentrations
are 0.05M and 2.0M, connected through a salt bridge. This type of cellwill generate a potential that can be predicted by the Nernst equation.
Both electrodes undergo the same chemistry (although the reaction
proceeds in reverse at the cathode)
Cu2+(aq) + 2 e Cu(s)
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Cu2+(aq) + 2e Cu(s)
Le Chateliers principle indicates that the reaction is more
favorable to reduction as the concentration of Cu2+ions
increases. Reduction will take place in the cell's
compartment where concentration is higher and oxidation
will occur on the more dilute side.
The following cell diagram describes the cell mentionedabove:
Cu(s) | Cu2+(0.05 M) || Cu2+(2.0 M) | Cu(s)
Where the half cell reactions for oxidation and reduction
are:Oxidation: Cu(s) Cu2+(0.05 M) + 2 e
Reduction: Cu2+(2.0 M) + 2 e Cu(s)
Overall reaction: Cu2+(2.0 M) Cu2+(0.05 M)