Spontaneity of Redox Reactions(1)

8/11/2019 Spontaneity of Redox Reactions(1)

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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)

Spontaneity of Redox Reactions(1)

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