Nerst Equation (2)

7/30/2019 Nerst Equation (2)

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Nerst Equation

The nerst equation expresses the emf of a cell in terms of activitiesof products and reactants taking place in a cell reaction.

Consider this cell reaction:

M1 and M 2 : rep metal electrodes such as Cu and Zn in a cell

Nerst equation :

(equation will be modified later on)

Application of Nerst equation to a corrosion reaction

A corrosion reaction can be considered as being composed of 2 half cell reaction.

At one half cell there will be oxidation reaction taking place.(ANODE).

At the other half cell reduction reaction will take place (CATHODE).

Each half cell reaction can be used together to derive a nerstexpression.


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Nerst equation for a complete cell reaction:

RT nF

ln can be evaluated

since it is a constant at 25 0C

NOTE: the 2.303 is theconversion factor from Ln toLog.

The more commonly used form of theequation is

Note: nerst equation isused only whenconcentration is different

in both half cells.

Problem 1:

Two half cell reactions are given below:

(+ve potential = reactionreadily occur-ve= reaction very difficult

to occur)

R=gas constant

T= temp in Kelvin

N= num of

F=faraday cst


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Note table eq are given in reduction format (gain of electrons =reduction)Calculatea)the emf of the cell

solution:

the more negative potential is the anode and oxidation willtake place.The less negative potential is the cathode and reduction willtake place.

Clearly in this case the anode is : Zn (more ve potential)

And the cathode is :Cu (less negative)

Emf of cell = Emf right(reduction) emf left(oxidation)= 0.34 - (-0.763) = +1.103 V

problem 2

Calculate the reversible potential for a zinc electrode in contact with ZnCl2when the activity of zinc is a Zn2+ = 10 -3 .

Solution:

We first write the half cell reaction :

Zn 2+ +2e Zn, E= -0.76V

Applying the nerst eq for this individual half cell:


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Faradays law of electrolysis and its application in determining corrosion rate

The laws

The first law:

The mass of primary products formed at an electrode by electrolysis is directlyproportional to the quantity of electricity passed.

m It or m = Z I t

The second law

The masses of different primary products formed by equal amounts of electricity areproportional to the ratio of molar mass to the number of electrons involved with a

particular reaction:


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Combining first and second law

m = Z I t

m = k M

nI t

m =1

F .

M n

. Itmt

= corrosion rate.

dm

dt =

M I nF

I = current

divide by area we have :

The above equation has been successfully used to determine the rates of corrosion.

A very useful practical unit for representing the corrosion rate is milligrams

per decimeter square per day (mg.dm _ 2 .day _ 1 ) or mdd.

m

= Mi

= I

=


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Other practical units are millimeter per year (mmy- 1 ) and mils per year (mpy).

Example 1

Steel corrodes in an aqueous solution, the corrosion current is measured as 0.1Acm -2.

Calculate the rate of weight loss per unit area in units of mdd.

Solution:

For Fe Fe2 + + 2e

m

At =

M inF

where,

M (molar mass) = 55.9g.mol -1 , i(current density) = 0.1A-cm -2 , n (number of electron

participating) =2, F=96 485 A. s/mol

replacing in the above formula we have,

m

At =

55.9 0.12 96485

= 2.897*10 -5 ( g

mol A mol

cm 2 A s)

= 2.897*10 -5 g. cm -2 . s -1

our aim : milligrams per decimeter square per day (mg.dm _ 2 .day _ 1 ) or mdd

first we have to convert g to mg and this is done by multiplying 10 3

=2.897*10 -5 *103 = 0.02897 mg. cm -2. s -1


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next step is to convert cm -2 to dm -2

1cm -2 = 100 dm -2

=0.02897 * 100 = 2.897 mg.dm-2

.s-1

we multiply by 24 h/day x 3600 s/h, and obtain the corrosion rate in the desired units:

(2.897 mgcm- 2 s-1 )(24)(3600) = 250300mg d m - 2 day- 1

Example 2

A sample of zinc anode corrodes uniformly with a current density of 4.27 x 10 -7

A/cm 2 in an aqueous solution. What is the corrosion rate of zinc in mdd?

Solution:


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Example 3


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MEASUREMENT OF E corr

(CORROSION POTENTIAL)

the potential of the metal electrode (working electrode) is measured with

respect to a standard Calomel electrode, which is non-polarizable.

(polarizations refers to any change in the equillibrium potential of an

electrochemical reaction. Polarization will cause net anodic or cathodic

current.)

The reference electrode is kept in a separate container and it is connected

electrically with the working electrode placed in a container in contact with

the electrolyte via a salt bridge.

A high impedance voltmeter is connected between the working electrode and

the reference electrode

the open circuit potential in the freely corroding state is shown by the

voltmeter.

The corrosion potential is also referred to as the open circuit potential as the

metal surface corrodes

freely.


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Measurement of corrosion current ( I corr )

Circuitry associated with controlled potential measurements.

o Po

te

nsiostats:

A potentiostat controls the potential between the working

electrode and the reference electrode while simultaneously

measuring the current flowing into or out of the working

electrode necessary to maintain the selected potential

Apply a voltage purposely

We can vary voltage over a range

Workpiece in solution we want to test


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See whether current flows.

o Galvanometer

Induce current.We measure voltage.

We always have to have a reference electrode (will be normally platinum) (corrosion

resistant)

In lab we cannot wait one month and come back again to measure the deviation

produced. Instead we use very small specimen (1 cm 2 ) we somehow accelerate therate of corrosion.

Working electrode is the one we are testing.

Counter electrode provide a path for electrons.

Reference electrode to which we can measure voltage and compare.

DETERMINATION OF CORROSION RATES BYELECTROCHEMICAL MEASUREMENTS

TAFEL EXTRAPOLATION METHOD

In this technique, the polarization curves for the anodic and cathodic reactions are

obtained by applying potentials about 300 mVscE well away from the corrosion

potential and recording the current.

Plotting the logarithms of current (log I) vs potential and extrapolating the currents in

the two Tafel regions gives the corrosion potential and the corrosion current Icorr.

A hypothetical Tafel plot is shown:


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ADVANTAGES AND DISADVANTAGES OF TAFEL TECHNIQUES

(1) The specimen geometry requires a strict control to obtain a uniform current.

(2) The specimen is liable to be damaged by high current.

(3) The Tafel region is often obscured by concentration polarization and by the

existence of more than one activation polarization process

POURBAIX DIAGRAMS (STABILITY DIAGRAMS)

Potential-pH diagrams are also called Pourbaix

A French scientist used the Nernst equation to predict the relationship between potential and the solution pH to predict whether an electrode would be immune, activeor passive in the environment.

In summary, Pourbaix diagrams use thermodynamic and some kinetic data to identifyregions of active corrosion, immunity when corrosion is thermodynamically notfavored and regions of passivity where the kinetics are the rate determining step.

The usefulness of Pourbaix diagrams is that they identify elemental coatings for protection and alloy additions which may transfer their electrochemical behavior to


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Consider, for instance, the case of 18-8 stainless steel placed in an aqueous solution of

H2 SO 4

If the electrode potential is increased then the current density rises to a maximum,

with the accompanying dissolution of the metal taking place in the active state.

The current density associated with the dissolution process indicates the magnitude of

corrosion.

At a certain potential, the current density is drastically reduced as the metal becomes

passivated because of the formation of a thick protective film

Iron shows passivity in acids containing SO 4 2-, NO 3-, ^CrO 42-


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The above metals show a transition from an active state to a passive state.

The phenomena of breakdown of passive films at more noble values of potential leads

to an accelerated rate of corrosion (transpassive corrosion). The potential at which the

breakdown or rupture of protective film takes place and the current density rises

sharply is called transpassive potential.

The transpassive region is the potential at which the dissolved oxygen in water

reaction transforms from cathodic to anodic and the films starts to break down.

Nerst Equation (2)

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