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# Electrode Potential

A redox reaction is a reaction in which one of the substances undergoes oxidation whereas another substance gains electrons and undergoes reduction. These reactions are accompanied by release of energy, known as chemical energy which can be converting in electrical energy. The arrangement or device which can convert chemical energy to electrical energy is called as electrochemical cell or galvanic cell or voltaic cell.

However for non-spontaneous reactions some electrical energy required for initiate the chemical reaction, hence show a conversion of electrical energy to chemical energy. Such types of device which show conversion of electrical energy to chemical energy are called as electrolytic cell. The stream of chemistry which deals with the relationship between electrical and chemical energy is known as electrochemistry.

In galvanic cells which are electrochemical cell, oxidation takes place at anode and acts as negative pole of cell Similarly reduction takes place at cathode and being a positive pole of cell. The electrons flow from negative pole to positive pole of cell in the external circuit.

For example, in denial cell, zinc road dipped in zinc sulphate solution is linked with cooper road dipped in copper sulphate solution. Both solutions are linked with salt bridge. Here zinc road acts as anode and copper road as cathode. The cell representation is as follow;

Zn|ZnSO4(aq)||CuSO4(aq)|Cu+2

Anode Salt bridge Cathode

Oxidation reaction takes place at anode i.e. at zinc electrode and copper electrode acts as cathode.

 Related Calculators Elastic Potential Energy Calculator Gravitational Potential Energy Calculator Nernst Potential Calculator Potential Energy Calculator

## What is EMF?

In a cell, electrodes are dipped in their salt solutions and can be linked through salt solutions or salt bridge. There is a certain potential creates on each electrode due to reactions accompanied on electrodes. For example, when a metal rod is dipped in a solution of its own ions, there will be some positive negative charge generates on rod with respect to the solution. It can be either positive or negative charge.

When metal ions and their solution are in contact with each other, a definite potential difference is developed between the metal and the solution which is known as electrode potential. There are three possibilities in this solution.

• Metal ions strike to electrode surface and deflected back to solution without nay change.
• Metal ions gain electrons and convert in metal atom, hence metal ions are reduced.
Mn+ + ne- M
• Metal atoms may lose electrons and change to metal ions, hence metal atoms get oxidized.
M(s) Mn+ + ne-

If metal ions have higher tendency to get reduced, they will gain electrons from metal rod and get reduced. This reaction generates positive charge on metal rod with respect to the solution and finally equilibrium will be maintained. If metal ions have higher tendency to get oxidized, electrons will accumulate on metal road and develop negative charge on metal rod and ultimately equilibrium will be maintained.

In both cases, there is a separation of charges between the metal rod and solutions and a potential difference exist between them. This potential difference between metal rod and its ion in solution is known as electrode potential also defined as tendency of an electrode to lose or gain electrons when it is in contact with the solution of its own ions. The potential of that electrode where oxidation takes place is called as oxidation potential and potential of electrode associated with reduction is called as reduction potential.

If the electrode is suspended in a solution of one molar concentration and the temperature is kept at 298 K, the electrode potential is called as standard electrode potential and represented as E°. If cell contains gaseous reactants, 1 atmosphere pressure and 298 K temperature will be standard conditions. The difference between the electrode potential of the two half cells is known as cell potential or cell voltage. It is called as electromotive force (emf or EMF) of the cell if no current is drawn from the cell.

The EMF of cell depends on the nature of the reactants involve in reaction, concentration of the solution taken in cell and reaction temperature. The emf of denial cell is 1.1 volt at 298 K temperature when the concentration of zinc sulphate and copper sulphate are one molar each.

Since an electrochemical cell is based on redox reaction which can be split into two half reactions.
1. Oxidation half reaction
2. Reduction half reaction
Hence the standard EMF of cell = [Standard oxidation potential of the oxidation half reaction] + [Standard reduction potential of the reduction half reaction]

As the Standard oxidation potential = -Standard Reduction potential

So standard EMF of cell can be written as = [Standard reduction potential of the reduction half reaction] - [Standard reduction potential of the oxidation half reaction]

As we know, oxidation takes place at anode and reduction takes place at cathode, the standard can be written as;

Standard EMF of cell = [Standard reduction potential of cathode] - [Standard reduction potential of anode]

E°cell = E°cathode - E°anode

For example, in denial cell Zinc rod dipped in zinc sulphate solution and copper rod in copper sulphate solution.

The half reactions occur in cell are as follows.

Oxidation half reaction at anode; Zn(s) Zn2+(aq) + 2e- ; Eo = -0.783
Reduction half reaction at cathode; Cu2+(aq) + 2e- Cu(s) Eo = +0.337

The overall cell reaction will be; Zn(s) + Cu2+(aq) Zn2+(aq) + Cu(s)

The EMF of the cell
E°cell = E°cathode -E°anode
= 0.337 – (-0.783)
=1.12 volt

Some other cell with Electromotive force value, negative and positive terminals are as follow.

 EMF of cell Negative electrode Positive electrode Cell chemistry 1.2V Hydrogen-absorbing alloy instead of cadmium Nickel oxyhydroxide (NiOOH), like the NiCd Nickel-cadmium 1.2V Hydrogen-absorbing alloy instead of cadmium Nickel oxyhydroxide (NiOOH), like the NiCd Nikel-metal hydride 1.5V Zinc Carbon rod surrounded by a mixture of manganese dioxide and carbon power. Zinc-carbon 2.1V Lead(II) sulfate (PbSO4) and the electrolyte Lead(II) sulfate ((PbSO4)) and the electrolyte Lead-acid 3.6V to 3.7V Carbon Metal oxide, and the electrolyte is a lithium salt in solvent Lithium-ion

## EMF Units

As the name implies EMF is not a force which can measured in newtons, it’s a potential i.e. energy per unit of charge, hence measured in volts. In other words, EMF is the work expanded per unit of charge to produce the potential difference between two terminals of cell.

If Q is the charge passes in cell to gains the energy W, the EMF of the device will be energy gained per unit charge, W/Q that is volts in SI units and equals to joules per coulomb or newton*meter/coulomb.

## Induced EMF

Two scientists Faraday and Henry discovered the principles of magnetically induced electromotive force and purposed the methods for converting mechanical into electrical energy independently. When a coil of wire connects to a galvanometer which used to measure current in the coil, with no power supply there will be no current in circuit. Now if we bring a magnet close to the coil, two things can happen.

1. In the stationary state of when a magnet placed near and inside the coil, there will be no current observed through the coil.
2. If we move the magnet, there will be a slight deflection in the galvanometer needle of which show the flow of through the coil.
3. The movement and direction of magnet influenced the flow of current in coil.
4. When the same magnet placed in a second coil and a current can be passed by using a battery, the coil will act as a bar magnet.
5. When the second coil comes in contact with the first coil, which is connected to the galvanometer, there will be no change in the second coil. When the current in the second coil is changed by either switched on or off, the galvanometer indicates the flow of current in the first coil.

Hence by changing the magnetic field, a voltage is produced in a coil, causing a current to flow.
This induce voltage is known as the induced emf which can be induced by changing the magnetic flux (ɸ) or by changing the area of the coil or by change in the angle between the magnetic field and the coil.

The relation between magnetic flux (ɸ), area of coil (A) and magnetic field (B) is given by

ɸ = BA cosɵ

where ɵ is the angle between magnetic field and vector A.

The change in flux through the coil related to induced field which is summarized in Faraday's law of induction.

If there are N loops in a coil, than the induced emf produced by a flux change within a given interval of time is represented by

Induced EMF = ( -N∆ɸ)/∆t
Since the magnetic flux through a loop of area A is given by
ɸ = BA cos ɵ
Hence, Faraday's law can be written
Induced EMF = (-N) ∆(BA cos ɵ)/∆t

The negative sign indicates that the induced emf in the coil acts in opposite direction in the magnetic flux. This is called as Lenz's law which states that the induced emf generates a current which sets up a magnetic field would act in order to oppose the magnetic flux change.

Hence if the coil has zero magnetic flux and a magnet is brought close, with the change in flux, the coil develops its own magnetic field which points opposite to the field as against the magnet. However if the external field is changed, a coil with certain flux from the external magnetic field would develop its own magnetic field to maintain the flux at a constant level.

## Electrical Potential Energy

There are two types of energy associate with any object, Kinetic energy and potential energy. Kinetic energy associated with its motion and potential energy related to its position.

The work done is related to change in kinetic energy and potential energy.

Work = ∆K.E. + ∆P.E.

The capacity of any object to do work which arise from its position and configuration is called as potential energy.

When a positive charge Q located at a fixed position and other positive charge is bring close to that, it will feel repulsion force and have some potential energy which is also taken as electric potential energy per unit charge or electrostatic potential energy or electric potential taken in voltage.

Potential energy is given by U = kqQ/r
where k = Coulomb’s constant

Let’s take an example, if two positively-charged balls are tied together by a string.
1. One ball has a mass of 50 g and a charge of 5 μc.
2. The mass of other ball is 70 g with charge of 7μc.
3. The distance between them is 10 cm.
4. Initially both balls are at rest, but when the string is cut they move from each other.
5. At the position of rest, there is only potential energy which will convert in kinetic energy.
Hence the electric potential energy will be equals to

k = 8.99 x 109 N m2C2-
q = 5 μc = 5 x 10-6
Q = 7 μc =7 x 10-6
r = 10 cm=0.1 m

Electric potential energy = k q Q / r = (8.99 x 109) (5 x 10-6 ) (7 x 10-6 ) / 0.1 = 3.14 J

## Electric Potential Equation

Any work involves a change in energy. It can be work done by the system or on the system. For example, if we bring two like charges close to each other, some work must be done which associated with change in energy. If we bring charges closer to each other, it will have more electrical potential energy.

When we release the charge, work gets done on the charge which changes its energy from electrical potential energy to kinetic energy. If we brought 2 or 3 charges instead of one, then we would have had to do more work so we would have created more electrical potential energy. Just like any other form of energy, electrical potential energy can be measured in Joules. Hence the electric potential equation is as follow.

Electrical potential = $\frac{Work\ or\ ∆\ electrical\ potential\ energy}{Unit\ of\ charge\ moved}$

Since work or energy can be measured in Joules and charge in Coulombs, hence the electrical potential can be measured in Joules per Coulomb which has been defined as a volt.

1 J/C = 1Volt = 1V

The electric potential at a point which locates at a distance r from a charge Q is given by:

V = k Q / r

Electric potential is just like pressure for fluids. As fluid flows from high pressure to low pressure between two ends of a pipe, charges are responding to differences in potential in a similar way. It is a measure of the potential energy per unit charge and is a scalar quantity. The electric potential and potential energy are related to each other as.

V = PE / q

## Electric Potential Formula

Hence, V = $\frac{W}{Q}$ = $\frac{70J}{70C}$ = 10 volts