Mobility of ions

• When an electrolyte is dissolved in plenty of water, it breaks up into positively and negatively charged particles called cations and anions respectively.
• When a potential difference is applied between the electrodes dipping in the electrolyte, the positive ions move towards the cathode and the negative ions move towards the anode.
• They will soon acquire a terminal velocity due to collisions with the rest of the ions and neutral molecules.
• The terminal velocity acquired by an ion depends chiefly on the potential gradient, the size of the ion and the viscosity of the electrolyte.

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Ionic mobility is defined as the uniform velocity acquired by an ion under unit potential gradient.

• Cations are generally heavier than the anions and so their mobility is less than that of the anions.
• As a result of this differing mobilities, the concentrations of the electrolyte near the electrodes become different.
• The study of ionic mobilities and the consequent change in concentrations near the electrodes is known as transport phenomena.

Battery

• Battery is an electrochemical cell or series of cells that produces an electric current. In principle, any galvanic cell could be used as a battery.
• An ideal battery would never run down, produce an unchanging voltage, and be capable of withstanding environmental extremes of heat and humidity.

• Battery
• Primary battery

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• Secondary battery

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Primary cell & Secondary cell

• Primary batteries are single-use batteries because they cannot be recharged.
• A common primary battery is the dry cell
• The dry cell is a zinc-carbon battery

• Secondary batteries are rechargeable.
• These are the types of batteries found in devices such as smartphones, electronic tablets, and automobiles.
• Nickel-cadmium is a secondary battery

Charge –discharging process

Charging is a process that reverses the electrochemical reaction. It converts the electrical energy of the charger into chemical energy. Remember, a battery does not store electricity; it stores the chemical energy necessary to produce electricity.

• Discharging or charging always occur inside a battery at any given time.
• The electrolyte solution contains charged ions.
• When an electrical load is placed across a battery’s terminals (starter motor, headlight, etc.) positive ions travel to the negative plates and react with the plate’s active material giving up their negative charge through ionisation.
• This causes the battery to discharge or produce electrical energy.
• This excess electron flow out of the negative side of the battery, through the electrical device, and back to the positive side of the battery is what creates DC current.
• Once the electrons arrive back at the positive battery terminal, they travel back into the cells and re-attach themselves to the positive plates.
• The discharge process continues until the battery is discharged and there is no more chemical energy left.

• A rechargeable battery, storage battery, or secondary cell, (or accumulator) is a type of electrical battery which can be charged, discharged into a load, and recharged many times, as opposed to a disposable or primary battery, which is supplied fully charged and discarded after use.
• Rechargeable batteries (also known as secondary cells) are batteries that potentially consist of reversible cell reactions that allow them to recharge, or regain their cell potential, through the work done by passing currents of electricity.
• Rechargeable batteries can charge and discharge numerous times.
• https://www.youtube.com/watch?v=p8ecZ5oK7Fc

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Lead acid accumulator

• In this accumulator the electrodes are lead dioxide (positive electrode) and spongy lead (negative electrode).
• Alternate plates are joined to the positive and the negative terminals.
• To prevent plates of opposite polarity from coming into contact suitable insulating separators are also used.
• The electrolyte is a solution of sulphuric acid.
• The container is a glass or bakelite case.

The reaction during the charging process

At the positive plate,

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At the negative plate,

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The total reaction during charging can be written as

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The chemical reactions taking place during the discharging process may be represented by the following equations:

At the positive plate,

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At the negative plate,

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The total reaction during discharging can be written as

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• The total reactions can be represented together as

• Thus during the discharging process whitish PbSO₄ is formed on both the electrodes.
• During charging however the positive plate gets its dark brown coating of lead peroxide while the negative plate is reduced to grey metallic lead.
• For proper maintenance of the cell the density of the sulphuric acid is maintained between 1220 to 1250 kg m^-3 .
• When the density becomes about 1700 kgm^-3 drawing of current from the cell is stopped and the cell is recharged.

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Nickel – iron accumulator

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• The positive electrode is perforated nickel plated steel-tube packed with the mixture of nickel hydroxide and finely divided nickel.
• The negative electrode is a nickel plated steel frame with rectangular compartments containing a mixture of finely divided iron oxide and graphite .

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• A 20% of solution of potassium hydroxide is the electrolyte.
• A little lithium hydroxide is added to the electrolyte to make it more conducting .
• The electrolyte has a density of about 1170 kg m^-3 .
• During the charging and discharging the electrolyte does not undergo any change in density.
• The emf of the cell is 1.35 V when fully charged.

• Advantages
• It is not very heavy like lead acid cell and is portable
• It is not spoiled by overcharging or over discharging
• It has a greater life time than the acid accumulator
• Disadvantages
• The emf, capacity and efficiency of NiFe cell are less than those of the lead acid accumulator.
• During discharge the emf falls continuously.

Gibbs-Helmholtz equation for a reversible cell

• Let A represent a reversible cell of emf E

kept in an enclosure.

• It is connected to an external source B of

emf E₁

• When E₁ is kept exactly equal to E,

no current flows and no reaction takes

place in the cell A.

• When E₁ is slightly greater than E, current flows through the cell A from positive to negative terminal.
• The cell A is charged due to chemical reaction takes place in the cell.

• When E₁ is slightly less than E, the cell supplies current to the external source due to reverse chemical action taking place in it.
• The cell A can be regarded as a reversible cell, if it can be restored to its original condition after discharge, by passing a reverse current through it.
• In an ideal reversible cell, the energy required for charging could be exactly equal to that obtained from the cell during discharge.
• In actual cases, when electric current charges passes through the cell, there may be heat evolved or heat absorbed by the cell, accompanying chemical reaction.
• The emf of the cell (E), the heat absorbed or liberated in the cell (H) and the temperature coefficient dE/dT at temperature T are all related through an equation known as Gibbs-Helmholtz equation.

Derivation

• Consider a reversible cell kept in an enclosure at temperature T.
• Let its emf be E at that temperature.
• Let dE/dT be its temperature coefficient at T.
• The reversible cell is capable of delivering electric charge q to an external circuit under isothermal and adiabatic condition and also to absorb the electric charge in the reverse direction from the external circuit under isothermal and adiabatic condition.
• The cell can be regarded as the working substance of Carnot’s heat engine and the performance of the cell can be represented by an indicator diagram connecting total charge (Q) on the x-axis and emf (E) on the y-axis.
• The principle of Carnot’s engine can be applied to the reversible cell.
• Let A represent the initial condition of the cell

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emf = E; temperature = T

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• Let the cell be allowed to send a small quantity of charge q through the external circuit at constant temperature T.
• The passage of charge occurring isothermally is represented by the line AB, parallel to X-axis in the indicator diagram.
• Let the cell be imagined to be thermally insulated from the surrounding and allowed to drive an infinitesimal charge dq in the same direction.

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• This would result in a fall of temperature and the temperature changes from T to (T-δT).
• Since dE/dT is the temperature coefficient, the emf of the cell is decreased by an amount (dE/dT ) δT
• ie., emf = E - (dE/dT ) δT ; temperature = (T-δT)
• This adiabatic change is represented by the line BC.
• To bring back the cell to the original condition, the

following two processes are carried out.

• A charge q from external source of emf is passed through the cell isothermally in the reverse direction.
• This flow of charge (q) at [E - (dE/dT ) δT ] the emf is represented by the line CD.
• Finally the cell is thermally isolated from the surroundings.
• A small quantity of charge dq is passed adiabatically in the reverse direction from the external source.

• This produces a heating effect which brings the cell back to its original temperature T and emf E.

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• The line DA represents this adiabatic change.
• Thus a complete cycle of operation has been performed on the cell.
• All the above said operations can be carried out in the reverse order as the cell is reversible cell.
• For the reversible cycle of operation, work is done by the cell during the change AB.
• Work is done on the cell during the change CD.
• The work done during the adiabatic changes BC and DA can be neglected as they are very small on the account of the flow of infinitesimal charge.

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emf = E; temperature = T

• If H₁ is the heat energy absorbed by the cell at T and H₂ be heat energy rejected by the cell at (T-δT) in a cycle, then the useful work done by the cell is (H₁ - H₂ ).
• Using equation (2) we have (H₁ - H₂ ) = q(dE/dT ) δT
• Let H₁ = h be the heat absorbed by the cell at temperature T.
• Also T₁ - T₂ = δT

That is the thermal energy taken by the cell from the surroundings.

In addition to this, the cell derives chemical energy due to chemical reaction taking place in the cell.

Let the chemical energy for the passage of unit charge from the cell be H.

Then the chemical energy liberated corresponding to q coulomb of charge is Hq

This equation for emf is known as Gibbs-Helmholtz equation for reversible cell.

H denotes chemical energy drawn for passage of unit charge from the cell.

• Special cases
• If dE/dT = 0 as in Daniel cell ; E = H

energy for sending current = energy supplied by chemical reaction within the cell.

2. If dE/dT is positive (emf rises with temperature)

E = H + T(dE/dT)

therefore E > H

Energy required for sending current is more than chemical energy.

So heat is drawn from the cell in order to maintain the current.

Consequently the cell cools.

3. If dE/dT is negative

E = H - T(dE/dT)

therefore E < H

The chemical energy is greater than required electrical energy.

Due to excess energy the cell will get warmed up,while it is sending a current.