Revision: Electrochemistry Chemistry Science (English Medium) Class 12 CBSE

The electrode at which the reduction occur is called cathode.

The electrode at which the oxidation occur is called anode.

Fuel cells are the galvanic cells in which the energy of combustion of fuels like hydrogen, methanol, etc., is directly converted into electrical energy.

Cell constant is the ratio of the distance between the electrodes divided by the area of cross-section of the electrode. It is denoted by b.
Thus, Cell constant = b =`l/a`. It is expressed in unit m⁻¹.

It is the inverse of resistance R and may be simply defined as the speed through which current flows in a conductor.

c = `1/R = A/(pl)`

k = `A/l`

Here k is the specific conductance. The SI unit of conductance is Siemens, which is denoted by the symbol ‘S’ and is equal to ohm⁻¹ or Ω⁻¹.

Molar conductivity is the conductance of a volume of solution containing 1 mole of dissolved electrolyte when placed between two parallel electrodes 1 cm apart and large enough to contain between them all the solution.

The conductivity, which is shown by all the ions when 1 mol of electrolyte is dissolved in the solution, is called molar conductivity; it is expressed by ∧_m (lambda). If 1 mol of electrolyte is present in V_m cm³ of electrolyte solution, then ∧_m = κ × V

= `(kappa xx 1000)/"Molarity" = (kappa xx 1000)/M`

Its unit is ohm⁻¹ cm² mol⁻¹ or S cm² mol⁻¹.

The limiting molar conductivity of an electrolyte is defined as its molar conductivity when the concentration of the electrolyte in the solution approaches zero.

When the concentration of an electrolytic solution placed between electrodes of a conductivity cell placed at a unit distance having an area of cross-section sufficient to accommodate enough volume of solution containing one mole of electrolyte approaches zero, then the conductance of the solution is known as limiting molar conductivity.

Corrosion is the gradual damage of metals caused by their reaction with components of the atmosphere, such as oxygen and moisture.

Whenever the number of magnetic lines of force (magnetic flux) passing through a coil changes, an electric current is induced in the coil. This current is called the induced current.

If the current-carrying conductor is held in the right hand such that the thumb points in the direction of the current, then the direction of the curl of the fingers will give the direction of the magnetic field.

The ratio of distance between electrodes to area of cross-section is called cell constant.

The resistance of a conductor of unit length and unit cross-sectional area is called resistivity.

An electrochemical cell in which electrical energy is used to bring about a non-spontaneous chemical reaction is called an electrolytic cell.

A cell in which the chemical reaction occurs only once and cannot be reversed is called a primary cell.

A cell in which the chemical reaction can be reversed by passing current in opposite direction is called a secondary cell.

A galvanic cell designed to convert the energy of combustion of fuels directly into electrical energy is called a fuel cell.

An electrochemical cell that converts chemical energy of a spontaneous redox reaction into electrical energy is called a galvanic cell.

The potential difference developed between an electrode and its electrolyte is called electrode potential.

The electrode potential measured under standard conditions (1 M, 1 bar, 298 K) is called standard electrode potential.

The reference electrode assigned zero potential at all temperatures is called the standard hydrogen electrode.

The equation which relates electrode potential with concentration of ions is called the Nernst equation.

The ratio of product concentration to reactant concentration at equilibrium is called equilibrium constant.

The thermodynamic quantity representing maximum obtainable work from a reaction is called Gibbs free energy.

The reciprocal of resistance is called conductance.

The conductance of a solution of unit length and unit cross-section is called conductivity.

Nernst equation can be given as,

`E = E^circ - (2.303 RT)/(nF) log_10  [["Products"]]/[["Reactants"]]`

where,

E° = Standard potential of electrode or cell,

n = Number of moles of electrons used in reaction,

F = Faraday = 96500 C/mol e⁻,

[Products] = Concentration of products,

[Reactants] = Concentration of reactants,

T = Temperature in K and

R = Gas constant = 8.314 J K⁻¹ mol⁻¹

\[E_{cell}=E_{cathode}-E_{anode}\]

\[E_{cell}^\circ=E_{cathode}^\circ-E_{anode}^\circ\]

\[R=\rho\frac{l}{A}\]

\[G=\frac{1}{R}\]

\[\kappa=\frac{1}{\rho}\]

\[\kappa=\frac{G^*}{R}\]

\[G^*=\frac{l}{A}\]

\[R_2=\frac{R_1R_4}{R_3}\]

For reaction:

aA + bB → cC + dD

\[E_{cell}=E_{cell}^\circ-\frac{RT}{nF}\ln\frac{[C]^c[D]^d}{[A]^a[B]^b}\]

\[\Lambda_m=\frac{\kappa}{C}\]

\[\Lambda_m=\kappa\times\frac{1000}{M}\]

Unit relation:

\[1Sm^2mol^{-1}=10^4Scm^2mol^{-1}\]

\[\Lambda_m=\Lambda_m^\circ-A\sqrt{C}\]

\[\alpha=\frac{\Lambda_m}{\Lambda_m^\circ}\]

Kohlrausch law states that at infinite dilution of the solution, each ion of electrolyte migrates independently of its co-ions and contribute independently to the total molar conductivity irrespective of the nature of other ion.

Kohlrausch’s law states that the molar conductivity of an electrolyte at infinite dilution is the same as the sum of the anions' and cations' limited molar conductivities.

`∧_m^° = v_+  λ_+^° + v_-  λ_-^°`

Here `λ_+^°` and `λ_-^°` are limiting molar conductivities of cations and anions.

It is stated that the direction of induced e.m.f. is always in such a direction that it opposes the change in magnetic flux.

e = `(d phi)/(dt)`
Consider a rectangular metal coil PQRS. Let ‘L’ be the length of the coil. It is placed in a partly magnetic field ‘B’. The direction of the magnetic field is perpendicular to the paper and into the paper. The ‘x’ part of the coil is in magnetic field at instant t. If the coil is moved towards the right with a velocity v = dx/dt with the help of an external agent, such as a hand. The magnetic flux through the coil is:

Φ = BA = BLx

∴ Φ = BLx     ...(1)

There is relative motion of a current through the coil. Let ‘i’ be current through the coil.

Three forces act on the coil.
F₁ on conductor PL ∴ F₁ = B_i x, vertically upward.
F₂ on conductor MS ∴ F₂ = B_i x, vertically downward.
F₃ on conductor SP ∴ F₃ = B_i L towards left.
F₁ & F₂ are equal and opposite and also on the same lines. They will cancel each other; F₃ is a resultant force. The external agent has to do work against this force.

∴ F₃ = −B_i l    ...(−ve sign indicates that force is opposite to dx.)
If dx is the displacement in time dt, then the work done (d_w) = F₃ dx.

∴ d_w = − B_iL dx

This power is an electrical energy ‘ei’ where ‘e’ is an induced e.m.f.

∴ e_i = `-(B_i ldx)/(dt)`

∴ e = `-(BLdx)/(dt)`

∴ e = −BLv

∴ e = `-d/dt (BLx)`

∴ e = `(-d phi)/(dt)`    ...[from eq (1)]

Lenz’s Law states that the direction of the induced electromotive force (EMF) and the resulting current in a conductor is always such that it opposes the change in magnetic flux that caused it. 

Mathematically, Lenz’s Law is expressed as:

ε = `(-d phi_B)/dt`

Where,

ε = Induced EMF

Φ_B = Magnetic flux

The negative sign indicates opposition to the change in flux.

Statement:

When the magnetic flux through a circuit is changing, an induced electromotive force (emf) is set up in the circuit whose magnitude is equal to the negative rate of change of magnetic flux. This is also known as Neumann’s Law.

Mathematical Expression:

If ΔΦ_B​ is the change in magnetic flux in a time interval Δt, then the induced emf e is given by:

e = \[-\frac{\Delta\Phi_B}{\Delta t}\]​​

In the limiting case as Δt → 0:

e = \[-\frac{d\Phi_{B}}{dt}\]​​

• If dΦ_B is in weber (Wb) and dtdtdt in seconds (s), then the emf eee will be in volts (V).
• This equation represents an independent experimental law, which cannot be derived from other experimental laws.

For a tightly-wound coil of N turns, the induced emf becomes:

e = \[-N\frac{d\Phi_B}{dt}\] or e = \[-\frac{d(N\Phi_B)}{dt}\]​

Here, NΦ_B is called the ‘number of magnetic flux linkages’ in the coil, and its unit is weber-turns.

Explanation:

Consider a magnet and a coil:

• When the north pole of a magnet is near a coil, a certain number of magnetic flux lines pass through the coil.
• If either the coil or the magnet is moved, the number of magnetic flux lines (i.e., the magnetic flux) through the coil changes.

Cases:

• Magnet moved away from the coil → Decrease in magnetic flux through the coil.
• Magnet brought closer to the coil → Increase in magnetic flux through the coil.

In both cases, an emf is induced in the coil during the motion of the magnet.

• Faster motion → Greater rate of change of flux → Higher induced emf.
• If both the magnet and coil are stationary, or both are moving in the same direction with the same velocity, there is no change in flux → No induced emf.

Special Case:

• If the coil is an open circuit (i.e., infinite resistance), emf is still induced, but no current flows.
• This shows that it is the change in magnetic flux that induces emf, not current.

Conclusion:

Neumann’s Law establishes that a changing magnetic flux through a circuit induces an emf, and the induced emf is proportional to the rate of change of flux, with a negative sign indicating the direction (as per Lenz’s law).

Limitations:

• The law applies to changing magnetic flux; it does not induce emf if the magnetic flux remains constant.
• No emf is induced if the coil and magnet move together at the same velocity or remain stationary.
• In open circuits, emf is induced, but no current is generated.

Statement:

The direction of the induced emf, or the induced current, in any circuit is such as to oppose the cause that produces it. This law is known as Lenz’s Law.

Explanation / Proof:

• When the north pole of a magnet is moved towards the coil, an induced current flows in the coil in such a direction that the near (left) face of the coil behaves like a north pole.
• Due to the repulsion between the like poles, the motion of the magnet towards the coil is opposed.
• When the north pole of the magnet is moved away from the coil, the induced current flows in such a direction that the near face of the coil becomes a south pole.
• The attraction between opposite poles then opposes the motion of the magnet away from the coil.

In both cases, the induced current opposes the magnet's motion, which is the cause of the current. Therefore, work has to be done to move the magnet, and this mechanical work appears as electrical energy in the coil.

Direction of Induced Current (Fleming’s Right-Hand Rule):

• Stretch the right-hand thumb, forefinger, and middle finger so that they are mutually perpendicular.
• The forefinger points in the direction of the magnetic field.
• The thumb points in the direction of motion of the conductor.
• The middle finger then gives the direction of the induced current.

Conclusion:

Lenz’s Law shows that the induced current always acts in such a direction as to oppose the cause that produces it. This ensures that mechanical energy is converted into electrical energy, and no energy is produced without work being done.

Limitations / Note:

• If the induced current were in a direction that did not oppose the motion of the magnet, electrical energy would be obtained continuously without doing any work, which is impossible.
• Hence, Lenz’s Law is consistent with the principle of conservation of energy.

Kohlrausch’s Law states that at infinite dilution, each ion contributes independently to the total molar conductivity of an electrolyte, and the limiting molar conductivity is equal to the sum of individual ionic conductivities.

Mathematically,

\[\Lambda_m^\circ=\nu_+\lambda_+^\circ+\nu_-\lambda_-^\circ\]

where λ^∘₊ and λ^∘₋​ are limiting molar conductivities of cation and anion respectively.

Electrode potential varies with concentration and temperature.

\[E=E^\circ-\frac{RT}{nF}\ln Q\]

At 298 K:

\[E=E^\circ-\frac{0.059}{n}\log Q\]

Faraday’s Second Law of Electrolysis states that when the same quantity of electricity is passed through different electrolytes, the masses of substances deposited are proportional to their chemical equivalent weights.

Mathematically,

\[\frac{m_1}{m_2}=\frac{E_1}{E_2}\]

where m is mass deposited and E is equivalent weight.

Faraday’s First Law of Electrolysis states that the mass of a substance deposited or liberated at an electrode during electrolysis is directly proportional to the quantity of electricity passed through the electrolyte.

Mathematically,

m ∝ Q

m = ZQ

where m is mass deposited, Q is charge passed, and Z is electrochemical equivalent.