-The branch of physical chemistry which study about the relation between electricity and chemical process involved is called electrochemistry.

Electrolytes:

• An electrolyte is a medium containing ions that is electrically conducting through the movement of those ions.
• This includes most soluble salts, acids, and bases dissolved in a polar solvent, such as water.
• Upon dissolving, the substance separates into cations and anions, which disperse uniformly throughout the solvent.

Strong Electrolytes:

• Electrolytes that completely dissociate into their constituent ions in an aqueous solution are strong electrolytes.
• High availability of free mobile ions.
• They have high electrical conductivity.
• Examples: Sodium Hydroxide $(NaOH),$ Potassium Hydroxide $(KOH),$ Sodium Chloride $(NaCl),HI,HBr,HCl$.

Weak Electrolytes:

• Electrolytes that partially dissociate into their constituent ions in an aqueous solution are called weak electrolytes.
• Less availability of free ions.
• They have low electrical conductivity.
• Examples: Acetic acid $(C{H}_{3}COOH)$ ,Ammonium hydroxide $(N{H}_{4}OH),HF,N{H}_3$

Non-Electrolytes:

• A nonelectrolyte is a compound that does not conduct electric current in either aqueous solution or in the molten state.
• Many molecular compounds, such as sugar or ethanol, are nonelectrolytes.
• When these compounds dissolve in water, they do not produce ions.

Electrolysis:

• Simply, Breaking of chemical compounds using electric current (electricity).
• Electrical energy $\to$ Chemical energy.
• Electrolytes exist in molten or aqueous state inside the electrolytic cell.
• This process is carried out in a vessel called electrolytic cell or voltmeter. The two metallic rods are connected to two terminals of battery in electrolytic solution with the help of electric wire. These metallic rods are called electrodes. The electrode connected to positive terminal of battery is called anode and the electrode connected to negative terminal of battery is called cathode. In cathode reduction takes place whereas in anode oxidation takes place.

If the electrolyte is $NaCl$ solution, then

At cathode : Reduction

$N{a}^{+}+e^{-}⟶Na$

At anode : Oxidation

$C{l}^{-}-e^{-}⟶Cl$

Applications of Electrolysis:

• Electrolysis can be used to extract the pure metals in electroplating, electro refining, etc.

• It can be used to manufacture oxygen and hydrogen gas from water.

Ostwald's dilution law:

• Ostwald's dilution law describes the dissociation constant of the weak electrolyte with the degree of dissociation α and the concentration of the weak electrolyte.
• It is applicable only for weak electrolyte such as Acetic acid $(C{H}_{3}COOH)$.

Derivation

1. Consider a binary electrolyte AB which dissociates into $A^{+}and{B}^{-}$ions,

$AB(1)\leftrightharpoons A^{+}(1)+B^{-}(1)$

1. At t=0 when no reaction is going on Concentration of $AB=C$ and Concentration of $A^{+}and{B}^{-}ions=0$ since there is no product formed.
2. At equilibrium Concentration of $AB=C-C\alpha$, Concentration of $A^{+}and{B}^{-}ions=C\alpha$.
3. $AB(1)\leftrightharpoons A^{+}(1)B^{-}(1)$,putting the values of an reactants and products concentration the equilibrium constant can be written as: $K=\frac{[A^{+}(1)][B^{+}(1)]}{[AB(1)]}$ which is also written as: $K=\frac{[C\alpha ][C\alpha ]}{[C-C\alpha ]}$$=\frac{(C\alpha {)}^2}{C(1-\alpha )}$
4. For very weak electrolytes since $\alpha <<<1,(1-\alpha )\approx 1$therefore the expression of equilibrium constant can be written as: $K=C{\alpha }^2$then $\alpha =\sqrt{\frac{K}{C}}$ where K= dissociation constant of weak acid, α= degree of dissociation, C= concentration.
5. Ostwald's dilution law states that only at infinite dilution the weak electrolyte undergoes complete ionization.

Therefore, Ostwald's dilution law relates dissociation constant with degree of dissociation and concentration.

Faraday's law of electrolysis:

-These show the quantitative relationship between the substance deposited at electrodes and the quantity of electric charge or electricity passed.

First Law:

-Faraday’s First Law of Electrolysis states that “The mass of a substance deposited at any electrode is directly proportional to the amount of charge passed.”

-Mathematically it can be expressed as follows –

$m\propto Q----------(1)$

Where:

•  m = mass of a substance (in grams) deposited or liberated at an electrode.
• Q = amount of charge (in coulombs) or electricity passed through it

On removing the proportionality in equation (1)

$m=zQ$ 

$m=zIt$ $[Q=It]$

Where;

• $z$ is the proportionality constant. Its unit is grams per coulomb $(g/C)$. It is also called the electrochemical equivalent. $z$ is the mass of a substance deposited at electrodes during electrolysis bypassing $1$ coulomb of charge. 
• $I$ is electric current.
• $t$is time.

Second Law:

-Faraday’s Second Law of Electrolysis states that “The mass of a substance deposited at any electrode on passing a certain amount of charge is directly proportional to its chemical equivalent weight.” Or “when the same quantity of electricity is passed through several electrolytes, the mass of the substances deposited are proportional to their respective chemical equivalent or equivalent weight”.

Mathematically it can be represented as follows –

$w\propto E$ 

Where $w=$ mass of the substance  

$E=$ equivalent weight of the substance 

-It can also be expressed as: $\frac{w_1}{w_2}=\frac{E_1}{E_2}$ 

-The equivalent weight or chemical equivalent of a substance can be defined as the ratio of its atomic weight and valency. 

$Equivalentweight=Atomicweight/Valency$

From the experiments:

$96500C$ is required to deposit $E$ gm of an ionic species.

$1C$ is required to deposit $\frac{E}{96500}$ gm of an ionic species.

i.e. $z=\frac{E}{96500}$ where;

$E=96500\times Z=Fz$ where $F$=faraday's constant=$96500C$

Also,

$F=N\times e$,

Where, N=Avogadro's number; e=charge of electron.