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Electrolysis is basically carrying out a chemical reaction (which is generally non-spontaneous) by externally applying electricity.

Electrolysis is carried out in an Electrolytic cell, which is a non-conducting vessel containing the electrolyte [in aqueous or fused state].

Electrolytes are chemical compounds which conduct electricity in aqueous solution state or in molten state. These conditions are satisfied by ionic compounds (formed by trasfer of electrons from one element to other) like NaCl or polar covalent compounds (formed by unequal sharing of electrons between two elements) like HCl. These electrolytes undergo dissociation or as I call it break-up of ions when current is passed through them.

On the basis of extent of break-up among molecules, the electrolytes can be classified as : strong electrolytes[electrolytes in which almost all the molecules undergo break-up] and weak electrolytes [electrolytes in which only a fraction of molecules undergoes break-up].

One such example of a break-up is:

NaCl → Na+ + Cl–

Strong acids and bases and their salts generally show almost complete dissociation, thus they are examples of strong electrolytes.

Weak acids and bases and their salts generally show partial dissociation, thus they are examples of weak electrolytes.

Coming back to construction of electrolytic cell. Two rods {made up of a metal or graphite(Carbon)} are dipped in the solution of electrolyte. These rods are called electrodes. These electrodes are the medium through which electric current enters and leaves the electrolytic solution.

These electrodes are connected externally with a battery such that positive terminal of the battery is connected with one rod and negative terminal of the battery is connected with another.

The battery acts as an electron pump. It pumps out electrons from the rod connected to positive terminal of the battery, thus developing a positive charge on the rod. These pumped electrons are then sent to the rod connected to negative terminal of the battery, thus developing a negative charge on the rod.

The electrode connected to positive terminal of the battery is called Anode [Positive electrode] and the electrode connected to negative terminal of the battery is called Cathode [Negative electrode].

The ions [atoms or group of atoms with a charge] formed by break-up of molecules of electrolyte are now attracted towards these charged electrodes. Positively charged ions are attracted towards negatively charged rod i.e. cathode, and thus positively charged ions are called Cations. Negatively charged ions are attracted towards positively charged rod i.e. anode, and thus negatively charged ions are called Anions.

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