Electrochemistry is a branch of chemistry, study of the relationship between electricity and chemical reactions. This branch of chemistry is deeply related with real life. Battery, solar cell, metal coating, and so on. Especially battery -or energy storage system- is important subject of electrochemistry, and also hot topic in industry. Development of battery can solve/improve many issues currently industry face to. State of art smartphone, electric automobiles, drone, grid energy storage for eco-energy sources... most of high-tech industries require the safe battery has higher energy density and output. Therefore, the introduction of electrochemistry will focus on the knowledge to understand battery.
Redox
Redox refers to reduction-oxidation, which involves electron transfer between molecules or ions. It is important concept, and all of principles of electrochemistry are based on this type of chemical reaction. Also it is notable that reduction and oxidation occurs at same time.
Reduction and oxidation can be simply described by electron :
Reduction : Gain electron(s)
Oxidation : Loss electron(s)
Or by oxidation state
Reduction : Decrease oxidation state
Oxidation : Increase oxidation state
We will see what is oxidation state later. During redox, one element/molecule donate its electron to counter-element/molecule. The element donates electron is called reducing agent (or reducer), and the counter element which accepts electron is called oxidizing agent (or oxidizer). Then why they donate/accept electron from others? It is because every atoms have the tendency to go more stable state.

Let's do simple physics. Imagine two linked water tank like the picture. One thank is full of water and the other thank is empty. Because of gravity, the water have potential energy (mgh, m=mass, g =gravity constant, and h = height). Water wants to minimize this potential energy, therefore water enters spontaneously to the empty tank when valve is open.
The principle of potential energy also applies to electrochemistry. Electrons of atoms also want to be stable state as much as they can. As you can see the picture above, the electron located outer shell of sodium transfers to chlorine and filled up chlorine's outer shell. The potential energy of total system of Na(+)Cl(-) is lower than sum of potential energies of Na and Cl. Therefore the salt stays in ion state, not neutral state of each elements.

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