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Ionization potential indicates a substance's tendency to loose electron and become a positive ion. So, a substance becomes ion more easily if it has a lower ionization potential (lower energy needed to make it an ion).

Oxidation potential indicates a substance's tendency to loose electron (oxidize) and become a positive ion. So, a substance should become oxidized more easily if it has a lower Oxidation potential. But it is NOT the case. A substance becomes oxidizied more easily if it has a higher oxidization potential.

Why is it so? Can anyone explain? And again, Potassium becomes ionized more easily than Lithium according to the reactivity series for metals, but Lithium becomes oxidized more easily than Potassium according to Electrochemical series. Why?

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You're confusing two related concepts.

Ionization energy is the amount of energy required to remove an electron.

Oxidation potential is the opposite of the reduction potential, which is electrical potential (i.e., voltage) derived from comparing the spontaneity of the reduction compared to reducing a standard hydrogen electrode.

The former is a measure of how easy it is to remove an electron in the absence of anything else.

The latter is used to determine, in conjugation with a reduction potential, the overall reaction spontaneity for electrochemistry.

There are two other issues with your question (which is probably several questions).

The first is that reaction spontaneity is not governed by energy alone. Ionization energy cannot determine whether or not a reaction takes place, especially in solution, where entropic effects are very relevant.

Secondly, it's also unclear if you are asking about kinetic effects (how fact the reaction goes), which is very different from asking how spontaneous the reaction is.

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