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I believe that the oxidization of a particular species allows the other species to be reduced, which is why the species being oxidized is referred to as the reducing agent. When that species is oxidized, it loses electrons that the other species then gains, allowing it to thus reduce the other species. You can apply this same logic to the reduced species being called the oxidizing agent.
For something to be reduced, it must gain electrons. Therefore, a donor of electrons is needed. This electron donor is giving electrons to reduce something else, therefore allowing reduction to occur (reducing agent). If this electron donor were not present, reduction could not occur. However, the electron donor itself is donating its electrons, so it is being oxidized. This is why the reducing agent is the substance being oxidized, because it is allowing reduction to occur (reducing another element).
Think of it like this: if something is being oxidized, that means it is losing electrons(or electron). Those electrons are going to go to another atom or molecule, which means that atom/molecule that gained those electrons is being reduced. This is why the original atom/molecule that was oxidized is a reducing agent, because the electrons it lost reduced another atom/molecule. It is the same but just opposite for why an oxidizing agent gets reduced.
Reducing agents are the ones being oxidized because, in order for them to become oxidized, they must give up electrons. And so, by giving up those electrons, they are acting as a reducing agent for whatever is being reduced. The opposite goes for oxidizing agents being the ones who are reduced.
This was confusing to me at first as well but one of my UA's mentioned that we can just remember that the agents are opposite of what they do so if its oxidation then it will a reduction agent but if it's reducing then it will be the oxidizing agent. But it is still important to understand it conceptually. Like the others above have mentioned, to reduce something or gain electrons it needs to get these electrons somewhere so it gets it from the one that's oxidizing or losing electrons. Thus, the one that's gaining electrons (reduction) will be the oxidizing agent because by gaining electrons it's oxidizing the other (making the other lose electrons). For the one that's losing electrons (oxidation) it loses electrons that get gained by the reduction so it is allowing the other to be reduced and thus becomes the reduction agent.
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