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Why is the oxidation potential given a positive sign and the reduction potential a negative one?

Also, in my book a bunch of formulas are given without any explanation:

$E^{o}_{cell}= $ Oxidation potential of anode + Reduction potential of cathode

$E^o_{cell}=$ Standard reduction potential of cathode - Standard reduction potential of anode

$E^o_{cell} =$ Oxidation potential of anode - Oxidation potential of cathode

I am unable to get any intuition for this and the physics behind these signs. Could someone please provide an intuitive explanation of what's going on?

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    $\begingroup$ Why, that's simple: negative sign means that the reaction is running in reverse direction. $\endgroup$ – Ivan Neretin Aug 29 '18 at 7:10
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We use a convention for the sign of potentials. The standard reduction potentials are referenced wrt hydrogen reaction $\ce{2H+ + 2e^- <=>H2_{(gas)}}$ which is given the value $0.0$ V. Oxidising agents have positive values, for example $\ce{Ag^+ + e^- <=> Ag_{solid}}$ $E^\mathrm{o}=+0.799$ V, or $\ce{Cl2_{(gas)} + 2e^- <=> 2Cl^-}$, $E^\mathrm{o}=+ 1.36$ V, and reducing agents negative values, e.g. $\ce{Cr^{2+} + 2e^- <=> Cr_{solid}}$, $E^\mathrm{o}=-0.91$ V.

The oxidation potentials of these reactions are just of the same magnitude but of opposite sign. Thus for the same species the oxidation potential + reduction potential add to zero. Normally we only deal with reduction potential so if you have an oxidation potential just reverse the sign and it becomes a reduction potential.

Note that the same species can be an oxidising agent or a reducing agent depending what it is being reacted with.

A reducing agent is an electron donor, and oxidising agent an electron acceptor. If a species is oxidised it looses electrons but gains electrons if reduced. Thus a reducing agent is itself oxidised; confusing, yes but its just how it is.

The cell potential is defined in your second definition as this uses the standard reduction potentials. The others are just variants by messing with reduction vs oxidation and changing signs as appropriate.

( Note that in some papers and books you may come across the redox potential values quoted wrt the saturated calomel electrode, not hydrogen, and this has a value $+0.246 $ V so its always worth a quick check. )

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